Unique Paths

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Problem

A robot sits at the top-left corner of an m x n grid and can only move right or down at each step. Return the number of distinct paths from the top-left corner to the bottom-right corner.

Examples

Example 1

Input:m = 3, n = 7

Output:28

Example 2

Input:m = 3, n = 2

Output:3

Constraints

1 <= m, n <= 100

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How to approach it: the 2-D Dynamic Programming pattern

The same DP idea as 1-D, but the state depends on two indices — often two positions in a grid, or a position in each of two sequences being compared.

Look for this pattern when

You're comparing two sequences (finding a longest common subsequence, edit distance).
You're computing paths or optimal values across a 2-D grid.

Read the full 2-D Dynamic Programming guide →

Video walkthroughs

Original problem on LeetCode ↗