LeetCode 62. Unique Paths 不同的路径

题目

https://leetcode.com/problems/unique-paths/description/

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.

 

讲解

这道题是每次可以向下走或者向右走,求到达最右下角的格子的所有不同走法的总数。

我们可以用一个二维的动态数组表示到每一个格子的不同走法总数。

最左边一列或者最上面一排的格子的走法总数是1。而对于其他的格子,走法总数则是左边的相邻格子走法总数加上相邻的上面那个格子的走法总数。

 

视频教学

Java参考代码

class Solution {
    public int uniquePaths(int m, int n) {
        if (m == 0 || n == 0) {
            return 0;
        }
        
        int[][] numberOfPaths = new int[m][n];
        
        for (int i = 0; i < m; i++) {
            numberOfPaths[i][0] = 1;
        }
        
        for (int j = 0; j < n; j++) {
            numberOfPaths[0][j] = 1;
        }
        
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                numberOfPaths[i][j] = numberOfPaths[i - 1][j] + numberOfPaths[i][j - 1];
            }
        }
        
        return numberOfPaths[m - 1][n - 1];
        
        // Time Complexity: O(m * n)
        // Space Complexity: O(m * n)        
    }
}

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