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COPYING
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edu/princeton/cs/algs4/Accumulator.java
edu/princeton/cs/algs4/Accumulator.java
/******************************************************************************
* Compilation: javac Accumulator.java
* Execution: java Accumulator < input.txt
* Dependencies: StdOut.java StdIn.java
*
* Mutable data type that calculates the mean, sample standard
* deviation, and sample variance of a stream of real numbers
* use a stable, one-pass algorithm.
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
Accumulator} class is a data type for computing the running
* mean, sample standard deviation, and sample variance of a stream of real
* numbers. It provides an example of a mutable data type and a streaming
* algorithm.
* <p>
* This implementation uses a one-pass algorithm that is less susceptible
* to floating-point roundoff error than the more straightforward
* implementation based on saving the sum of the squares of the numbers.
* This technique is due to
* <a href = "https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm">B. P. Welford</a>.
* Each operation takes constant time in the worst case.
* The amount of memory is constant - the data values are not stored.
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/12oop">Section 1.2</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
Accumulator
{
private
int
n
=
0
;
// number of data values
private
double
sum
=
0.0
;
// sample variance * (n-1)
private
double
mu
=
0.0
;
// sample mean
/**
* Initializes an accumulator.
*/
public
Accumulator
()
{
}
/**
* Adds the specified data value to the accumulator.
*
@param
x the data value
*/
public
void
addDataValue
(
double
x
)
{
n
++
;
double
delta
=
x
-
mu
;
mu
+=
delta
/
n
;
sum
+=
(
double
)
(
n
-
1
)
/
n
*
delta
*
delta
;
}
/**
* Returns the mean of the data values.
*
@return
the mean of the data values
*/
public
double
mean
()
{
return
mu
;
}
/**
* Returns the sample variance of the data values.
*
@return
the sample variance of the data values
*/
public
double
var
()
{
if
(
n
<=
1
)
return
Double
.
NaN
;
return
sum
/
(
n
-
1
);
}
/**
* Returns the sample standard deviation of the data values.
*
@return
the sample standard deviation of the data values
*/
public
double
stddev
()
{
return
Math
.
sqrt
(
this
.
var
());
}
/**
* Returns the number of data values.
*
@return
the number of data values
*/
public
int
count
()
{
return
n
;
}
/**
* Returns a string representation of this accumulator.
*
@return
a string representation of this accumulator
*/
public
String
toString
()
{
return
"n = "
+
n
+
", mean = "
+
mean
()
+
", stddev = "
+
stddev
();
}
/**
* Unit tests the {
@code
Accumulator} data type.
* Reads in a stream of real number from standard input;
* adds them to the accumulator; and prints the mean,
* sample standard deviation, and sample variance to standard
* output.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
Accumulator
stats
=
new
Accumulator
();
while
(
!
StdIn
.
isEmpty
())
{
double
x
=
StdIn
.
readDouble
();
stats
.
addDataValue
(
x
);
}
StdOut
.
printf
(
"n = %d\n"
,
stats
.
count
());
StdOut
.
printf
(
"mean = %.5f\n"
,
stats
.
mean
());
StdOut
.
printf
(
"stddev = %.5f\n"
,
stats
.
stddev
());
StdOut
.
printf
(
"var = %.5f\n"
,
stats
.
var
());
StdOut
.
println
(
stats
);
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AcyclicLP.java
edu/princeton/cs/algs4/AcyclicLP.java
/******************************************************************************
* Compilation: javac AcyclicLP.java
* Execution: java AcyclicP V E
* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
* Data files: https://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
*
* Computes longeset paths in an edge-weighted acyclic digraph.
*
* Remark: should probably check that graph is a DAG before running
*
* % java AcyclicLP tinyEWDAG.txt 5
* 5 to 0 (2.44) 5->1 0.32 1->3 0.29 3->6 0.52 6->4 0.93 4->0 0.38
* 5 to 1 (0.32) 5->1 0.32
* 5 to 2 (2.77) 5->1 0.32 1->3 0.29 3->6 0.52 6->4 0.93 4->7 0.37 7->2 0.34
* 5 to 3 (0.61) 5->1 0.32 1->3 0.29
* 5 to 4 (2.06) 5->1 0.32 1->3 0.29 3->6 0.52 6->4 0.93
* 5 to 5 (0.00)
* 5 to 6 (1.13) 5->1 0.32 1->3 0.29 3->6 0.52
* 5 to 7 (2.43) 5->1 0.32 1->3 0.29 3->6 0.52 6->4 0.93 4->7 0.37
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
AcyclicLP} class represents a data type for solving the
* single-source longest paths problem in edge-weighted directed
* acyclic graphs (DAGs). The edge weights can be positive, negative, or zero.
* <p>
* This implementation uses a topological-sort based algorithm.
* The constructor takes Θ(<em>V</em> + <em>E</em>) time in the
* worst case, where <em>V</em> is the number of vertices and
* <em>E</em> is the number of edges.
* Each instance method takes Θ(1) time.
* It uses Θ(<em>V</em>) extra space (not including the
* edge-weighted digraph).
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
AcyclicLP
{
private
double
[]
distTo
;
// distTo[v] = distance of longest s->v path
private
DirectedEdge
[]
edgeTo
;
// edgeTo[v] = last edge on longest s->v path
/**
* Computes a longest paths tree from {
@code
s} to every other vertex in
* the directed acyclic graph {
@code
G}.
*
@param
G the acyclic digraph
*
@param
s the source vertex
*
@throws
IllegalArgumentException if the digraph is not acyclic
*
@throws
IllegalArgumentException unless {
@code
0 <= s < V}
*/
public
AcyclicLP
(
EdgeWeightedDigraph
G
,
int
s
)
{
distTo
=
new
double
[
G
.
V
()];
edgeTo
=
new
DirectedEdge
[
G
.
V
()];
validateVertex
(
s
);
for
(
int
v
=
0
;
v
<
G
.
V
();
v
++
)
distTo
[
v
]
=
Double
.
NEGATIVE_INFINITY
;
distTo
[
s
]
=
0.0
;
// relax vertices in topological order
Topological
topological
=
new
Topological
(
G
);
if
(
!
topological
.
hasOrder
())
throw
new
IllegalArgumentException
(
"Digraph is not acyclic."
);
for
(
int
v
:
topological
.
order
())
{
for
(
DirectedEdge
e
:
G
.
adj
(
v
))
relax
(
e
);
}
}
// relax edge e, but update if you find a *longer* path
private
void
relax
(
DirectedEdge
e
)
{
int
v
=
e
.
from
(),
w
=
e
.
to
();
if
(
distTo
[
w
]
<
distTo
[
v
]
+
e
.
weight
())
{
distTo
[
w
]
=
distTo
[
v
]
+
e
.
weight
();
edgeTo
[
w
]
=
e
;
}
}
/**
* Returns the length of a longest path from the source vertex {
@code
s} to vertex {
@code
v}.
*
@param
v the destination vertex
*
@return
the length of a longest path from the source vertex {
@code
s} to vertex {
@code
v};
* {
@code
Double.NEGATIVE_INFINITY} if no such path
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
double
distTo
(
int
v
)
{
validateVertex
(
v
);
return
distTo
[
v
];
}
/**
* Is there a path from the source vertex {
@code
s} to vertex {
@code
v}?
*
@param
v the destination vertex
*
@return
{
@code
true} if there is a path from the source vertex
* {
@code
s} to vertex {
@code
v}, and {
@code
false} otherwise
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
boolean
hasPathTo
(
int
v
)
{
validateVertex
(
v
);
return
distTo
[
v
]
>
Double
.
NEGATIVE_INFINITY
;
}
/**
* Returns a longest path from the source vertex {
@code
s} to vertex {
@code
v}.
*
@param
v the destination vertex
*
@return
a longest path from the source vertex {
@code
s} to vertex {
@code
v}
* as an iterable of edges, and {
@code
null} if no such path
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
Iterable
<
DirectedEdge
>
pathTo
(
int
v
)
{
validateVertex
(
v
);
if
(
!
hasPathTo
(
v
))
return
null
;
Stack
<
DirectedEdge
>
path
=
new
Stack
<
DirectedEdge
>
();
for
(
DirectedEdge
e
=
edgeTo
[
v
];
e
!=
null
;
e
=
edgeTo
[
e
.
from
()])
{
path
.
push
(
e
);
}
return
path
;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private
void
validateVertex
(
int
v
)
{
int
V
=
distTo
.
length
;
if
(
v
<
0
||
v
>=
V
)
throw
new
IllegalArgumentException
(
"vertex "
+
v
+
" is not between 0 and "
+
(
V
-
1
));
}
/**
* Unit tests the {
@code
AcyclicLP} data type.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
In
in
=
new
In
(
args
[
0
]);
int
s
=
Integer
.
parseInt
(
args
[
1
]);
EdgeWeightedDigraph
G
=
new
EdgeWeightedDigraph
(
in
);
AcyclicLP
lp
=
new
AcyclicLP
(
G
,
s
);
for
(
int
v
=
0
;
v
<
G
.
V
();
v
++
)
{
if
(
lp
.
hasPathTo
(
v
))
{
StdOut
.
printf
(
"%d to %d (%.2f) "
,
s
,
v
,
lp
.
distTo
(
v
));
for
(
DirectedEdge
e
:
lp
.
pathTo
(
v
))
{
StdOut
.
print
(
e
+
" "
);
}
StdOut
.
println
();
}
else
{
StdOut
.
printf
(
"%d to %d no path\n"
,
s
,
v
);
}
}
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AcyclicSP.java
edu/princeton/cs/algs4/AcyclicSP.java
/******************************************************************************
* Compilation: javac AcyclicSP.java
* Execution: java AcyclicSP V E
* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
* Data files: https://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
*
* Computes shortest paths in an edge-weighted acyclic digraph.
*
* % java AcyclicSP tinyEWDAG.txt 5
* 5 to 0 (0.73) 5->4 0.35 4->0 0.38
* 5 to 1 (0.32) 5->1 0.32
* 5 to 2 (0.62) 5->7 0.28 7->2 0.34
* 5 to 3 (0.61) 5->1 0.32 1->3 0.29
* 5 to 4 (0.35) 5->4 0.35
* 5 to 5 (0.00)
* 5 to 6 (1.13) 5->1 0.32 1->3 0.29 3->6 0.52
* 5 to 7 (0.28) 5->7 0.28
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
AcyclicSP} class represents a data type for solving the
* single-source shortest paths problem in edge-weighted directed acyclic
* graphs (DAGs). The edge weights can be positive, negative, or zero.
* <p>
* This implementation uses a topological-sort based algorithm.
* The constructor takes Θ(<em>V</em> + <em>E</em>) time in the
* worst case, where <em>V</em> is the number of vertices and
* <em>E</em> is the number of edges.
* Each instance method takes Θ(1) time.
* It uses Θ(<em>V</em>) extra space (not including the
* edge-weighted digraph).
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
AcyclicSP
{
private
double
[]
distTo
;
// distTo[v] = distance of shortest s->v path
private
DirectedEdge
[]
edgeTo
;
// edgeTo[v] = last edge on shortest s->v path
/**
* Computes a shortest paths tree from {
@code
s} to every other vertex in
* the directed acyclic graph {
@code
G}.
*
@param
G the acyclic digraph
*
@param
s the source vertex
*
@throws
IllegalArgumentException if the digraph is not acyclic
*
@throws
IllegalArgumentException unless {
@code
0 <= s < V}
*/
public
AcyclicSP
(
EdgeWeightedDigraph
G
,
int
s
)
{
distTo
=
new
double
[
G
.
V
()];
edgeTo
=
new
DirectedEdge
[
G
.
V
()];
validateVertex
(
s
);
for
(
int
v
=
0
;
v
<
G
.
V
();
v
++
)
distTo
[
v
]
=
Double
.
POSITIVE_INFINITY
;
distTo
[
s
]
=
0.0
;
// visit vertices in topological order
Topological
topological
=
new
Topological
(
G
);
if
(
!
topological
.
hasOrder
())
throw
new
IllegalArgumentException
(
"Digraph is not acyclic."
);
for
(
int
v
:
topological
.
order
())
{
for
(
DirectedEdge
e
:
G
.
adj
(
v
))
relax
(
e
);
}
}
// relax edge e
private
void
relax
(
DirectedEdge
e
)
{
int
v
=
e
.
from
(),
w
=
e
.
to
();
if
(
distTo
[
w
]
>
distTo
[
v
]
+
e
.
weight
())
{
distTo
[
w
]
=
distTo
[
v
]
+
e
.
weight
();
edgeTo
[
w
]
=
e
;
}
}
/**
* Returns the length of a shortest path from the source vertex {
@code
s} to vertex {
@code
v}.
*
@param
v the destination vertex
*
@return
the length of a shortest path from the source vertex {
@code
s} to vertex {
@code
v};
* {
@code
Double.POSITIVE_INFINITY} if no such path
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
double
distTo
(
int
v
)
{
validateVertex
(
v
);
return
distTo
[
v
];
}
/**
* Is there a path from the source vertex {
@code
s} to vertex {
@code
v}?
*
@param
v the destination vertex
*
@return
{
@code
true} if there is a path from the source vertex
* {
@code
s} to vertex {
@code
v}, and {
@code
false} otherwise
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
boolean
hasPathTo
(
int
v
)
{
validateVertex
(
v
);
return
distTo
[
v
]
<
Double
.
POSITIVE_INFINITY
;
}
/**
* Returns a shortest path from the source vertex {
@code
s} to vertex {
@code
v}.
*
@param
v the destination vertex
*
@return
a shortest path from the source vertex {
@code
s} to vertex {
@code
v}
* as an iterable of edges, and {
@code
null} if no such path
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
Iterable
<
DirectedEdge
>
pathTo
(
int
v
)
{
validateVertex
(
v
);
if
(
!
hasPathTo
(
v
))
return
null
;
Stack
<
DirectedEdge
>
path
=
new
Stack
<
DirectedEdge
>
();
for
(
DirectedEdge
e
=
edgeTo
[
v
];
e
!=
null
;
e
=
edgeTo
[
e
.
from
()])
{
path
.
push
(
e
);
}
return
path
;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private
void
validateVertex
(
int
v
)
{
int
V
=
distTo
.
length
;
if
(
v
<
0
||
v
>=
V
)
throw
new
IllegalArgumentException
(
"vertex "
+
v
+
" is not between 0 and "
+
(
V
-
1
));
}
/**
* Unit tests the {
@code
AcyclicSP} data type.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
In
in
=
new
In
(
args
[
0
]);
int
s
=
Integer
.
parseInt
(
args
[
1
]);
EdgeWeightedDigraph
G
=
new
EdgeWeightedDigraph
(
in
);
// find shortest path from s to each other vertex in DAG
AcyclicSP
sp
=
new
AcyclicSP
(
G
,
s
);
for
(
int
v
=
0
;
v
<
G
.
V
();
v
++
)
{
if
(
sp
.
hasPathTo
(
v
))
{
StdOut
.
printf
(
"%d to %d (%.2f) "
,
s
,
v
,
sp
.
distTo
(
v
));
for
(
DirectedEdge
e
:
sp
.
pathTo
(
v
))
{
StdOut
.
print
(
e
+
" "
);
}
StdOut
.
println
();
}
else
{
StdOut
.
printf
(
"%d to %d no path\n"
,
s
,
v
);
}
}
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AdjMatrixEdgeWeightedDigraph.java
edu/princeton/cs/algs4/AdjMatrixEdgeWeightedDigraph.java
/******************************************************************************
* Compilation: javac AdjMatrixEdgeWeightedDigraph.java
* Execution: java AdjMatrixEdgeWeightedDigraph V E
* Dependencies: StdOut.java
*
* An edge-weighted digraph, implemented using an adjacency matrix.
* Parallel edges are disallowed; self-loops are allowed.
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
import
java
.
util
.
Iterator
;
import
java
.
util
.
NoSuchElementException
;
/**
* The {
@code
AdjMatrixEdgeWeightedDigraph} class represents a edge-weighted
* digraph of vertices named 0 through <em>V</em> - 1, where each
* directed edge is of type {
@link
DirectedEdge} and has a real-valued weight.
* It supports the following two primary operations: add a directed edge
* to the digraph and iterate over all of edges incident from a given vertex.
* It also provides
* methods for returning the number of vertices <em>V</em> and the number
* of edges <em>E</em>. Parallel edges are disallowed; self-loops are permitted.
* <p>
* This implementation uses an adjacency-matrix representation.
* All operations take constant time (in the worst case) except
* iterating over the edges incident from a given vertex, which takes
* time proportional to <em>V</em>.
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
AdjMatrixEdgeWeightedDigraph
{
private
static
final
String
NEWLINE
=
System
.
getProperty
(
"line.separator"
);
private
final
int
V
;
private
int
E
;
private
DirectedEdge
[][]
adj
;
/**
* Initializes an empty edge-weighted digraph with {
@code
V} vertices and 0 edges.
*
@param
V the number of vertices
*
@throws
IllegalArgumentException if {
@code
V < 0}
*/
public
AdjMatrixEdgeWeightedDigraph
(
int
V
)
{
if
(
V
<
0
)
throw
new
IllegalArgumentException
(
"number of vertices must be nonnegative"
);
this
.
V
=
V
;
this
.
E
=
0
;
this
.
adj
=
new
DirectedEdge
[
V
][
V
];
}
/**
* Initializes a random edge-weighted digraph with {
@code
V} vertices and <em>E</em> edges.
*
@param
V the number of vertices
*
@param
E the number of edges
*
@throws
IllegalArgumentException if {
@code
V < 0}
*
@throws
IllegalArgumentException if {
@code
E < 0}
*/
public
AdjMatrixEdgeWeightedDigraph
(
int
V
,
int
E
)
{
this
(
V
);
if
(
E
<
0
)
throw
new
IllegalArgumentException
(
"number of edges must be nonnegative"
);
if
(
E
>
V
*
V
)
throw
new
IllegalArgumentException
(
"too many edges"
);
// can be inefficient
while
(
this
.
E
!=
E
)
{
int
v
=
StdRandom
.
uniform
(
V
);
int
w
=
StdRandom
.
uniform
(
V
);
double
weight
=
Math
.
round
(
100
*
StdRandom
.
uniform
())
/
100.0
;
addEdge
(
new
DirectedEdge
(
v
,
w
,
weight
));
}
}
/**
* Returns the number of vertices in the edge-weighted digraph.
*
@return
the number of vertices in the edge-weighted digraph
*/
public
int
V
()
{
return
V
;
}
/**
* Returns the number of edges in the edge-weighted digraph.
*
@return
the number of edges in the edge-weighted digraph
*/
public
int
E
()
{
return
E
;
}
/**
* Adds the directed edge {
@code
e} to the edge-weighted digraph (if there
* is not already an edge with the same endpoints).
*
@param
e the edge
*/
public
void
addEdge
(
DirectedEdge
e
)
{
int
v
=
e
.
from
();
int
w
=
e
.
to
();
validateVertex
(
v
);
validateVertex
(
w
);
if
(
adj
[
v
][
w
]
==
null
)
{
E
++
;
adj
[
v
][
w
]
=
e
;
}
}
/**
* Returns the directed edges incident from vertex {
@code
v}.
*
@param
v the vertex
*
@return
the directed edges incident from vertex {
@code
v} as an Iterable
*
@throws
IllegalArgumentException unless {
@code
0 <= v < V}
*/
public
Iterable
<
DirectedEdge
>
adj
(
int
v
)
{
validateVertex
(
v
);
return
new
AdjIterator
(
v
);
}
// support iteration over graph vertices
private
class
AdjIterator
implements
Iterator
<
DirectedEdge
>
,
Iterable
<
DirectedEdge
>
{
private
int
v
;
private
int
w
=
0
;
public
AdjIterator
(
int
v
)
{
this
.
v
=
v
;
}
public
Iterator
<
DirectedEdge
>
iterator
()
{
return
this
;
}
public
boolean
hasNext
()
{
while
(
w
<
V
)
{
if
(
adj
[
v
][
w
]
!=
null
)
return
true
;
w
++
;
}
return
false
;
}
public
DirectedEdge
next
()
{
if
(
!
hasNext
())
{
throw
new
NoSuchElementException
();
}
return
adj
[
v
][
w
++
];
}
public
void
remove
()
{
throw
new
UnsupportedOperationException
();
}
}
/**
* Returns a string representation of the edge-weighted digraph. This method takes
* time proportional to <em>V</em><sup>2</sup>.
*
@return
the number of vertices <em>V</em>, followed by the number of edges <em>E</em>,
* followed by the <em>V</em> adjacency lists of edges
*/
public
String
toString
()
{
StringBuilder
s
=
new
StringBuilder
();
s
.
append
(
V
+
" "
+
E
+
NEWLINE
);
for
(
int
v
=
0
;
v
<
V
;
v
++
)
{
s
.
append
(
v
+
": "
);
for
(
DirectedEdge
e
:
adj
(
v
))
{
s
.
append
(
e
+
" "
);
}
s
.
append
(
NEWLINE
);
}
return
s
.
toString
();
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private
void
validateVertex
(
int
v
)
{
if
(
v
<
0
||
v
>=
V
)
throw
new
IllegalArgumentException
(
"vertex "
+
v
+
" is not between 0 and "
+
(
V
-
1
));
}
/**
* Unit tests the {
@code
AdjMatrixEdgeWeightedDigraph} data type.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
int
V
=
Integer
.
parseInt
(
args
[
0
]);
int
E
=
Integer
.
parseInt
(
args
[
1
]);
AdjMatrixEdgeWeightedDigraph
G
=
new
AdjMatrixEdgeWeightedDigraph
(
V
,
E
);
StdOut
.
println
(
G
);
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/Alphabet.java
edu/princeton/cs/algs4/Alphabet.java
/******************************************************************************
* Compilation: javac Alphabet.java
* Execution: java Alphabet
* Dependencies: StdOut.java
*
* A data type for alphabets, for use with string-processing code
* that must convert between an alphabet of size R and the integers
* 0 through R-1.
*
* Warning: supports only the basic multilingual plane (BMP), i.e,
* Unicode characters between U+0000 and U+FFFF.
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
public
class
Alphabet
{
/**
* The binary alphabet { 0, 1 }.
*/
public
static
final
Alphabet
BINARY
=
new
Alphabet
(
"01"
);
/**
* The octal alphabet { 0, 1, 2, 3, 4, 5, 6, 7 }.
*/
public
static
final
Alphabet
OCTAL
=
new
Alphabet
(
"01234567"
);
/**
* The decimal alphabet { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }.
*/
public
static
final
Alphabet
DECIMAL
=
new
Alphabet
(
"0123456789"
);
/**
* The hexadecimal alphabet { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }.
*/
public
static
final
Alphabet
HEXADECIMAL
=
new
Alphabet
(
"0123456789ABCDEF"
);
/**
* The DNA alphabet { A, C, T, G }.
*/
public
static
final
Alphabet
DNA
=
new
Alphabet
(
"ACGT"
);
/**
* The lowercase alphabet { a, b, c, ..., z }.
*/
public
static
final
Alphabet
LOWERCASE
=
new
Alphabet
(
"abcdefghijklmnopqrstuvwxyz"
);
/**
* The uppercase alphabet { A, B, C, ..., Z }.
*/
public
static
final
Alphabet
UPPERCASE
=
new
Alphabet
(
"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
);
/**
* The protein alphabet { A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y }.
*/
public
static
final
Alphabet
PROTEIN
=
new
Alphabet
(
"ACDEFGHIKLMNPQRSTVWY"
);
/**
* The base-64 alphabet (64 characters).
*/
public
static
final
Alphabet
BASE64
=
new
Alphabet
(
"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"
);
/**
* The ASCII alphabet (0-127).
*/
public
static
final
Alphabet
ASCII
=
new
Alphabet
(
128
);
/**
* The extended ASCII alphabet (0-255).
*/
public
static
final
Alphabet
EXTENDED_ASCII
=
new
Alphabet
(
256
);
/**
* The Unicode 16 alphabet (0-65,535).
*/
public
static
final
Alphabet
UNICODE16
=
new
Alphabet
(
65536
);
private
char
[]
alphabet
;
// the characters in the alphabet
private
int
[]
inverse
;
// indices
private
final
int
R
;
// the radix of the alphabet
/**
* Initializes a new alphabet from the given set of characters.
*
*
@param
alpha the set of characters
*/
public
Alphabet
(
String
alpha
)
{
// check that alphabet contains no duplicate chars
boolean
[]
unicode
=
new
boolean
[
Character
.
MAX_VALUE
];
for
(
int
i
=
0
;
i
<
alpha
.
length
();
i
++
)
{
char
c
=
alpha
.
charAt
(
i
);
if
(
unicode
[
c
])
throw
new
IllegalArgumentException
(
"Illegal alphabet: repeated character = '"
+
c
+
"'"
);
unicode
[
c
]
=
true
;
}
alphabet
=
alpha
.
toCharArray
();
R
=
alpha
.
length
();
inverse
=
new
int
[
Character
.
MAX_VALUE
];
for
(
int
i
=
0
;
i
<
inverse
.
length
;
i
++
)
inverse
[
i
]
=
-
1
;
// can't use char since R can be as big as 65,536
for
(
int
c
=
0
;
c
<
R
;
c
++
)
inverse
[
alphabet
[
c
]]
=
c
;
}
/**
* Initializes a new alphabet using characters 0 through R-1.
*
*
@param
radix the number of characters in the alphabet (the radix R)
*/
private
Alphabet
(
int
radix
)
{
this
.
R
=
radix
;
alphabet
=
new
char
[
R
];
inverse
=
new
int
[
R
];
// can't use char since R can be as big as 65,536
for
(
int
i
=
0
;
i
<
R
;
i
++
)
alphabet
[
i
]
=
(
char
)
i
;
for
(
int
i
=
0
;
i
<
R
;
i
++
)
inverse
[
i
]
=
i
;
}
/**
* Initializes a new alphabet using characters 0 through 255.
*/
public
Alphabet
()
{
this
(
256
);
}
/**
* Returns true if the argument is a character in this alphabet.
*
*
@param
c the character
*
@return
{
@code
true} if {
@code
c} is a character in this alphabet;
* {
@code
false} otherwise
*/
public
boolean
contains
(
char
c
)
{
return
inverse
[
c
]
!=
-
1
;
}
/**
* Returns the number of characters in this alphabet (the radix).
*
*
@return
the number of characters in this alphabet
*
@deprecated
Replaced by {
@link
#radix()}.
*/
@
Deprecated
public
int
R
()
{
return
R
;
}
/**
* Returns the number of characters in this alphabet (the radix).
*
*
@return
the number of characters in this alphabet
*/
public
int
radix
()
{
return
R
;
}
/**
* Returns the binary logarithm of the number of characters in this alphabet.
*
*
@return
the binary logarithm (rounded up) of the number of characters in this alphabet
*/
public
int
lgR
()
{
int
lgR
=
0
;
for
(
int
t
=
R
-
1
;
t
>=
1
;
t
/=
2
)
lgR
++
;
return
lgR
;
}
/**
* Returns the index corresponding to the argument character.
*
*
@param
c the character
*
@return
the index corresponding to the character {
@code
c}
*
@throws
IllegalArgumentException unless {
@code
c} is a character in this alphabet
*/
public
int
toIndex
(
char
c
)
{
if
(
c
>=
inverse
.
length
||
inverse
[
c
]
==
-
1
)
{
throw
new
IllegalArgumentException
(
"Character "
+
c
+
" not in alphabet"
);
}
return
inverse
[
c
];
}
/**
* Returns the indices corresponding to the argument characters.
*
*
@param
s the characters
*
@return
the indices corresponding to the characters {
@code
s}
*
@throws
IllegalArgumentException unless every character in {
@code
s}
* is a character in this alphabet
*/
public
int
[]
toIndices
(
String
s
)
{
char
[]
source
=
s
.
toCharArray
();
int
[]
target
=
new
int
[
s
.
length
()];
for
(
int
i
=
0
;
i
<
source
.
length
;
i
++
)
target
[
i
]
=
toIndex
(
source
[
i
]);
return
target
;
}
/**
* Returns the character corresponding to the argument index.
*
*
@param
index the index
*
@return
the character corresponding to the index {
@code
index}
*
@throws
IllegalArgumentException unless {
@code
0 <= index < R}
*/
public
char
toChar
(
int
index
)
{
if
(
index
<
0
||
index
>=
R
)
{
throw
new
IllegalArgumentException
(
"index must be between 0 and "
+
R
+
": "
+
index
);
}
return
alphabet
[
index
];
}
/**
* Returns the characters corresponding to the argument indices.
*
*
@param
indices the indices
*
@return
the characters corresponding to the indices {
@code
indices}
*
@throws
IllegalArgumentException unless {
@code
0 < indices[i] < R}
* for every {
@code
i}
*/
public
String
toChars
(
int
[]
indices
)
{
StringBuilder
s
=
new
StringBuilder
(
indices
.
length
);
for
(
int
i
=
0
;
i
<
indices
.
length
;
i
++
)
s
.
append
(
toChar
(
indices
[
i
]));
return
s
.
toString
();
}
/**
* Unit tests the {
@code
Alphabet} data type.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
int
[]
encoded1
=
Alphabet
.
BASE64
.
toIndices
(
"NowIsTheTimeForAllGoodMen"
);
String
decoded1
=
Alphabet
.
BASE64
.
toChars
(
encoded1
);
StdOut
.
println
(
decoded1
);
int
[]
encoded2
=
Alphabet
.
DNA
.
toIndices
(
"AACGAACGGTTTACCCCG"
);
String
decoded2
=
Alphabet
.
DNA
.
toChars
(
encoded2
);
StdOut
.
println
(
decoded2
);
int
[]
encoded3
=
Alphabet
.
DECIMAL
.
toIndices
(
"01234567890123456789"
);
String
decoded3
=
Alphabet
.
DECIMAL
.
toChars
(
encoded3
);
StdOut
.
println
(
decoded3
);
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AmericanFlag.java
edu/princeton/cs/algs4/AmericanFlag.java
/******************************************************************************
* Compilation: javac AmericanFlag.java
* Execution: java AmericanFlag < input.txt
* java AmericanFlag int < input-non-negative-ints.txt
* Dependencies: StdIn.java StdOut.java Stack.java
* Data files: https://algs4.cs.princeton.edu/51radix/words3.txt
* https://algs4.cs.princeton.edu/51radix/shells.txt
*
* Sort an array of strings or integers in-place using American flag sort.
*
* % java AmericanFlag < shells.txt
* are
* by
* sea
* seashells
* seashells
* sells
* sells
* she
* she
* shells
* shore
* surely
* the
* the
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
AmericanFlag} class provides static methods for sorting an
* array of extended ASCII strings or integers in-place using
* American flag sort. This is a non-recursive implementation.
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/51radix">Section 5.1</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne
* and <a href = "http://static.usenix.org/publications/compsystems/1993/win_mcilroy.pdf">
* Engineering Radix Sort</a> by McIlroy and Bostic.
* For a version that uses only one auxilary array, see {
@link
AmericanFlagX}.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*
@author
Ivan Pesin
*/
public
class
AmericanFlag
{
private
static
final
int
BITS_PER_BYTE
=
8
;
private
static
final
int
BITS_PER_INT
=
32
;
// each Java int is 32 bits
private
static
final
int
R
=
256
;
// extend ASCII alphabet size
private
static
final
int
CUTOFF
=
15
;
// cutoff to insertion sort
// do not instantiate
private
AmericanFlag
()
{
}
// return dth character of s, -1 if d = length of string
private
static
int
charAt
(
String
s
,
int
d
)
{
assert
d
>=
0
&&
d
<=
s
.
length
();
if
(
d
==
s
.
length
())
return
-
1
;
return
s
.
charAt
(
d
);
}
/**
* Rearranges the array of extended ASCII strings in ascending order.
* This is an unstable sorting algorithm.
*
*
@param
a the array to be sorted
*/
public
static
void
sort
(
String
[]
a
)
{
sort
(
a
,
0
,
a
.
length
-
1
);
}
// sort from a[lo] to a[hi], starting at the dth character
public
static
void
sort
(
String
[]
a
,
int
lo
,
int
hi
)
{
// one-time allocation of data structures
Stack
<
Integer
>
st
=
new
Stack
<
Integer
>
();
int
[]
first
=
new
int
[
R
+
2
];
int
[]
next
=
new
int
[
R
+
2
];
int
d
=
0
;
// character index to sort by
st
.
push
(
lo
);
st
.
push
(
hi
);
st
.
push
(
d
);
while
(
!
st
.
isEmpty
())
{
d
=
st
.
pop
();
hi
=
st
.
pop
();
lo
=
st
.
pop
();
if
(
hi
<=
lo
+
CUTOFF
)
{
insertion
(
a
,
lo
,
hi
,
d
);
continue
;
}
// compute frequency counts
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
{
int
c
=
charAt
(
a
[
i
],
d
)
+
1
;
// account for -1 representing end-of-string
first
[
c
+
1
]
++
;
}
// first[c] = location of first string whose dth character = c
first
[
0
]
=
lo
;
for
(
int
c
=
0
;
c
<=
R
;
c
++
)
{
first
[
c
+
1
]
+=
first
[
c
];
if
(
c
>
0
&&
first
[
c
+
1
]
-
1
>
first
[
c
])
{
// add subproblem for character c (excludes sentinel c == 0)
st
.
push
(
first
[
c
]);
st
.
push
(
first
[
c
+
1
]
-
1
);
st
.
push
(
d
+
1
);
}
}
// next[c] = location to place next string whose dth character = c
for
(
int
c
=
0
;
c
<
R
+
2
;
c
++
)
next
[
c
]
=
first
[
c
];
// permute data in place
for
(
int
k
=
lo
;
k
<=
hi
;
k
++
)
{
int
c
=
charAt
(
a
[
k
],
d
)
+
1
;
while
(
first
[
c
]
>
k
)
{
exch
(
a
,
k
,
next
[
c
]
++
);
c
=
charAt
(
a
[
k
],
d
)
+
1
;
}
next
[
c
]
++
;
}
// clear first[] and next[] arrays
for
(
int
c
=
0
;
c
<
R
+
2
;
c
++
)
{
first
[
c
]
=
0
;
next
[
c
]
=
0
;
}
}
}
// insertion sort a[lo..hi], starting at dth character
private
static
void
insertion
(
String
[]
a
,
int
lo
,
int
hi
,
int
d
)
{
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
for
(
int
j
=
i
;
j
>
lo
&&
less
(
a
[
j
],
a
[
j
-
1
],
d
);
j
--
)
exch
(
a
,
j
,
j
-
1
);
}
// exchange a[i] and a[j]
private
static
void
exch
(
String
[]
a
,
int
i
,
int
j
)
{
String
temp
=
a
[
i
];
a
[
i
]
=
a
[
j
];
a
[
j
]
=
temp
;
}
// is v less than w, starting at character d
private
static
boolean
less
(
String
v
,
String
w
,
int
d
)
{
// assert v.substring(0, d).equals(w.substring(0, d));
for
(
int
i
=
d
;
i
<
Math
.
min
(
v
.
length
(),
w
.
length
());
i
++
)
{
if
(
v
.
charAt
(
i
)
<
w
.
charAt
(
i
))
return
true
;
if
(
v
.
charAt
(
i
)
>
w
.
charAt
(
i
))
return
false
;
}
return
v
.
length
()
<
w
.
length
();
}
/**
* Rearranges the array of 32-bit integers in ascending order.
* Currently assumes that the integers are nonnegative.
*
*
@param
a the array to be sorted
*/
public
static
void
sort
(
int
[]
a
)
{
sort
(
a
,
0
,
a
.
length
-
1
);
}
// MSD sort from a[lo] to a[hi]
private
static
void
sort
(
int
[]
a
,
int
lo
,
int
hi
)
{
// one-time allocation of data structures
Stack
<
Integer
>
st
=
new
Stack
<
Integer
>
();
int
[]
first
=
new
int
[
R
+
1
];
int
[]
next
=
new
int
[
R
+
1
];
int
mask
=
R
-
1
;
// 0xFF;
int
d
=
0
;
// byte to sort by
st
.
push
(
lo
);
st
.
push
(
hi
);
st
.
push
(
d
);
while
(
!
st
.
isEmpty
())
{
d
=
st
.
pop
();
hi
=
st
.
pop
();
lo
=
st
.
pop
();
if
(
hi
<=
lo
+
CUTOFF
)
{
insertion
(
a
,
lo
,
hi
,
d
);
continue
;
}
// compute frequency counts (need R = 256)
int
shift
=
BITS_PER_INT
-
BITS_PER_BYTE
*
d
-
BITS_PER_BYTE
;
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
{
int
c
=
(
a
[
i
]
>>
shift
)
&
mask
;
first
[
c
+
1
]
++
;
}
// first[c] = location of first int whose dth byte = c
first
[
0
]
=
lo
;
for
(
int
c
=
0
;
c
<
R
;
c
++
)
{
first
[
c
+
1
]
+=
first
[
c
];
if
(
d
<
3
&&
first
[
c
+
1
]
-
1
>
first
[
c
])
{
// add subproblem for byte c
st
.
push
(
first
[
c
]);
st
.
push
(
first
[
c
+
1
]
-
1
);
st
.
push
(
d
+
1
);
}
}
// next[c] = location to place next string whose dth byte = c
for
(
int
c
=
0
;
c
<
R
+
1
;
c
++
)
next
[
c
]
=
first
[
c
];
// permute data in place
for
(
int
k
=
lo
;
k
<=
hi
;
k
++
)
{
int
c
=
(
a
[
k
]
>>
shift
)
&
mask
;
while
(
first
[
c
]
>
k
)
{
exch
(
a
,
k
,
next
[
c
]
++
);
c
=
(
a
[
k
]
>>
shift
)
&
mask
;
}
next
[
c
]
++
;
}
// clear first[] and next[] arrays
for
(
int
c
=
0
;
c
<
R
+
1
;
c
++
)
{
first
[
c
]
=
0
;
next
[
c
]
=
0
;
}
}
}
// insertion sort a[lo..hi], starting at dth byte
private
static
void
insertion
(
int
[]
a
,
int
lo
,
int
hi
,
int
d
)
{
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
for
(
int
j
=
i
;
j
>
lo
&&
less
(
a
[
j
],
a
[
j
-
1
],
d
);
j
--
)
exch
(
a
,
j
,
j
-
1
);
}
// exchange a[i] and a[j]
private
static
void
exch
(
int
[]
a
,
int
i
,
int
j
)
{
int
temp
=
a
[
i
];
a
[
i
]
=
a
[
j
];
a
[
j
]
=
temp
;
}
// is v less than w, starting at byte d
private
static
boolean
less
(
int
v
,
int
w
,
int
d
)
{
int
mask
=
R
-
1
;
// 0xFF;
for
(
int
i
=
d
;
i
<
4
;
i
++
)
{
int
shift
=
BITS_PER_INT
-
BITS_PER_BYTE
*
i
-
BITS_PER_BYTE
;
int
a
=
(
v
>>
shift
)
&
mask
;
int
b
=
(
w
>>
shift
)
&
mask
;
if
(
a
<
b
)
return
true
;
if
(
a
>
b
)
return
false
;
}
return
false
;
}
/**
* Reads in a sequence of extended ASCII strings or non-negative ints from standard input;
* American flag sorts them;
* and prints them to standard output in ascending order.
*
*
@param
args the command-line arguments: "int" to read input as non-negative integers
*/
public
static
void
main
(
String
[]
args
)
{
if
(
args
.
length
>
0
&&
args
[
0
].
equals
(
"int"
))
{
int
[]
a
=
StdIn
.
readAllInts
();
sort
(
a
);
// print results
for
(
int
i
=
0
;
i
<
a
.
length
;
i
++
)
StdOut
.
println
(
a
[
i
]);
}
else
{
String
[]
a
=
StdIn
.
readAllStrings
();
sort
(
a
);
// print results
for
(
int
i
=
0
;
i
<
a
.
length
;
i
++
)
StdOut
.
println
(
a
[
i
]);
}
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AmericanFlagX.java
edu/princeton/cs/algs4/AmericanFlagX.java
/******************************************************************************
* Compilation: javac AmericanFlagX.java
* Execution: java AmericanFlagX < input.txt
* Dependencies: StdIn.java StdOut.java Stack.java
* Data files: https://algs4.cs.princeton.edu/51radix/words3.txt
* https://algs4.cs.princeton.edu/51radix/shells.txt
*
* Sort an array of strings or integers in-place using American Flag sort.
*
* % java AmericanFlagX < shells.txt
* are
* by
* sea
* seashells
* seashells
* sells
* sells
* she
* she
* shells
* shore
* surely
* the
* the
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
AmericanFlagX} class provides static methods for sorting an
* array of extended ASCII strings or integers in-place using
* American Flag sort. This implementation is non-recursive and uses only
* one auxiliary array.
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/51radix">Section 5.1</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne
* and <a href = "http://static.usenix.org/publications/compsystems/1993/win_mcilroy.pdf">
* Engineering Radix Sort</a> by McIlroy and Bostic.
* For a version that uses two auxilary arrays, see {
@link
AmericanFlag}.
*
*
@author
Ivan Pesin
*/
public
class
AmericanFlagX
{
private
static
final
int
R
=
256
;
// extend ASCII alphabet size
private
static
final
int
CUTOFF
=
15
;
// cutoff to insertion sort
// do not instantiate
private
AmericanFlagX
()
{
}
// return dth character of s, -1 if d = length of string
private
static
int
charAt
(
String
s
,
int
d
)
{
assert
d
>=
0
&&
d
<=
s
.
length
();
if
(
d
==
s
.
length
())
return
-
1
;
return
s
.
charAt
(
d
);
}
/**
* Rearranges the array of extended ASCII strings in ascending order.
* This is an unstable in-place sorting algorithm.
*
*
@param
a the array to be sorted
*/
public
static
void
sort
(
String
[]
a
)
{
sort
(
a
,
0
,
a
.
length
-
1
);
}
// sort from a[lo] to a[hi], starting at the dth character
public
static
void
sort
(
String
[]
a
,
int
lo
,
int
hi
)
{
// one-time allocation of data structures
Stack
<
Integer
>
st
=
new
Stack
<
Integer
>
();
int
[]
count
=
new
int
[
R
+
1
];
int
d
=
0
;
// character index to sort by
st
.
push
(
lo
);
st
.
push
(
hi
);
st
.
push
(
d
);
while
(
!
st
.
isEmpty
())
{
d
=
st
.
pop
();
hi
=
st
.
pop
();
lo
=
st
.
pop
();
if
(
hi
<=
lo
+
CUTOFF
)
{
insertion
(
a
,
lo
,
hi
,
d
);
continue
;
}
// compute frequency counts
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
{
int
c
=
charAt
(
a
[
i
],
d
)
+
1
;
// account for -1 representing end-of-string
count
[
c
]
++
;
}
// accumulate counts relative to a[0], so that
// count[c] is the number of keys <= c
count
[
0
]
+=
lo
;
for
(
int
c
=
0
;
c
<
R
;
c
++
)
{
count
[
c
+
1
]
+=
count
[
c
];
if
(
c
>
0
&&
count
[
c
+
1
]
-
1
>
count
[
c
])
{
// add subproblem for character c (excludes sentinel c == 0)
st
.
push
(
count
[
c
]);
st
.
push
(
count
[
c
+
1
]
-
1
);
st
.
push
(
d
+
1
);
}
}
// permute data in place
// for details and proof see Knuth Theorem 5.1.2B and ch 5.2 excercise 13.
for
(
int
r
=
hi
;
r
>=
lo
;
r
--
)
{
// locate element that must be shifted right of r
int
c
=
charAt
(
a
[
r
],
d
)
+
1
;
while
(
r
>=
lo
&&
count
[
c
]
-
1
<=
r
)
{
if
(
count
[
c
]
-
1
==
r
)
count
[
c
]
--
;
r
--
;
if
(
r
>=
lo
)
c
=
charAt
(
a
[
r
],
d
)
+
1
;
}
// if r < lo the subarray is sorted.
if
(
r
<
lo
)
break
;
// permute a[r] until correct element is in place
while
(
--
count
[
c
]
!=
r
)
{
exch
(
a
,
r
,
count
[
c
]);
c
=
charAt
(
a
[
r
],
d
)
+
1
;
}
}
// clear count[] array
for
(
int
c
=
0
;
c
<
R
+
1
;
c
++
)
count
[
c
]
=
0
;
}
}
// insertion sort a[lo..hi], starting at dth character
private
static
void
insertion
(
String
[]
a
,
int
lo
,
int
hi
,
int
d
)
{
for
(
int
i
=
lo
;
i
<=
hi
;
i
++
)
for
(
int
j
=
i
;
j
>
lo
&&
less
(
a
[
j
],
a
[
j
-
1
],
d
);
j
--
)
exch
(
a
,
j
,
j
-
1
);
}
// exchange a[i] and a[j]
private
static
void
exch
(
String
[]
a
,
int
i
,
int
j
)
{
String
temp
=
a
[
i
];
a
[
i
]
=
a
[
j
];
a
[
j
]
=
temp
;
}
// is v less than w, starting at character d
private
static
boolean
less
(
String
v
,
String
w
,
int
d
)
{
// assert v.substring(0, d).equals(w.substring(0, d));
for
(
int
i
=
d
;
i
<
Math
.
min
(
v
.
length
(),
w
.
length
());
i
++
)
{
if
(
v
.
charAt
(
i
)
<
w
.
charAt
(
i
))
return
true
;
if
(
v
.
charAt
(
i
)
>
w
.
charAt
(
i
))
return
false
;
}
return
v
.
length
()
<
w
.
length
();
}
/**
* Reads in a sequence of extended ASCII strings or non-negative ints from standard input;
* American flag sorts them;
* and prints them to standard output in ascending order.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
String
[]
a
=
StdIn
.
readAllStrings
();
sort
(
a
);
// print results
for
(
int
i
=
0
;
i
<
a
.
length
;
i
++
)
StdOut
.
println
(
a
[
i
]);
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/Arbitrage.java
edu/princeton/cs/algs4/Arbitrage.java
/******************************************************************************
* Compilation: javac Arbitrage.java
* Execution: java Arbitrage < input.txt
* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java
* BellmanFordSP.java
* Data file: https://algs4.cs.princeton.edu/44sp/rates.txt
*
* Arbitrage detection.
*
* % more rates.txt
* 5
* USD 1 0.741 0.657 1.061 1.005
* EUR 1.349 1 0.888 1.433 1.366
* GBP 1.521 1.126 1 1.614 1.538
* CHF 0.942 0.698 0.619 1 0.953
* CAD 0.995 0.732 0.650 1.049 1
*
* % java Arbitrage < rates.txt
* 1000.00000 USD = 741.00000 EUR
* 741.00000 EUR = 1012.20600 CAD
* 1012.20600 CAD = 1007.14497 USD
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
Arbitrage} class provides a client that finds an arbitrage
* opportunity in a currency exchange table by constructing a
* complete-digraph representation of the exchange table and then finding
* a negative cycle in the digraph.
* <p>
* This implementation uses the Bellman-Ford algorithm to find a
* negative cycle in the complete digraph.
* The running time is proportional to <em>V</em><sup>3</sup> in the
* worst case, where <em>V</em> is the number of currencies.
* <p>
* For additional documentation,
* see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
Arbitrage
{
// this class cannot be instantiated
private
Arbitrage
()
{
}
/**
* Reads the currency exchange table from standard input and
* prints an arbitrage opportunity to standard output (if one exists).
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
// V currencies
int
V
=
StdIn
.
readInt
();
String
[]
name
=
new
String
[
V
];
// create complete network
EdgeWeightedDigraph
G
=
new
EdgeWeightedDigraph
(
V
);
for
(
int
v
=
0
;
v
<
V
;
v
++
)
{
name
[
v
]
=
StdIn
.
readString
();
for
(
int
w
=
0
;
w
<
V
;
w
++
)
{
double
rate
=
StdIn
.
readDouble
();
DirectedEdge
e
=
new
DirectedEdge
(
v
,
w
,
-
Math
.
log
(
rate
));
G
.
addEdge
(
e
);
}
}
// find negative cycle
BellmanFordSP
spt
=
new
BellmanFordSP
(
G
,
0
);
if
(
spt
.
hasNegativeCycle
())
{
double
stake
=
1000.0
;
for
(
DirectedEdge
e
:
spt
.
negativeCycle
())
{
StdOut
.
printf
(
"%10.5f %s "
,
stake
,
name
[
e
.
from
()]);
stake
*=
Math
.
exp
(
-
e
.
weight
());
StdOut
.
printf
(
"= %10.5f %s\n"
,
stake
,
name
[
e
.
to
()]);
}
}
else
{
StdOut
.
println
(
"No arbitrage opportunity"
);
}
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AssignmentProblem.java
edu/princeton/cs/algs4/AssignmentProblem.java
/******************************************************************************
* Compilation: javac AssignmentProblem.java
* Execution: java AssignmentProblem n
* Dependencies: DijkstraSP.java DirectedEdge.java
*
* Solve an n-by-n assignment problem in n^3 log n time using the
* successive shortest path algorithm.
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
AssignmentProblem} class represents a data type for computing
* an optimal solution to an <em>n</em>-by-<em>n</em> <em>assignment problem</em>.
* The assignment problem is to find a minimum weight matching in an
* edge-weighted complete bipartite graph.
* <p>
* The data type supplies methods for determining the optimal solution
* and the corresponding dual solution.
* <p>
* This implementation uses the <em>successive shortest paths algorithm</em>.
* The order of growth of the running time in the worst case is
* O(<em>n</em>^3 log <em>n</em>) to solve an <em>n</em>-by-<em>n</em>
* instance.
* <p>
* For additional documentation, see
* <a href="https://algs4.cs.princeton.edu/65reductions">Section 6.5</a>
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
AssignmentProblem
{
private
static
final
double
FLOATING_POINT_EPSILON
=
1E-14
;
private
static
final
int
UNMATCHED
=
-
1
;
private
int
n
;
// number of rows and columns
private
double
[][]
weight
;
// the n-by-n cost matrix
private
double
minWeight
;
// minimum value of any weight
private
double
[]
px
;
// px[i] = dual variable for row i
private
double
[]
py
;
// py[j] = dual variable for col j
private
int
[]
xy
;
// xy[i] = j means i-j is a match
private
int
[]
yx
;
// yx[j] = i means i-j is a match
/**
* Determines an optimal solution to the assignment problem.
*
*
@param
weight the <em>n</em>-by-<em>n</em> matrix of weights
*
@throws
IllegalArgumentException unless all weights are nonnegative
*
@throws
IllegalArgumentException if {
@code
weight} is {
@code
null}
*/
public
AssignmentProblem
(
double
[][]
weight
)
{
if
(
weight
==
null
)
throw
new
IllegalArgumentException
(
"constructor argument is null"
);
n
=
weight
.
length
;
this
.
weight
=
new
double
[
n
][
n
];
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
Double
.
isNaN
(
weight
[
i
][
j
]))
throw
new
IllegalArgumentException
(
"weight "
+
i
+
"-"
+
j
+
" is NaN"
);
if
(
weight
[
i
][
j
]
<
minWeight
)
minWeight
=
weight
[
i
][
j
];
this
.
weight
[
i
][
j
]
=
weight
[
i
][
j
];
}
}
// dual variables
px
=
new
double
[
n
];
py
=
new
double
[
n
];
// initial matching is empty
xy
=
new
int
[
n
];
yx
=
new
int
[
n
];
for
(
int
i
=
0
;
i
<
n
;
i
++
)
xy
[
i
]
=
UNMATCHED
;
for
(
int
j
=
0
;
j
<
n
;
j
++
)
yx
[
j
]
=
UNMATCHED
;
// add n edges to matching
for
(
int
k
=
0
;
k
<
n
;
k
++
)
{
assert
isDualFeasible
();
assert
isComplementarySlack
();
augment
();
}
assert
certifySolution
();
}
// find shortest augmenting path and upate
private
void
augment
()
{
// build residual graph
EdgeWeightedDigraph
G
=
new
EdgeWeightedDigraph
(
2
*
n
+
2
);
int
s
=
2
*
n
,
t
=
2
*
n
+
1
;
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
if
(
xy
[
i
]
==
UNMATCHED
)
G
.
addEdge
(
new
DirectedEdge
(
s
,
i
,
0.0
));
}
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
yx
[
j
]
==
UNMATCHED
)
G
.
addEdge
(
new
DirectedEdge
(
n
+
j
,
t
,
py
[
j
]));
}
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
xy
[
i
]
==
j
)
G
.
addEdge
(
new
DirectedEdge
(
n
+
j
,
i
,
0.0
));
else
G
.
addEdge
(
new
DirectedEdge
(
i
,
n
+
j
,
reducedCost
(
i
,
j
)));
}
}
// compute shortest path from s to every other vertex
DijkstraSP
spt
=
new
DijkstraSP
(
G
,
s
);
// augment along alternating path
for
(
DirectedEdge
e
:
spt
.
pathTo
(
t
))
{
int
i
=
e
.
from
(),
j
=
e
.
to
()
-
n
;
if
(
i
<
n
)
{
xy
[
i
]
=
j
;
yx
[
j
]
=
i
;
}
}
// update dual variables
for
(
int
i
=
0
;
i
<
n
;
i
++
)
px
[
i
]
+=
spt
.
distTo
(
i
);
for
(
int
j
=
0
;
j
<
n
;
j
++
)
py
[
j
]
+=
spt
.
distTo
(
n
+
j
);
}
// reduced cost of i-j
// (subtracting off minWeight reweights all weights to be non-negative)
private
double
reducedCost
(
int
i
,
int
j
)
{
double
reducedCost
=
(
weight
[
i
][
j
]
-
minWeight
)
+
px
[
i
]
-
py
[
j
];
// to avoid issues with floating-point precision
double
magnitude
=
Math
.
abs
(
weight
[
i
][
j
])
+
Math
.
abs
(
px
[
i
])
+
Math
.
abs
(
py
[
j
]);
if
(
Math
.
abs
(
reducedCost
)
<=
FLOATING_POINT_EPSILON
*
magnitude
)
return
0.0
;
assert
reducedCost
>=
0.0
;
return
reducedCost
;
}
/**
* Returns the dual optimal value for the specified row.
*
*
@param
i the row index
*
@return
the dual optimal value for row {
@code
i}
*
@throws
IllegalArgumentException unless {
@code
0 <= i < n}
*
*/
// dual variable for row i
public
double
dualRow
(
int
i
)
{
validate
(
i
);
return
px
[
i
];
}
/**
* Returns the dual optimal value for the specified column.
*
*
@param
j the column index
*
@return
the dual optimal value for column {
@code
j}
*
@throws
IllegalArgumentException unless {
@code
0 <= j < n}
*
*/
public
double
dualCol
(
int
j
)
{
validate
(
j
);
return
py
[
j
];
}
/**
* Returns the column associated with the specified row in the optimal solution.
*
*
@param
i the row index
*
@return
the column matched to row {
@code
i} in the optimal solution
*
@throws
IllegalArgumentException unless {
@code
0 <= i < n}
*
*/
public
int
sol
(
int
i
)
{
validate
(
i
);
return
xy
[
i
];
}
/**
* Returns the total weight of the optimal solution
*
*
@return
the total weight of the optimal solution
*
*/
public
double
weight
()
{
double
total
=
0.0
;
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
if
(
xy
[
i
]
!=
UNMATCHED
)
total
+=
weight
[
i
][
xy
[
i
]];
}
return
total
;
}
private
void
validate
(
int
i
)
{
if
(
i
<
0
||
i
>=
n
)
throw
new
IllegalArgumentException
(
"index is not between 0 and "
+
(
n
-
1
)
+
": "
+
i
);
}
/**************************************************************************
*
* The code below is solely for testing correctness of the data type.
*
**************************************************************************/
// check that dual variables are feasible
private
boolean
isDualFeasible
()
{
// check that all edges have >= 0 reduced cost
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
reducedCost
(
i
,
j
)
<
0
)
{
StdOut
.
println
(
"Dual variables are not feasible"
);
return
false
;
}
}
}
return
true
;
}
// check that primal and dual variables are complementary slack
private
boolean
isComplementarySlack
()
{
// check that all matched edges have 0-reduced cost
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
if
((
xy
[
i
]
!=
UNMATCHED
)
&&
(
reducedCost
(
i
,
xy
[
i
])
!=
0
))
{
StdOut
.
println
(
"Primal and dual variables are not complementary slack"
);
return
false
;
}
}
return
true
;
}
// check that primal variables are a perfect matching
private
boolean
isPerfectMatching
()
{
// check that xy[] is a perfect matching
boolean
[]
perm
=
new
boolean
[
n
];
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
if
(
perm
[
xy
[
i
]])
{
StdOut
.
println
(
"Not a perfect matching"
);
return
false
;
}
perm
[
xy
[
i
]]
=
true
;
}
// check that xy[] and yx[] are inverses
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
xy
[
yx
[
j
]]
!=
j
)
{
StdOut
.
println
(
"xy[] and yx[] are not inverses"
);
return
false
;
}
}
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
if
(
yx
[
xy
[
i
]]
!=
i
)
{
StdOut
.
println
(
"xy[] and yx[] are not inverses"
);
return
false
;
}
}
return
true
;
}
// check optimality conditions
private
boolean
certifySolution
()
{
return
isPerfectMatching
()
&&
isDualFeasible
()
&&
isComplementarySlack
();
}
/**
* Unit tests the {
@code
AssignmentProblem} data type.
* Takes a command-line argument n; creates a random n-by-n matrix;
* solves the n-by-n assignment problem; and prints the optimal
* solution.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
// create random n-by-n matrix
int
n
=
Integer
.
parseInt
(
args
[
0
]);
double
[][]
weight
=
new
double
[
n
][
n
];
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
weight
[
i
][
j
]
=
StdRandom
.
uniform
(
900
)
+
100
;
// 3 digits
}
}
// solve assignment problem
AssignmentProblem
assignment
=
new
AssignmentProblem
(
weight
);
StdOut
.
printf
(
"weight = %.0f\n"
,
assignment
.
weight
());
StdOut
.
println
();
// print n-by-n matrix and optimal solution
if
(
n
>=
20
)
return
;
for
(
int
i
=
0
;
i
<
n
;
i
++
)
{
for
(
int
j
=
0
;
j
<
n
;
j
++
)
{
if
(
j
==
assignment
.
sol
(
i
))
StdOut
.
printf
(
"*%.0f "
,
weight
[
i
][
j
]);
else
StdOut
.
printf
(
" %.0f "
,
weight
[
i
][
j
]);
}
StdOut
.
println
();
}
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/Average.java
edu/princeton/cs/algs4/Average.java
/******************************************************************************
* Compilation: javac Average.java
* Execution: java Average < data.txt
* Dependencies: StdIn.java StdOut.java
*
* Reads in a sequence of real numbers, and computes their average.
*
* % java Average
* 10.0 5.0 6.0
* 3.0 7.0 32.0
* [Ctrl-d]
* Average is 10.5
*
* Note [Ctrl-d] signifies the end of file on Unix.
* On windows use [Ctrl-z].
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
/**
* The {
@code
Average} class provides a client for reading in a sequence
* of real numbers and printing out their average.
* <p>
* For additional documentation, see <a href="https://algs4.cs.princeton.edu/11model">Section 1.1</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
*
@author
Robert Sedgewick
*
@author
Kevin Wayne
*/
public
class
Average
{
// this class should not be instantiated
private
Average
()
{
}
/**
* Reads in a sequence of real numbers from standard input and prints
* out their average to standard output.
*
*
@param
args the command-line arguments
*/
public
static
void
main
(
String
[]
args
)
{
int
count
=
0
;
// number input values
double
sum
=
0.0
;
// sum of input values
// read data and compute statistics
while
(
!
StdIn
.
isEmpty
())
{
double
value
=
StdIn
.
readDouble
();
sum
+=
value
;
count
++
;
}
// compute the average
double
average
=
sum
/
count
;
// print results
StdOut
.
println
(
"Average is "
+
average
);
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/
edu/princeton/cs/algs4/AVLTreeST.java
edu/princeton/cs/algs4/AVLTreeST.java
/******************************************************************************
* Compilation: javac AVLTreeST.java
* Execution: java AVLTreeST < input.txt
* Dependencies: StdIn.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/33balanced/tinyST.txt
*
* A symbol table implemented using an AVL tree.
*
* % more tinyST.txt
* S E A R C H E X A M P L E
*
* % java AVLTreeST < tinyST.txt
* A 8
* C 4
* E 12
* H 5
* L 11
* M 9
* P 10
* R 3
* S 0
* X 7
*
******************************************************************************/
package
edu
.
princeton
.
cs
.
algs4
;
import
java
.
util
.
NoSuchElementException
;
/**
* The {
@code
AVLTreeST} class represents an ordered symbol table of
* generic key-value pairs. It supports the usual <em>put</em>, <em>get</em>,
* <em>contains</em>, <em>delete</em>, <em>size</em>, and <em>is-empty</em>
* methods. It also provides ordered methods for finding the <em>minimum</em>,
* <em>maximum</em>, <em>floor</em>, and <em>ceiling</em>. It also provides a
* <em>keys</em> method for iterating over all of the keys. A symbol table
* implements the <em>associative array</em> abstraction: when associating a
* value with a key that is already in the symbol table, the convention is to
* replace the old value with the new value. Unlike {
@link
java.util.Map}, this
* class uses the convention that values cannot be {
@code
null}
* —setting the value associated with a key to {
@code
null} is
* equivalent to deleting the key from the symbol table.
* <p>
* This symbol table implementation uses internally an
* <a href="https://en.wikipedia.org/wiki/AVL_tree"> AVL tree </a> (Georgy
* Adelson-Velsky and Evgenii Landis' tree) which is a self-balancing BST.
* In an AVL tree, the heights of the two child subtrees of any
* node differ by at most one; if at any time they differ by more than one,
* rebalancing is done to restore this property.
* <p>
* This implementation requires that the key type implements the
* {
@code
Comparable} interface and calls the {
@code
compareTo()} and
* method to compare two keys. It does not call either {
@code
equals()} or
* {
@code
hashCode()}. The <em>put</em>, <em>get</em>, <em>contains</em>,
* <em>delete</em>, <em>minimum</em>, <em>maximum</em>, <em>ceiling</em>, and
* <em>floor</em> operations each take logarithmic time in the worst case. The
* <em>size</em>, and <em>is-empty</em> operations take constant time.
* Construction also takes constant time.
*
* For other implementations of the same API, see {
@link
ST}, {
@link
BinarySearchST},
* {
@link
SequentialSearchST}, {
@link
BST}, {
@link
RedBlackBST},
* {
@link
SeparateChainingHashST}, and {
@link
LinearProbingHashST}.
*
*
@author
Marcelo Silva
*/
public
class
AVLTreeST
<
Key
extends
Comparable
<
Key
>
,
Value
>
{
/**
* The root node.
*/
private
Node
root
;
/**
* This class represents an inner node of the AVL tree.
*/
private
class
Node
{
private
final
Key
key
;
// the key
private
Value
val
;
// the associated value
private
int
height
;
// height of the subtree
private
int
size
;
// number of nodes in subtree
private
Node
left
;
// left subtree
private
Node
right
;
// right subtree
public
Node
(
Key
key
,
Value
val
,
int
height
,
int
size
)
{
this
.
key
=
key
;
this
.
val
=
val
;
this
.
size
=
size
;
this
.
height
=
height
;
}
}
/**
* Initializes an empty symbol table.
*/
public
AVLTreeST
()
{
}
/**
* Checks if the symbol table is empty.
*
*
@return
{
@code
true} if the symbol table is empty.
*/
public
boolean
isEmpty
()
{
return
root
==
null
;
}
/**
* Returns the number key-value pairs in the symbol table.
*
*
@return
the number key-value pairs in the symbol table
*/
public
int
size
()
{
return
size
(
root
);
}
/**
* Returns the number of nodes in the subtree.
*
*
@param
x the subtree
*
*
@return
the number of nodes in the subtree
*/
private
int
size
(
Node
x
)
{
if
(
x
==
null
)
return
0
;
return
x
.
size
;
}
/**
* Returns the height of the internal AVL tree. It is assumed that the
* height of an empty tree is -1 and the height of a tree with just one node
* is 0.
*
*
@return
the height of the internal AVL tree
*/
public
int
height
()
{
return
height
(
root
);
}
/**
* Returns the height of the subtree.
*
*
@param
x the subtree
*
*
@return
the height of the subtree.
*/
private
int
height
(
Node
x
)
{
if
(
x
==
null
)
return
-
1
;
return
x
.
height
;
}
/**
* Returns the value associated with the given key.
*
*
@param
key the key
*
@return
the value associated with the given key if the key is in the
* symbol table and {
@code
null} if the key is not in the
* symbol table
*
@throws
IllegalArgumentException if {
@code
key} is {
@code
null}
*/
public
Value
get
(
Key
key
)
{
if
(
key
==
null
)
throw
new
IllegalArgumentException
(
"argument to get() is null"
);
Node
x
=
get
(
root
,
key
);
if
(
x
==
null
)
return
null
;
return
x
.
val
;
}
/**
* Returns value associated with the given key in the subtree or
* {
@code
null} if no such key.
*
*
@param
x the subtree
*
@param
key the key
*
@return
value associated with the given key in the subtree or
* {
@code
null} if no such key
*/
private
Node
get
(
Node
x
,
Key
key
)
{
if
(
x
==
null
)
return
null
;
int
cmp
=
key
.
compareTo
(
x
.
key
);
if
(
cmp
<
0
)
return
get
(
x
.
left
,
key
);
else
if
(
cmp
>
0
)
return
get
(
x
.
right
,
key
);
else
return
x
;
}
/**
* Checks if the symbol table contains the given key.
*
*
@param
key the key
*
@return
{
@code
true} if the symbol table contains {
@code
key}
* and {
@code
false} otherwise
*
@throws
IllegalArgumentException if {
@code
key} is {
@code
null}
*/
public
boolean
contains
(
Key
key
)
{
return
get
(
key
)
!=
null
;
}
/**
* Inserts the specified key-value pair into the symbol table, overwriting
* the old value with the new value if the symbol table already contains the
* specified key. Deletes the specified key (and its associated value) from
* this symbol table if the specified value is {
@code
null}.
*
*
@param
key the key
*
@param
val the value
*
@throws
IllegalArgumentException if {
@code
key} is {
@code
null}
*/
public
void
put
(
Key
key
,
Value
val
)
{
if
(
key
==
null
)
throw
new
IllegalArgumentException
(
"first argument to put() is null"
);
if
(
val
==
null
)
{
delete
(
key
);
return
;
}
root
=
put
(
root
,
key
,
val
);
assert
check
();
}
/**
* Inserts the key-value pair in the subtree. It overrides the old value
* with the new value if the symbol table already contains the specified key
* and deletes the specified key (and its associated value) from this symbol
* table if the specified value is {
@code
null}.
*
*
@param
x the subtree
*
@param
key the key
*
@param
val the value
*
@return
the subtree
*/
private
Node
put
(
Node
x
,
Key
key
,
Value
val
)
{
if
(
x
==
null
)
return
new
Node
(
key
,
val
,
0
,
1
);
int
cmp
=
key
.
compareTo
(
x
.
key
);
if
(
cmp
<
0
)
{
x
.
left
=
put
(
x
.
left
,
key
,
val
);
}
else
if
(
cmp
>
0
)
{
x
.
right
=
put
(
x
.
right
,
key
,
val
);
}
else
{
x
.
val
=
val
;
return
x
;
}
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
return
balance
(
x
);
}
/**
* Restores the AVL tree property of the subtree.
*
*
@param
x the subtree
*
@return
the subtree with restored AVL property
*/
private
Node
balance
(
Node
x
)
{
if
(
balanceFactor
(
x
)
<
-
1
)
{
if
(
balanceFactor
(
x
.
right
)
>
0
)
{
x
.
right
=
rotateRight
(
x
.
right
);
}
x
=
rotateLeft
(
x
);
}
else
if
(
balanceFactor
(
x
)
>
1
)
{
if
(
balanceFactor
(
x
.
left
)
<
0
)
{
x
.
left
=
rotateLeft
(
x
.
left
);
}
x
=
rotateRight
(
x
);
}
return
x
;
}
/**
* Returns the balance factor of the subtree. The balance factor is defined
* as the difference in height of the left subtree and right subtree, in
* this order. Therefore, a subtree with a balance factor of -1, 0 or 1 has
* the AVL property since the heights of the two child subtrees differ by at
* most one.
*
*
@param
x the subtree
*
@return
the balance factor of the subtree
*/
private
int
balanceFactor
(
Node
x
)
{
return
height
(
x
.
left
)
-
height
(
x
.
right
);
}
/**
* Rotates the given subtree to the right.
*
*
@param
x the subtree
*
@return
the right rotated subtree
*/
private
Node
rotateRight
(
Node
x
)
{
Node
y
=
x
.
left
;
x
.
left
=
y
.
right
;
y
.
right
=
x
;
y
.
size
=
x
.
size
;
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
y
.
height
=
1
+
Math
.
max
(
height
(
y
.
left
),
height
(
y
.
right
));
return
y
;
}
/**
* Rotates the given subtree to the left.
*
*
@param
x the subtree
*
@return
the left rotated subtree
*/
private
Node
rotateLeft
(
Node
x
)
{
Node
y
=
x
.
right
;
x
.
right
=
y
.
left
;
y
.
left
=
x
;
y
.
size
=
x
.
size
;
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
y
.
height
=
1
+
Math
.
max
(
height
(
y
.
left
),
height
(
y
.
right
));
return
y
;
}
/**
* Removes the specified key and its associated value from the symbol table
* (if the key is in the symbol table).
*
*
@param
key the key
*
@throws
IllegalArgumentException if {
@code
key} is {
@code
null}
*/
public
void
delete
(
Key
key
)
{
if
(
key
==
null
)
throw
new
IllegalArgumentException
(
"argument to delete() is null"
);
if
(
!
contains
(
key
))
return
;
root
=
delete
(
root
,
key
);
assert
check
();
}
/**
* Removes the specified key and its associated value from the given
* subtree.
*
*
@param
x the subtree
*
@param
key the key
*
@return
the updated subtree
*/
private
Node
delete
(
Node
x
,
Key
key
)
{
int
cmp
=
key
.
compareTo
(
x
.
key
);
if
(
cmp
<
0
)
{
x
.
left
=
delete
(
x
.
left
,
key
);
}
else
if
(
cmp
>
0
)
{
x
.
right
=
delete
(
x
.
right
,
key
);
}
else
{
if
(
x
.
left
==
null
)
{
return
x
.
right
;
}
else
if
(
x
.
right
==
null
)
{
return
x
.
left
;
}
else
{
Node
y
=
x
;
x
=
min
(
y
.
right
);
x
.
right
=
deleteMin
(
y
.
right
);
x
.
left
=
y
.
left
;
}
}
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
return
balance
(
x
);
}
/**
* Removes the smallest key and associated value from the symbol table.
*
*
@throws
NoSuchElementException if the symbol table is empty
*/
public
void
deleteMin
()
{
if
(
isEmpty
())
throw
new
NoSuchElementException
(
"called deleteMin() with empty symbol table"
);
root
=
deleteMin
(
root
);
assert
check
();
}
/**
* Removes the smallest key and associated value from the given subtree.
*
*
@param
x the subtree
*
@return
the updated subtree
*/
private
Node
deleteMin
(
Node
x
)
{
if
(
x
.
left
==
null
)
return
x
.
right
;
x
.
left
=
deleteMin
(
x
.
left
);
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
return
balance
(
x
);
}
/**
* Removes the largest key and associated value from the symbol table.
*
*
@throws
NoSuchElementException if the symbol table is empty
*/
public
void
deleteMax
()
{
if
(
isEmpty
())
throw
new
NoSuchElementException
(
"called deleteMax() with empty symbol table"
);
root
=
deleteMax
(
root
);
assert
check
();
}
/**
* Removes the largest key and associated value from the given subtree.
*
*
@param
x the subtree
*
@return
the updated subtree
*/
private
Node
deleteMax
(
Node
x
)
{
if
(
x
.
right
==
null
)
return
x
.
left
;
x
.
right
=
deleteMax
(
x
.
right
);
x
.
size
=
1
+
size
(
x
.
left
)
+
size
(
x
.
right
);
x
.
height
=
1
+
Math
.
max
(
height
(
x
.
left
),
height
(
x
.
right
));
return
balance
(
x
);
}
/**
* Returns the smallest key in the symbol table.
*
*
@return
the smallest key in the symbol table
*
@throws
NoSuchElementException if the symbol table is empty
*/
public
Key
min
()
{
if
(
isEmpty
())
throw
new
NoSuchElementException
(
"called min() with empty symbol table"
);
return
min
(
root
).
key
;
}
/**
* Returns the node with the smallest key in the subtree.
*
*
@param
x the subtree
*
@return
the node with the smallest key in the subtree
*/
private
Node
min
(
Node
x
)
{
if
(
x
.
left
==
null
)
return
x
;
return
min
(
x
.
left
);
}
/**
* Returns the largest key in the symbol table.
*
*
@return
the largest key in the symbol table
*
@throws
NoSuchElementException if the symbol table is empty
*/