Question

I am learning dynamic programming and have attempted solve Problem 15 of Project Euler using dynamic programming.
Although I do know that the problem is solvable using binomial co-efficient, I wanted to see how much have I learned dynamic programming and thus tried. Here is the code:

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstdlib>

using namespace std;

int main()
{
    int gridsize;
    cin>>gridsize;


    int** grid = new int*[gridsize+1];
    for ( int i = 0; i < gridsize+1; i++) {
        grid[i] = new int[gridsize+1];
    }

    //Initialize the grid distances

    for ( int i = 1; i <= gridsize ; i++) {
        grid[i][0] = 1;
        grid[0][i] = 1;
    }
    grid[0][0] = 0;

    for ( int i = 1; i <= gridsize ; i++) {
        for ( int j = 1; j <= gridsize ; j++) {
            grid[i][j] = grid[i-1][j] + grid[i][j-1];
        }
    }
    cout<<grid[gridsize][gridsize]<<endl;
    delete(grid);   
    return 0;
}

The expected answer is 137846528820, while the answer that I am getting is 407575348.

Answer 1

Your logic is fairly correct, the problem is that you are getting a case of integer overflow. Here is a modified version of your code that works perfectly. Simply change the int to an long long unsigned type.

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstdlib>

using namespace std;
typedef unsigned long long ull;
int main()
{
    ull gridsize;
    cin>>gridsize;


    ull** grid = (ull**) malloc((gridsize+1)*sizeof(ull*));
    for ( int i = 0; i < gridsize+1; i++) {
        grid[i] = (ull*) malloc((gridsize +1)*sizeof(ull));
    }

    //Initialize the grid distances

    for ( int i = 1; i <= gridsize ; i++) {
        grid[i][0] = 1;
        grid[0][i] = 1;
    }
    grid[0][0] = 0;

    for ( int i = 1; i <= gridsize ; i++) {
        for ( int j = 1; j <= gridsize ; j++) {
            grid[i][j] = grid[i-1][j] + grid[i][j-1];
        }
    }
    cout<<grid[gridsize][gridsize];
    free(grid);
    return 0;
}