LeetCode 62. Unique Paths

[Woodyiiiiiii]

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?

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

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空间一维dp数组：

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

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参考资料:
LeetCode原题