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Solve Minimize Array Maximum with Bit Operations using Java Language

Solve Minimize Array Maximum with Bit Operations using Java to enhance your skills with java coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Minimize Array Maximum with Bit Operations

Difficulty : Hard

Categories :

  • Bit manipulation

You are given an array of non-negative integers nums. Your task is to minimize the maximum value in the array by performing at most k operations, where in each operation you can:

  • Choose any element in the array
  • Perform any number of right shifts (>>) on the chosen element
  • Each right shift divides the number by 2 and rounds down

Return the minimum possible maximum value in the array after at most k operations.

Constraints:

  • 1 ≤ nums.length ≤ 10^5
  • 0 ≤ nums[i] ≤ 10^9
  • 0 ≤ k ≤ 15
  • Solution must use bit manipulation for efficiency

Examples:

Input: nums = [3,5,2,6], k = 2
Output: 2
Explanation:
Operation 1: Right shift 6 >> 1 = 3, array becomes [3,5,2,3]
Operation 2: Right shift 5 >> 2 = 1, array becomes [3,1,2,3]
Maximum value is now 3, which is minimum possible
Input: nums = [10,8,6,12], k = 1
Output: 8
Explanation:
Optimal operation: Right shift 12 >> 1 = 6
Array becomes [10,8,6,6], maximum is 8

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Choose from the following categories

Strings A sequence of characters used to represent text, with problems focused on manipulation, searching, and pattern matching.

Arrays A collection of elements stored in contiguous memory locations, allowing efficient random access and manipulation.

Linked Lists A linear data structure where each element (node) points to the next, offering dynamic memory allocation and efficient insertions/deletions.

Trees A hierarchical data structure with nodes connected by edges, used in applications like databases, file systems, and parsing.

Graphs A collection of nodes (vertices) connected by edges, representing relationships, widely used in networking, routing, and social networks.

Dynamic Programming An optimization technique that solves problems by breaking them into overlapping subproblems and storing their results.

Backtracking A problem-solving method that explores all possibilities recursively, backtracking when a solution is not feasible.

Sorting Algorithms Techniques for arranging elements in a specific order, such as quicksort, mergesort, and bubble sort, essential for data organization.

Searching Algorithms Methods for finding elements in a dataset, such as binary search, linear search, and graph traversal techniques.

Mathematics A field of study involving numbers, calculations, and logical reasoning, forming the foundation for algorithms and problem-solving.

Recursion A programming technique where a function calls itself to solve smaller instances of the same problem, often used in divide-and-conquer approaches.

Bit Manipulation Operations performed directly on binary representations of data, used for efficient computations and optimization tasks.