Fill in the C++ Code.

// Triangle via top down dynamic programming

#include<fstream>

#include<sstream>

#include<iostream>

using namespace std;

const int max_rows=4;

int memo[max_rows][max_rows+1];

void init_memo(){

for(int i=0; i<max_rows; i++)

for(int j=0; j<max_rows+1; j++)

memo[i][j]=-1;

}

int max_value(int t[][max_rows+1], int i, int j){

if(__________________________)

return t[____________][_______________];

if(______________________________)

return memo[i][j];

return memo[i][j]= t[____][____]+max( _______________________________ );

}

int main()

{ init_memo(); // set all entries = -1

ifstream in("http://venus.cs.qc.cuny.edu/~waxman/211/triangle.txt");

string line;

int t[max_rows][max_rows+1]={0};

for(int i=0; i<max_rows;i++){

getline(in,line);

stringstream si(line);

t[i][0]=0;

for(int j=1;j< i+2;j++ )

si>>t[i][j];

}

int result=max_value(t,max_rows-1,1);

for(int i=2; i<=max_rows;i++){

int k=max_value(t,max_rows-1,i);

if(result<max_value(t,max_rows-1,i))

result=max_value(t,max_rows-1,i);

}

cout<<"the result is: "<<result<<endl;

system("PAUSE");

return 0;

}