LeetCode - Unique Paths

Posted 2021-01-24 IncredibleThings

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?

Note: m and n will be at most 100.

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


我们需要用动态规划Dynamic Programming来解，我们可以维护一个二维数组dp，其中dp[i][j]表示到当前位置不同的走法的个数，然后可以得到递推式为: dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

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