62. 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.
题目大意：机器人从左到右的唯一路径的条数，每次只能往右或者下，参考莱维汀的《算法设计与分析基础》的动态规划章节硬币收集问题。
思路就是F[i][j] = F[i - 1][j] + F[i][j - 1]，因为走边界路径唯一，所以上边界和左边界都为1.

class Solution {public:    int uniquePaths(int m, int n) {        int F[100][100];        memset(F, 0, sizeof(F));        F[0][0] = 1;        for(int j = 1; j < n; ++j)            F[0][j] = F[0][j - 1];        for(int i = 1; i < m; ++i){            F[i][0] = F[i - 1][0];            for(int j = 1; j < n; ++j)                F[i][j] = F[i - 1][j] + F[i][j - 1];        }        return F[m - 1][n - 1];    }};