Leetcode–Unique Paths

The Problem:

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?

Notes:

  1. A basic DP problem, and also can be done by directly calculate choose m from (m+n).

Java Solution

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