[Leetcode]Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

典型动规，注意边界条件就可以了。

class Solution {
public:
int uniquePaths(int m, int n) {
    int* path = new int[m*n];
    for (int i = 0; i != m; i++){
        for (int j = 0; j != n; j++){
            if (i == 0){
                if (j == 0)
                    path[i*n + j] = 1;
                else
                    path[i*n + j] = path[i*n + j - 1];
            }
            else{
                if (j == 0)
                    path[i*n + j] = path[(i - 1)*n + j];
                else
                    path[i*n + j] = path[i*n + j - 1] + path[(i - 1)*n + j];
            }
        }
    }
    return path[m*n - 1];
}
};