The thief problem in Java

Given an array arr[] and an integer K, find the maximum possible sum of any K elements.

Examples:

Input: arr[] = {3, 7, 2, 5, 12, 30}, K = 3
Output: 49
Explanation: Pick 30, 12, and 7. Sum = 30 + 12 + 7 = 49

Naive Approach

Follow these steps to find the maximum sum of K items using the naive approach:

• Initialize a variable sum to 0.
• Traverse the array to find the largest element.
• Add the largest element to the sum.
• Repeat the process K times to select the K largest elements.
• Return the total sum.

Maximum sum of 3 items: 49

• Time Complexity: O(N × K) where N is the number of elements in the array and K is the number of items to be selected.
• Space Complexity: O(1) since no extra space is used.

Note: The naive approach is inefficient for large inputs.

Optimized Approach

Follow these steps to maximize the sum of K items:

• Sort the array in descending order so the largest values come first.
• Pick the first K elements from the sorted array.
• Compute and return the sum of these K elements.

Maximum sum of 3 items: 49

• Time Complexity: O(N log N) where N is the number of elements in the array.
• Space Complexity: O(1) since no extra space is used (ignoring the internal space used by sorting).