Leetcode - Unique Paths

最新推荐文章于 2024-06-03 23:52:00 发布

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本文介绍了一个经典的动态规划问题——计算机器人从网格左上角到右下角的不同路径数量。通过使用动态规划的方法，文章详细解释了如何填充二维数组来得到最终答案。

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?

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