2x2 grid
Input
rows=2, cols=2
Output
2
Two paths: right->down or down->right.
Full lesson preview
Count paths in a grid recursively
Count distinct paths from top-left to bottom-right moving only right or down using recursion with memoization.
Python practice9 minRecursion & BacktrackingBeginnerLast updated March 27, 2026
Problem statement
Given two positive integers rows and cols representing the number of rows and columns in a grid, count how many unique paths exist from the top-left corner to the bottom-right corner if you may only move right or down at each step. Implement the solution using recursion and memoization (to avoid exponential time).
Task
Practice recursive problem solving and memoization by counting grid paths.
Examples
Input format
Two integers: rows and cols (both >= 1).
Output format
An integer: the number of distinct paths.
Constraints
1 <= rows, cols <= 20 (answers fit in a 64-bit integer for these ranges).
Samples
Sample 1
Input
rows=3, cols=3
Output
6
Paths count equals binomial coefficient C(4,2) = 6.