问题

该文章已迁移至个人博客【比特飞】，单击链接 https://www.byteflying.com/archives/3666 访问。

给定一个数组 candidates 和一个目标数 target ，找出 candidates 中所有可以使数字和为 target 的组合。

candidates 中的每个数字在每个组合中只能使用一次。

说明：

• 所有数字（包括目标数）都是正整数。
• 解集不能包含重复的组合。

输入: candidates = [10,1,2,7,6,1,5],

target = 8,

所求解集为: [ [1, 7], [1, 2, 5], [2, 6], [1, 1, 6] ]

输入: candidates = [2,5,2,1,2],

target = 5,

所求解集为: [ [1,2,2], [5] ]

Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sums to target.

Each number in candidates may only be used once in the combination.

Note:

• All numbers (including target) will be positive integers.
• The solution set must not contain duplicate combinations.

Input: candidates = [10,1,2,7,6,1,5],

target = 8,

A solution set is: [ [1, 7], [1, 2, 5], [2, 6], [1, 1, 6] ]

Input: candidates = [2,5,2,1,2],

target = 5,

A solution set is: [ [1,2,2], [5] ]

示例

该文章已迁移至个人博客【比特飞】，单击链接 https://www.byteflying.com/archives/3666 访问。

public class Program {

    public static void Main(string[] args) {
        var candidates = new int[] { 10, 1, 2, 7, 6, 1, 5 };
        var target = 8;

        var res = CombinationSum2(candidates, target);
        ShowArray(res);

        Console.ReadKey();
    }

    private static void ShowArray(IList<IList<int>> candidates) {
        foreach(var candi in candidates) {
            foreach(var num in candi) {
                Console.Write($"{num} ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }

    public static IList<IList<int>> CombinationSum2(int[] candidates, int target) {
        var res = new List<IList<int>>();
        if(candidates.Length == 1) {
            if(candidates[0] == target) {
                res.Add(candidates);
                return res;
            }
        }
        var candi = new List<int>();
        Array.Sort(candidates);
        Combination(candidates, -1, target, candi, ref res);
        return res;
    }

    public static void Combination(int[] candidates,
                                   int start,
                                   int target,
                                   List<int> candi,
                                   ref List<IList<int>> res) {
        if(target < 0) return;
        if(target == 0) {
            if(!res.Any(r => r.SequenceEqual(candi))) {
                res.Add(candi);
            }
            return;
        }
        for(var i = start + 1; i < candidates.Length; i++) {
            candi.Add(candidates[i]);
            Combination(candidates, i, target - candidates[i], candi.ToList(), ref res);
            candi.RemoveAt(candi.Count - 1);
            while(i < candidates.Length - 1 && candidates[i] == candidates[i + 1]) i++;
        }
    }

}

以上给出1种算法实现，以下是这个案例的输出结果：

该文章已迁移至个人博客【比特飞】，单击链接 https://www.byteflying.com/archives/3666 访问。

1 2 5
1 7
1 1 6
2 6

分析

显而易见， 以上算法的时间复杂度为： $O(n^2)$ 。