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剑指 Offer II 081. 允许重复选择元素的组合

题目描述

给定一个无重复元素的正整数数组 candidates 和一个正整数 target ，找出 candidates 中所有可以使数字和为目标数 target 的唯一组合。

candidates 中的数字可以无限制重复被选取。如果至少一个所选数字数量不同，则两种组合是唯一的。 

对于给定的输入，保证和为 target 的唯一组合数少于 150 个。

 

示例 1：

输入: candidates = [2,3,6,7], target = 7
输出: [[7],[2,2,3]]

示例 2：

输入: candidates = [2,3,5], target = 8
输出: [[2,2,2,2],[2,3,3],[3,5]]

示例 3：

输入: candidates = [2], target = 1
输出: []

示例 4：

输入: candidates = [1], target = 1
输出: [[1]]

示例 5：

输入: candidates = [1], target = 2
输出: [[1,1]]

 

提示：

  • 1 <= candidates.length <= 30
  • 1 <= candidates[i] <= 200
  • candidate 中的每个元素都是独一无二的。
  • 1 <= target <= 500

 

注意：本题与主站 39 题相同： https://leetcode.cn/problems/combination-sum/

解法

方法一

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class Solution:
    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
        ans = []
        n = len(candidates)

        def dfs(s, u, t):
            if s == target:
                ans.append(t.copy())
                return
            if s > target:
                return
            for i in range(u, n):
                c = candidates[i]
                t.append(c)
                dfs(s + c, i, t)
                t.pop()

        dfs(0, 0, [])
        return ans

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class Solution {
    private List<List<Integer>> ans;
    private int target;
    private int[] candidates;

    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        ans = new ArrayList<>();
        this.target = target;
        this.candidates = candidates;
        dfs(0, 0, new ArrayList<>());
        return ans;
    }

    private void dfs(int s, int u, List<Integer> t) {
        if (s == target) {
            ans.add(new ArrayList<>(t));
            return;
        }
        if (s > target) {
            return;
        }
        for (int i = u; i < candidates.length; ++i) {
            int c = candidates[i];
            t.add(c);
            dfs(s + c, i, t);
            t.remove(t.size() - 1);
        }
    }
}

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class Solution {
public:
    vector<vector<int>> ans;
    vector<int> candidates;
    int target;

    vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
        this->candidates = candidates;
        this->target = target;
        vector<int> t;
        dfs(0, 0, t);
        return ans;
    }

    void dfs(int s, int u, vector<int>& t) {
        if (s == target) {
            ans.push_back(t);
            return;
        }
        if (s > target) return;
        for (int i = u; i < candidates.size(); ++i) {
            int c = candidates[i];
            t.push_back(c);
            dfs(s + c, i, t);
            t.pop_back();
        }
    }
};

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func combinationSum(candidates []int, target int) [][]int {
    var ans [][]int

    var dfs func(s, u int, t []int)
    dfs = func(s, u int, t []int) {
        if s == target {
            ans = append(ans, append([]int(nil), t...))
            return
        }
        if s > target {
            return
        }
        for i := u; i < len(candidates); i++ {
            c := candidates[i]
            t = append(t, c)
            dfs(s+c, i, t)
            t = t[:len(t)-1]
        }
    }

    var t []int
    dfs(0, 0, t)
    return ans
}

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using System;
using System.Collections.Generic;
using System.Linq;

public class Solution
{
    public IList<IList<int>> CombinationSum(int[] candidates, int target)
    {
        Array.Sort(candidates);
        candidates = candidates.Distinct().ToArray();

        var paths = new List<int>[target + 1];
        paths[0] = new List<int>();
        foreach (var c in candidates)
        {
            for (var j = c; j <= target; ++j)
            {
                if (paths[j - c] != null)
                {
                    if (paths[j] == null)
                    {
                        paths[j] = new List<int>();
                    }
                    paths[j].Add(c);
                }
            }
        }

        var results = new List<IList<int>>();
        if (paths[target] != null) GenerateResults(results, new Stack<int>(), paths, target, paths[target].Count - 1);
        return results;
    }

    private void GenerateResults(IList<IList<int>> results, Stack<int> result, List<int>[] paths, int remaining,
        int maxIndex)
    {
        if (remaining == 0)
        {
            results.Add(new List<int>(result));
            return;
        }
        for (var i = maxIndex; i >= 0; --i)
        {
            var value = paths[remaining][i];
            result.Push(value);
            var nextMaxIndex = paths[remaining - value].BinarySearch(value);
            if (nextMaxIndex < 0)
            {
                nextMaxIndex = ~nextMaxIndex - 1;
            }
            GenerateResults(results, result, paths, remaining - value, nextMaxIndex);
            result.Pop();
        }
    }
}

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