0062.Unique Paths

Link: 62. Unique Paths - Medium
Track: Amazon Tag

Question

Restate

Edge Case

• m = 1, n = 1, return 1

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Method 1 - DP
Method 2

Method 1 - DP

Approach

Define dp[r][c] = number of ways to reach cell (r,c) from (0,0).
To arrive at (r,c), the last move must be:

• from top (r-1,c) (move down), or

• from left (r,c-1) (move right)

• Q: Why start from 1?

• Row 0 and col 0 are base cases (only 1 way), so we start filling from (1,1).

Complexity

• Time Complexity: O($m\ast n$)
• Space Complexity: O($m\ast n$)

Code

class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        rows, cols = m, n
        dp = [[1] * cols for _ in range(rows)]
 
        for row in range(1, rows):
            for col in range(1, cols):
                print(row, col)
                dp[row][col] = dp[row - 1][col] + dp[row][col - 1]
 
        return dp[rows-1][cols-1]

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History

• Feb-19-2026 Peeked