leetcode-698. Partition to K Equal Sum Subsets

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本文探讨了如何将一个整数数组等分为K个子集，每个子集的和相等的问题，并提供了一种递归解决方案。该问题类似于背包问题，通过递归方法实现子集划分，确保满足题目要求。

一、问题描述

Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal.

Example 1:

Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
Output: True
Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.

Note:

1 <= k <= len(nums) <= 16.
0 < nums[i] < 10000.

二、思路分析

类似于背包问题

三、代码

class Solution {
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        for(int num:nums)sum+=num;
        if(k <= 0 || sum%k != 0)return false;
        vector<int> visited(nums.size(), 0);
        return rec(nums, visited, 0, k, 0, 0, sum/k);
    }

    bool rec(vector<int>& nums, vector<int>& visited, int start_index, int k, int cur_sum, int cur_num, int target){
        if(k==1)return true;
        if(cur_sum > target) return false;
        if(cur_sum == target && cur_num >0 )return rec(nums, visited, 0, k-1, 0, 0, target);
        for(int i = start_index; i<nums.size(); i++){
            if(!visited[i]){
                visited[i] = 1;
                if(rec(nums, visited, i+1, k, cur_sum + nums[i], cur_num++, target))return true;
                visited[i] = 0;
            }
        }
        return false;
    }
};