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组合总和

Combination Sum

专题
Algorithmic Programming / 算法编程
难度
L3
来源
Citadel

题目详情

问题:组合总和

考察:数组、递归

来源:Citadel

链接:https://www.jointaro.com/interviews/questions/combination-sum/

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

The test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

 

Example 1:

Input: candidates = [2,3,6,7], target = 7
Output: [[2,2,3],[7]]
Explanation:
2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.
7 is a candidate, and 7 = 7.
These are the only two combinations.

Example 2:

Input: candidates = [2,3,5], target = 8
Output: [[2,2,2,2],[2,3,3],[3,5]]

Example 3:

Input: candidates = [2], target = 1
Output: []

 

Constraints:

  • 1 <= candidates.length <= 30
  • 2 <= candidates[i] <= 40
  • All elements of candidates are distinct.
  • 1 <= target <= 40
解析

思路:先排序候选数,然后回溯枚举。每次从当前下标及之后选择数字,选择后仍允许使用当前数字;若剩余目标为 0 就记录方案,若候选数超过剩余目标就剪枝。

复杂度:复杂度取决于解空间,最坏指数级;递归深度 O(target / min(candidates))。