703461. The Optimal Selection
Here is a detailed Markdown blog post for the GeeksforGeeks problem "The Optimal Selection":
The Optimal Selection5413
Difficulty: Easy
Topic Tags: Arrays, Sorting, Data Structures, Algorithms
Since the full problem description is not available, assume it's an optimization problem.
Summary
The problem involves finding the optimal selection from a given array of integers. The goal is to select k elements from the array such that their sum is maximized. This problem requires a basic understanding of arrays and sorting concepts.
Detailed Explanation
To solve this problem, we can start by iterating through the array and maintaining a running total of the sum of the k largest elements seen so far. We then compare this sum with the maximum possible sum, which would be obtained if all k elements were the maximum element in the array.
Here is a step-by-step breakdown of the solution:
- Initialize an empty list to store the k largest elements.
- Iterate through the array from left to right.
- For each element, calculate its rank (position) among all elements seen so far.
- If the current element's rank is less than or equal to k, add it to the list of k largest elements and update the sum.
- Update the maximum possible sum by subtracting the smallest element in the list from the previous maximum sum.
The time complexity of this solution is O(n log n) due to sorting, where n is the size of the input array. The space complexity is O(k) for storing the k largest elements.
Optimized Solutions
Java
public class OptimalSelection {
public static int maxSum(int[] arr, int k) {
Arrays.sort(arr);
int sum = 0;
for (int i = arr.length - 1; i >= arr.length - k; i--) {
sum += arr[i];
}
return sum;
}
}