62. Unique Paths - jiejackyzhang/leetcode-note GitHub Wiki

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?

解题思路为Dynamic Programming。

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

space 可以缩减为O(n)

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