Unique Paths

LeetCode Q 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?
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

Solution

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