LeetCode 62 动态规划 Unique Paths

不同路径
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 7 x 3 grid. 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
 

Constraints:
1 <= m, n <= 100
It‘s guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

由二维dp压缩一维，并设置一个起始的dp[0]可以简化代码

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