Problem

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]]

Note

题目为求从1到n的自然数里取k个数的所有组合全集。使用递归的模板，建立helper函数。
模板如下：

void helper(range S, target T, start A, tempArray B) {
    if (B met T or other requirement) {
        res.add(B);
        return;
    }
    for (int i starts from A in S) {
        tempArray C = new tempArray (B);
        C.add(i);
        helper(S, T-i, i+1, C);
    }
} 

也可以不建立新的tempArray C，而是递归调用helper之后删去B中最后一个元素：

void helper(range S, target T, start A, tempArray B) {
    if (B met T or other requirement) {
        res.add(B);
        return;
    }
    for (int i starts from A in S) {
        B.add(i);
        helper(S, T-i, i+1, C);
        B.remove(B.size()-1);
    }
}

Solution

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