62. Unique Paths

最新推荐文章于 2025-04-02 22:31:45 发布

dici5041

最新推荐文章于 2025-04-02 22:31:45 发布

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原文链接：http://www.cnblogs.com/wentiliangkaihua/p/11553565.html

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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所有可能路径数量的算法。通过动态规划方法，利用一维数组优化空间复杂度，实现高效路径计数。

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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?

机器人长得真几把欠打

https://blog.youkuaiyun.com/zxzxzx0119/article/details/81807910

public class Solution {
    public int uniquePaths(int m, int n) {
        /*
        int[][] ways = new int[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 || j == 0) ways[i][j] = 1;
                else ways[i][j] = ways[i-1][j] + ways[i][j-1];
            }
        }
        return ways[m-1][n-1];
        */
        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];
    }
}