Project Euler Problem 15 Lattice paths

Lattice paths

Problem 15

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20×20 grid?

C++:

#include <iostream>
#include <cstring>

using namespace std;

const int MAXN = 20;

long grid[MAXN+1][MAXN+1];

long pathcount(int row, int col)
{
    long count;

    if(grid[row][col])
        return grid[row][col];

    if(row == 0 && col == 0)
        return 1;
    else if(row == 0)
        count = pathcount(row, col - 1);
    else if(col == 0)
        count = pathcount(row - 1, col);
    else
        count = pathcount(row - 1, col) + pathcount(row, col -1);

    grid[row][col] = count;

    return count;
}

int main()
{
    int n;

    memset(grid, 0, sizeof(grid));

    while(cin >> n && n <=MAXN) {
        long ans = pathcount(n, n);

        cout << ans << endl;
    }

    return 0;
}

C++:

#include <iostream>

using namespace std;

const int MAXN = 20;

long grid[MAXN+1][MAXN+1];

int main()
{
    int n;

    while(cin >> n && n <=MAXN) {
        for(int j=0; j<=n; j++)
            grid[0][j] = 1;
        for(int i=1; i<=n; i++) {
            grid[i][0] = 1;
            for(int j=1; j<=n; j++)
                grid[i][j] = grid[i][j-1] + grid[i-1][j];
        }

        cout << grid[n][n] << endl;
    }

    return 0;
}