Question

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

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

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);
    }
  }
}

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();
    }
  }
};

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
}

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();
    }
  }
}