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.
Input: m = 3, n = 2
Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
- Right -> Right -> Down
- Right -> Down -> Right
- Down -> Right -> Right
Input: m = 7, n = 3
from typing import List class Solution: def uniquePaths(self, m: int, n: int) -> int: if m <= 1 or n <= 1: return 1 path = [[1 for i in range(m)] for j in range(n)] for i in range(n-2, -1, -1): for j in range(m-2, -1, -1): path[i][j] = path[i+1][j] + path[i][j+1] return path
test = Solution() assert test.uniquePaths(3, 2) == 3 assert test.uniquePaths(7, 3) == 28 print('All Passed!')
Big O Analysis
Space Complexity: O(NM)
Time Complexity: O(NM)