leetcode_62. Unique Paths

題目：

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?

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

Note: m and n will be at most 100.

典型的一個動態規劃的題目。思路比較簡單，當前格子的路徑數等於當前格子左一格子的路徑數加上當前格子上一個格子的路徑數。

注意的是邊界情況。如果行列有爲1的話 直接返回。否則下面的處理會越界。

貼上代碼：

class Solution {
public:
    int uniquePaths(int m, int n) {
        int grid[m][n];
        grid[0][0] = 0;
        if(m == 1 || n == 1){return 1;}
        for(int j = 1; j < n; ++j){
            grid[0][j] = 1;
        }
        for(int i = 1; i < m; ++i){
            grid[i][0] = 1;
        }
        for(int i = 1; i < m; ++i){
            for(int j = 1; j < n; ++j){
                grid[i][j] = grid[i-1][j]+grid[i][j-1];
            }
        }
    return grid[m-1][n-1];
    }
};