Unique Path

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?

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

Constraints:

  • 1 <= m, n <= 100
  • It’s guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

Solution

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

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