LeetCode 77. 组合 Combinations

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8-4 组合问题 Combinations

题目: LeetCode 77. 组合

给定两个整数 n 和 k，返回 1 … n 中所有可能的 k 个数的组合。

示例:

输入: n = 4, k = 2
输出:
[
[2,4],
[3,4],
[2,3],
[1,2],
[1,3],
[1,4],
]

import java.util.List;
import java.util.ArrayList;
import java.util.LinkedList;

/// 77. Combinations
/// https://leetcode.com/problems/combinations/description/
/// 时间复杂度: O(n^k)
/// 空间复杂度: O(k)
public class Solution {

    private ArrayList<List<Integer>> res;

    public List<List<Integer>> combine(int n, int k) {

        res = new ArrayList<List<Integer>>();
        if(n <= 0 || k <= 0 || k > n)
            return res;

        LinkedList<Integer> c = new LinkedList<Integer>();
        generateCombinations(n, k, 1, c);

        return res;
    }

    // 求解C(n,k), 当前已经找到的组合存储在c中, 需要从start开始搜索新的元素
    private void generateCombinations(int n, int k, int start, LinkedList<Integer> c){

        if(c.size() == k){
            res.add((List<Integer>)c.clone());
            return;
        }

        for(int i = start ; i <= n ; i ++){
            c.addLast(i);
            generateCombinations(n, k, i + 1, c);
            c.removeLast();
        }

        return;
    }

    private static void printList(List<Integer> list){
        for(Integer e: list)
            System.out.print(e + " ");
        System.out.println();
    }

    public static void main(String[] args) {

        List<List<Integer>> res = (new Solution()).combine(4, 2);
        for(List<Integer> list: res)
            printList(list);
    }
}

import java.util.List;
import java.util.ArrayList;
import java.util.LinkedList;

/// 77. Combinations
/// https://leetcode.com/problems/combinations/description/
/// 时间复杂度: O(n^k)
/// 空间复杂度: O(k)
public class Solution {

    private ArrayList<List<Integer>> res;

    public List<List<Integer>> combine(int n, int k) {

        res = new ArrayList<List<Integer>>();
        if(n <= 0 || k <= 0 || k > n)
            return res;

        LinkedList<Integer> c = new LinkedList<Integer>();
        generateCombinations(n, k, 1, c);

        return res;
    }

    // 求解C(n,k), 当前已经找到的组合存储在c中, 需要从start开始搜索新的元素
    private void generateCombinations(int n, int k, int start, LinkedList<Integer> c){

        if(c.size() == k){
            res.add((List<Integer>)c.clone());
            return;
        }

        // 还有k - c.size()个空位, 所以, [i...n] 中至少要有 k - c.size() 个元素
        // i最多为 n - (k - c.size()) + 1
        for(int i = start ; i <= n - (k - c.size()) + 1 ; i ++){
            c.addLast(i);
            generateCombinations(n, k, i + 1, c);
            c.removeLast();
        }

        return;
    }

    private static void printList(List<Integer> list){
        for(Integer e: list)
            System.out.print(e + " ");
        System.out.println();
    }

    public static void main(String[] args) {

        List<List<Integer>> res = (new Solution()).combine(4, 2);
        for(List<Integer> list: res)
            printList(list);
    }
}