Leetcode Unique Paths

rosepicker

于 2017-06-23 10:29:01 发布

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分类专栏： leetcode 文章标签： leetcode

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本文介绍了一个经典的动态规划问题——计算从网格左上角到右下角的不同路径数量。机器人只能向下或向右移动，通过动态规划算法高效地解决了该问题。

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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?

当前状态与前一状态相关，而且只需要求出路径数，而不需要具体的路径信息，那当然是动态规划大法。

动态规划方程：dp[i][j] = dp[i-1][j] + dp[i][j-1]

代码如下：

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