[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?

Note: m and n will be at most 100.

 解题思路：

设到i, j位置的path个数为path[i][j], 则i = 0 or j = 0时，path[i][j] = 1;否则path[i][j] = path[i - 1][j] + path[i][j - 1];

class Solution {

public:

    int uniquePaths(int m, int n) {

        // IMPORTANT: Please reset any member data you declared, as

        // the same Solution instance will be reused for each test case.

        int **path = new int*[m + 1];

        for(int i = 0;i < m;i++) path[i] = new int[n + 1];

        for(int i = 0;i < m;i++)

        {

            for(int j = 0;j < n;j++)

            {

                if(i == 0) path[i][j] = 1;

                else

                {

                    if(j == 0) path[i][j] = 1;

                    else path[i][j] = path[i - 1][j] + path[i][j - 1];

                }

            }

        }

        return path[m - 1][n - 1];

    }

};