Unique Path

题目：

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?

接口：

class Solution {
public:
    /**
     * @param n, m: positive integer (1 <= n ,m <= 100)
     * @return an integer
     */
    int uniquePaths(int m, int n) {
        // wirte your code here

    }
};

分析：

要求统计方案的个数，同时很明显每个格子unique path的数量等于上一格子+左一格子，所以使用DP。

解法：

class Solution {
public:
    /**
     * @param n, m: positive integer (1 <= n ,m <= 100)
     * @return an integer
     */
    int uniquePaths(int m, int n) {
        // wirte your code here
        if (m == 0 || n == 0) {
            return 0;
        }

        vector<vector<int> >f(m, vector<int>(n) );
        for (int i = 0; i < m; i++) {
            f[i][0] = 1;
        }
        for (int j = 0; j < n; j++) {
            f[0][j] = 1;
        }

        int path = 0;
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                f[i][j] = f[i - 1][j] + f[i][j - 1];
            }
        }

        return f[m - 1][n - 1];
    }
};