LeetCode | 0039. Combination Sum组合总和【Python】

比眉伴天荒 2023-07-12 05:21 83阅读 0赞

> LeetCode 0039. Combination Sum组合总和【Medium】【Python】【回溯】

### Problem ###

[LeetCode][]

Given a **set** of candidate numbers (`candidates`) **(without duplicates)** and a target number (`target`), find all unique combinations in `candidates` where the candidate numbers sums to `target`.

The **same** repeated number may be chosen from `candidates` unlimited number of times.

**Note:**

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

**Example 1:**

Input: candidates = [2,3,6,7], target = 7,
    A solution set is:
    [
      [7],
      [2,2,3]
    ]

**Example 2:**

Input: candidates = [2,3,5], target = 8,
    A solution set is:
    [
      [2,2,2,2],
      [2,3,3],
      [3,5]
    ]

### 问题 ###

[力扣][Link 1]

给定一个**无重复元素**的数组 `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` 中的数字可以无限制重复被选取。

说明：

*  所有数字（包括 `target`）都是正整数。
 *  解集不能包含重复的组合。

**示例 1:**

输入: candidates = [2,3,6,7], target = 7,
    所求解集为:
    [
      [7],
      [2,2,3]
    ]

**示例 2:**

输入: candidates = [2,3,5], target = 8,
    所求解集为:
    [
      [2,2,2,2],
      [2,3,3],
      [3,5]
    ]

### 思路 ###

**回溯模板**

res = []
    def backtrack(路径, 选择列表):
        if 满足结束条件:
            res.append(路径)
            return
    
    for 选择 in 选择列表:
        做选择
        backtrack(路径, 选择列表)
        撤销选择
    
    作者：jeromememory
    链接：https://leetcode-cn.com/problems/combination-sum/solution/hui-su-suan-fa-tao-mo-ban-ji-ke-by-jeromememory/
    来源：力扣（LeetCode）
    著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。

##### Python3代码 #####

class Solution:
        def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
            n = len(candidates)
            if n == 0:
                return []
            
            # accelerate 剪枝提速，非必需
            candidates.sort()
    
            path, res = [], []
            self.dfs(candidates, 0, n, path, res, target)
            return res
        
        def dfs(self, candidates, start, n, path, res, target):
            # 1.valid result 递归终止情况
            if target == 0:
                res.append(path[:])
                return
            
            for i in range(start, n):
                tmp = target - candidates[i]
                # 3.pruning 剪枝
                if tmp < 0:
                    break
                # 2.backtrack and update 回溯以及更新 path
                path.append(candidates[i])
                self.dfs(candidates, i, n, path, res, tmp)
                path.pop()

### 代码地址 ###

[GitHub链接][GitHub]

### 参考 ###

[回溯算法 + 剪枝][Link 2]

[LeetCode]: https://leetcode.com/problems/combination-sum/description/
[Link 1]: https://leetcode-cn.com/problems/combination-sum/
[GitHub]: https://github.com/Wonz5130/LeetCode-Solutions/blob/master/solutions/0039-Combination-Sum/0039.py
[Link 2]: https://leetcode-cn.com/problems/combination-sum/solution/hui-su-suan-fa-jian-zhi-python-dai-ma-java-dai-m-2/