LeetCode -- 62. Unique Paths

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?

Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.

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思路：

这是一道简单的动态规划题。到达第一行或者第一列的每个位置都只有1种走法，因为机器人只能向右或者向下行走。当i, j>0时，可以从(i-1,j)和(i,j-1)两个位置到达位置(i,j)。

设d[i][j]表示到达位置(i,j)的路径数。

初始状态：

d[i][j]=1,i=0或j=0

状态转移方程：

d[i][j]=d[i−1][j]+d[i][j−1],i>0且j>0

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C++代码：

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