How to Generate All k‑Number Combinations from 1 to n in Java (with Interview Tips)

Interview Communication Tips

Technical candidates often fail interviews due to ineffective self‑presentation. Common issues and corrective actions:

Over‑explaining: Avoid teaching the interviewer; instead, frame your experience as a solution to the problem they care about.

Lack of structured storytelling: Connect projects with a clear narrative that highlights strategic thinking and impact.

Nervousness: Practice speaking in meetings and conduct regular mock interviews to improve composure under pressure.

Inappropriate attitude: Maintain confidence without arrogance and avoid excessive timidity.

Insufficient role knowledge: Research the target position and tailor answers to match the employer’s requirements.

Problem: Generate All k‑Element Combinations

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n]. The order of the combinations does not matter.

Example 1

Input: n = 4, k = 2
Output:
[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4]
]

Example 2

Input: n = 1, k = 1
Output: [[1]]

Solution Idea

Use depth‑first search (backtracking) with pruning. At each recursion level, iterate the next candidate number from start up to n - k + 1 to guarantee enough remaining numbers for a complete combination. When k reaches zero, add the current list to the result.

Java Implementation

class Solution {
    private List<List<Integer>> ans = new ArrayList<>();

    public List<List<Integer>> combine(int n, int k) {
        backtrack(n, k, 1, new ArrayList<>());
        return ans;
    }

    private void backtrack(int n, int k, int start, List<Integer> path) {
        if (k == 0) {
            ans.add(new ArrayList<>(path));
            return;
        }
        for (int i = start; i <= n - k + 1; i++) {
            path.add(i);
            backtrack(n, k - 1, i + 1, path);
            path.remove(path.size() - 1);
        }
    }
}