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Leetcode 62. Unique Paths

Question Description

Original Question: Leetcode 62. Unique Paths

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

Solution

class Solution {
    public int uniquePaths(int m, int n) {
        if(m == 0|| n==0) return 0;
        int[][] dp = new int[m][n];
        for(int i = 0; i < m; i++){
            dp[i][n-1] = 1;
        }
        for(int i = 0; i < n; i++){
            dp[m-1][i] = 1;
        }
        for(int j = m-2; j>=0; j--){
            for(int i = n-2; i>=0;i--){
                dp[j][i] = dp[j+1][i] + dp[j][i+1];
            }
        }
        return dp[0][0];
    }
}