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🔥Unique Paths: Grid Combinatorics DPMedium
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MediumDynamic Programming•Acceptance: 64.1%

Unique Paths: Grid Combinatorics DP

Targeted in FAANG & Tech OA:AmazonGoogleSwiggy
Real-World Engineering Context
Used in routing layout ASIC chip physical design, Manhattan distance path routing, and combinatorics probability distributions.
There is a robot on an `m x n` grid. The robot is initially located at the top-left corner (`grid[0][0]`). The robot tries to move to the bottom-right corner (`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.

Sample Test Cases

Input: [3,7]
Expected: 28
Input: [3,2]
Expected: 3
Input: [1,1]
Expected: 1

Constraints

  • 1 <= m, n <= 100
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