Unique Paths
You are given two integers m and n, representing an m x n grid.
A robot is initially located at the top-left corner of the grid and wants to reach the bottom-right corner.
The robot can only move:
- Right
- Down
Return the number of possible unique paths the robot can take to reach the bottom-right corner.
Example 1
Input
m = 3 n = 7
Output
28
Explanation
The robot has to make:
- 2 moves down
- 6 moves right
There are 28 different ways to arrange these moves.
Therefore, the answer is 28.
Example 2
Input
m = 3 n = 2
Output
3
Explanation
The possible paths are:
Right → Down → Down
Down → Right → Down
Down → Down → Right
Therefore, there are 3 unique paths.
Constraints
Hints:
Hint 1
Define dp[i][j] as the number of unique ways to reach cell (i, j).
Hint 2
Each cell can be reached from:
- The cell above it
- The cell to its left
Therefore:
dp[i][j] = dp[i-1][j] + dp[i][j-1]
Author & Technical Reviewer
Technically reviewed by: ExamAdda Technical Review Team
Technical Reviewers, ExamAdda
Software engineers at ExamAdda who check every article's definitions, complexity claims and code examples before and after publishing.
Published
Aug 26, 2026
Last updated
Aug 26, 2026
Content Verification Methodology
Definitions and complexity claims were checked against authoritative computer-science references. Code examples were compiled and tested with standard, boundary and edge-case inputs.
Expected Output