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Minimize sum with halving operations

OracleSoftware Engineer · Onsite
MediumSoftware EngineerOnsiteCoding & Algorithms

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This interview question evaluates algorithm design, data structures, correctness, complexity, edge cases, and implementation details in a realistic interview setting. A strong answer for Minimize sum with halving operations states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

You are given an array of non-negative integers nums and an integer k. In one operation, choose any index i and replace nums[i] with ceil(nums[i] / 2). You may perform at most k operations. Return the minimum possible sum of the array after the operations. Describe an efficient algorithm, prove why it works, analyze time and space complexity, and discuss edge cases such as zeros and very large k.