Unitque_Path_1.png

u_p_2.png

/**
* Abstract: A DP problem, immediately from the problem specs.
*/
int uniquePaths(int m, int n) {
    int **dp = (int**)malloc((m + 1) * sizeof(*dp));
    for (int i = 1; i <= m; i++) { 
        dp[i] = (int*)malloc((n + 1) * sizeof(int));
        for (int j = 1; j <= n; j++) { 
            if (i == 1 || j == 1) {
                dp[i][j] = 1;
            } else {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        } 
    }
    return dp[m][n];
}