Combination Sum II

描述

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

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

Note:

  • All numbers (including target) will be positive integers.
  • Elements in a combination (a1,a2,…,aka_1, a_2, …, a_ka​1​​,a​2​​,…,a​k​​) must be in non-descending order. (ie, a1>a2>…>aka_1 > a_2 > … > a_ka​1​​>a​2​​>…>a​k​​).
  • The solution set must not contain duplicate combinations.
    For example, given candidate set 10,1,2,7,6,1,5 and target 8, A solution set is: 
  1. [1, 7] 
  2. [1, 2, 5] 
  3. [2, 6] 
  4. [1, 1, 6]

分析

无

代码

  1. // Combination Sum II
  2. // 时间复杂度O(n!)，空间复杂度O(n)
  3. public class Solution {
  4.     public List<List<Integer>> combinationSum2(int[] nums, int target) {
  5.         Arrays.sort(nums); // 跟第 50 行配合，
  6.         // 确保每个元素最多只用一次
  7.         List<List<Integer>> result = new ArrayList<>();
  8.         List<Integer> path = new ArrayList<>();
  9.         dfs(nums, path, result, target, 0);
  10.         return result;
  11.     }
  12.     // 使用nums[start, nums.size())之间的元素，能找到的所有可行解
  13.     private static void dfs(int[] nums, List<Integer> path,
  14.                             List<List<Integer>> result, int gap, int start) {
  15.         if (gap == 0) {  //  找到一个合法解
  16.             result.add(new ArrayList<>(path));
  17.             return;
  18.         }
  20.         int previous = -1;
  21.         for (int i = start; i < nums.length; i++) {
  22.             // 如果上一轮循环已经使用了nums[i]，则本次循环就不能再选nums[i]，
  23.             // 确保nums[i]最多只用一次
  24.             if (previous == nums[i]) continue;
  26.             if (gap < nums[i]) return;  // 剪枝
  28.             previous = nums[i];
  30.             path.add(nums[i]);
  31.             dfs(nums, path, result, gap - nums[i], i + 1);
  32.             path.remove(path.size() - 1);  // 恢复环境
  33.         }
  34.     }
  35. }

相关题目

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/dfs/combination-sum-ii.html