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 
     
      #include 
      
       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 
     
      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;}