62. Unique Paths

Updated: 2023-04-13
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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[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:

LeetCode 62. Unique Paths

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 = [[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]