Combinations

Question

• leetcode: Combinations | LeetCode OJ
• lintcode: (152) Combinations

Problem Statement

Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.

Example

For example, If n = 4 and k = 2, a solution is: [[2,4],[3,4],[2,3],[1,2],[1,3],[1,4]]

题解

套用 Permutations 模板。

Java

public class Solution {
    public List<List<Integer>> combine(int n, int k) {
        assert(n >= 1 && n >= k && k >= 1);

        List<List<Integer>> result = new ArrayList<List<Integer>>();
        List<Integer> list = new ArrayList<Integer>();
        dfs(n, k, 1, list, result);

        return result;
    }

    private void dfs(int n, int k, int pos, List<Integer> list,
                     List<List<Integer>> result) {

        if (list.size() == k) {
            result.add(new ArrayList<Integer>(list));
            return;
        }
        for (int i = pos; i <= n; i++) {
            list.add(i);
            dfs(n, k, i + 1, list, result);
            list.remove(list.size() - 1);
        }
    }
}

源码分析

注意递归helper(n, k, i + 1, list, result);中的i + 1，不是pos + 1。

复杂度分析

状态数 $C_n^2$, 每组解有两个元素，故时间复杂度应为 $O(n^2)$. list 只保留最多两个元素，空间复杂度 $O(1)$.