leetcode---62. Unique Paths

最新推荐文章于 2021-05-24 10:47:29 发布

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本文介绍了一种计算机器人从网格左上角到右下角唯一路径数量的方法。通过动态规划，利用二维数组或一维数组优化空间复杂度，实现高效求解。

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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?
这里写图片描述

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

Note: m and n will be at most 100.

public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        for(int i = 0; i < m; i++){
            dp[i][0] = 1;
        }
        for(int i = 0; i < n; i++){
            dp[0][i] = 1;
        }
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
    }

版本二：

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