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Unique Paths

Dynamic Programming·Medium

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 the robot can take to reach the bottom-right corner.

Examples

Input: m = 3, n = 7

Output: 28

Input: m = 3, n = 2

Output: 3

Constraints

1 <= m, n <= 100
The answer is guaranteed to be less than or equal to 2 * 10^9.

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Tests

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Passed32 ms

First attempt — retry to track metric movement here.

Your approach

Pattern:Dynamic Programming
Time:O(N)
Space:O(1)

Complete approach — pattern and complexity both named.

Coach

What you got right

You correctly matched the sorted input requirement and implemented a linear-time scan using two pointers.

Where it diverged

No divergence detected. The code correctly aligns with the stated approach.

Next attempt: focus on

Try solving related sliding window problems to build familiarity with two-pointer variants.

Signals

No signals fired — clean run, you stayed in flow.