077 Combinations

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

Example：

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

解释下题目：

说白了就是加了点条件的全排列罢了。

1. 方法1

实际耗时：51ms

public static List> combine(int n, int k) {
        List> combs = new ArrayList<>();
        combine(combs, new ArrayList(), 1, n, k);
        return combs;
    }

    public static void combine(List> combs, List comb, int start, int n, int k) {
        if (k == 0) {
            combs.add(new ArrayList(comb));
            return;
        }
        for (int i = start; i <= n; i++) {
            comb.add(i);
            combine(combs, comb, i + 1, n, k - 1);
            comb.remove(comb.size() - 1);
        }
    }

  思路很简单。就是全排列的思路。深度优先的算法

时间复杂度O(n(n-1)(n-2)......(n-k))

空间复杂度O(n(n-1)(n-2)......(n-k))

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