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Unique Paths
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01 · 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.
02 · Examples
Example 01
Input
m = 3, n = 7
Output
28
The robot must make exactly 2 moves down and 6 moves right (in any order), giving C(8,2) = 28 unique paths.
Example 02
Input
m = 3, n = 2
Output
3
Three paths: RDD, DRD, DDR (where R = right, D = down).
03 · Constraints
- 011 <= m, n <= 100
04 · Optimal complexity
- Time
- O(m * n)
- Space
- O(n)
05 · Two ways to work on it
Practice it alone or rehearse it as an interview.
Practice Mode gives you an editor and test runs, nothing else. AI Interview Mode puts a voice interviewer on the other side, adds a clock, and ends with a scored summary of the round.