Unique Paths
A robot is located at the top-left corner of a m x n grid. 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. How many possible unique paths are there?
Constraints:
- 1 <= m, n <= 100
- m and n are integers
Examples:
Input: m = 3, n = 7
Output: 28
Explanation: There are 28 unique paths from the top-left corner to the bottom-right corner of a 3x7 grid.
Solutions
Dynamic Programming
Time: O(m*n)Space: O(m*n)
The solution uses dynamic programming to build up a 2D array where each cell represents the number of unique paths to that cell. The final result is the value in the bottom-right cell of the array.
def uniquePaths(m:
int, n:
int) -> int:
dp = [[1]*n for _ in range(m)]
for i in range(1, m):
for j in range(1, n):
dp[i][j] = dp[i-1][j] + dp[i][j-1]
return dp[m-1][n-1]Follow-up:
What if the robot can move in all four directions (up, down, left, right)?
