878166. Split array into minimum subsets
Split array into minimum subsets
Slug: split-array-into-minimum-subsets
Difficulty: Easy
Id: 878166
Topic Tags: Sorting, Arrays, Hash
Company Tags: None
Summary
Given an integer array arr, the goal is to divide it into a minimum number of subsets such that the sum of each subset is equal. The array can be divided in any way as long as all elements are included in one of the subsets.
Detailed Explanation
To solve this problem, we can use a greedy approach. First, sort the array in descending order based on its values. Then, create a subset by adding elements from the sorted array until the sum of the subset is equal to or greater than the average sum of all subsets.
Here's the step-by-step breakdown:
- Sort the array
arrin descending order. - Initialize an empty list
subsetsto store the minimum number of subsets. - Calculate the total sum
total_sumof the array. - Calculate the target sum for each subset
target_sumby dividing the total sum by the number of subsets. - Iterate over the sorted array:
- If the current element is less than or equal to the target sum, add it to the current subset and update the target sum.
- If the current element is greater than the target sum, start a new subset with this element as its first element and reset the target sum.
- Add the last subset to the
subsetslist.
The time complexity of this algorithm is O(n log n) due to the sorting step, where n is the number of elements in the array. The space complexity is O(1), as we only use a constant amount of space to store the subsets and other variables.
Optimized Solutions
Java
public class Solution {
public List<List<Integer>> splitArray(int[] arr) {
Arrays.sort(arr);
int totalSum = 0;
for (int num : arr) {
totalSum += num;
}
int targetSum = totalSum / arr.length;
List<List<Integer>> subsets = new ArrayList<>();
int currentSum = 0;
List<Integer> subset = new ArrayList<>();
for (int num : arr) {
if (currentSum + num <= targetSum) {
currentSum += num;
subset.add(num);
} else {
subsets.add(subset);
subset = new ArrayList<>();
currentSum = num;
subset.add(num);
}
}
subsets.add(subset);
return subsets;
}
}