62. Unique Paths

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LeetCode

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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?

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

Code

class Solution {
    public int uniquePaths(int m, int n) {
        int[] dp = new int[m];

        for(int i = 0; i < m; i++){
            dp[i] = 1;
        }

        for(int j = 1; j < n; j++){
            for(int i = 1; i < m; i++){
                dp[i] = dp[i] + dp[i - 1];
            }
        }

        return dp[m - 1];
    }
}