709863. Smallest Subset with Greater Sum
Easy
Here is the detailed Markdown blog post for the problem "Smallest Subset with Greater Sum":
Smallest Subset with Greater Sum
Slug: smallest-subset-with-greater-sum
Difficulty: Easy
Id: 709863
Topic Tags: Arrays, Greedy, Sorting, Data Structures, Algorithms
Company Tags: None
Summary
Given a set of integers, find the smallest subset whose sum is greater than or equal to a given target sum. This problem involves finding the minimum-sized subset that meets a certain condition.
Detailed Explanation
To solve this problem, we can use a greedy algorithm. The idea is to keep adding elements to our subset as long as their sum is less than the target sum. When we reach the target sum or exceed it, we stop and return the current subset.
Here's a step-by-step breakdown of the solution:
- Initialize an empty subset
resultand a variablecurrent_sumset to 0. - Sort the input array in non-decreasing order.
- Iterate through the sorted array. For each element, check if adding it to
resultwould exceed the target sum. If not, add it toresultand updatecurrent_sum. - When we reach an element that would exceed the target sum or when we reach the end of the array, return
result.
Time complexity: O(n log n) due to sorting Space complexity: O(1) since we only use a few extra variables
Optimized Solutions
Java
public static List<Integer> smallestSubset(int[] arr, int targetSum) {
Arrays.sort(arr);
List<Integer> result = new ArrayList<>();
int currentSum = 0;
for (int num : arr) {
if (currentSum + num > targetSum) break;
result.add(num);
currentSum += num;
}
return result;
}