 # 62. Unique Paths

Updated: 2023-09-01

LeetCode problem

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 10^9.

Example 1: Input: m = 3, n = 7
Output: 28


Example 2:

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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down


Approach 1:

LeetCode Submission

class Solution:
def uniquePaths(self, m: int, n: int) -> int:
if m == 1 or n == 1:
return 1
matrix = [ [1 for j in range(n)] for i in range(m)]

for i in range(1, m):
for j in range(1, n):
max_above = 0
max_left = 1
if i > 0:
max_above = matrix[i-1][j]
if j > 0:
max_left = matrix[i][j-1]
matrix[i][j] = max_above + max_left

m = matrix[i][j]
return m

class Solution:
def uniquePaths(self, m: int, n: int) -> int:
matrix = [ * n for _ in range(m)]

for i in range(1, m):
for j in range(1, n):
matrix[i][j] = matrix[i - 1][j] + matrix[i][j - 1]

return matrix[-1][-1]