Combinations

Problem

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n].

Examples

The brute-force approach

Generate all possible subsets of size k using nested loops. This only works for fixed k — you'd need k nested loops.

# For k=2 specifically:
for i in range(1, n+1):
    for j in range(i+1, n+1):
        result.append([i, j])

Requires k nested loops — only works for a fixed known k. Backtracking handles any k with a single recursive function.

Spotting the pattern

This is a Backtracking problem. The key question to ask yourself:

Why does starting each recursive call from start+1 (not 1) prevent duplicate combinations?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.