Problem #77: Combinations

Intuition & Strategy Breakdown

Use backtracking to generate combinations of K numbers from 1 to N, maintaining current combination list and starting candidate number.

Python Solution

def combine(n, k):
    res = []
    def backtrack(start, path):
        if len(path) == k:
            res.append(path[:])
            return
        
        for i in range(start, n + 1):
            path.append(i)
            backtrack(i + 1, path)
            path.pop()
            
    backtrack(1, [])
    return res

Java Solution

class Solution {
    public List> combine(int n, int k) {
        List> res = new ArrayList<>();
        backtrack(1, n, k, new ArrayList<>(), res);
        return res;
    }
    
    private void backtrack(int start, int n, int k, List path, List> res) {
        if (path.size() == k) {
            res.add(new ArrayList<>(path));
            return;
        }
        
        for (int i = start; i <= n; i++) {
            path.add(i);
            backtrack(i + 1, n, k, path, res);
            path.remove(path.size() - 1);
        }
    }
}