62. Unique Paths
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There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). 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:
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 = [[1] * 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]
