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Maximize Sum with No Adjacent Elements

Given a list of integers, find the maximum sum you can obtain by choosing elements such that no two chosen elements are adjacent in the list. You may choose no elements, so the answer is 0 for an empty list or when every choice would reduce the sum.

1. Problem Statement

Given a list of integers, return the maximum sum you can obtain by selecting elements such that no two selected elements are adjacent. You may choose no elements, so return 0 for an empty list or when every value is negative. The list has at most 100000 elements, and each value is between -10000 and 10000 inclusive. Start with any clarifying questions.

2. Live Coding Format

Work in the provided coding workspace while explaining your decisions to the live interviewer. Validation may use inline tests, examples, comments, or a verbal walkthrough.

3. Key Focus Areas

  • 1
    Contract clarification (empty input, all-negative, empty selection allowed)
  • 2
    Approach derivation and correctness argument
  • 3
    Time and space complexity
  • 4
    Edge cases and validation
  • 5
    Follow-up performance

4. What Strong Candidates Should Demonstrate

  • Clarify the adjacency constraint, empty selection behaviour, and all-negative edge case.
  • Derive a correct approach before coding and argue why it is optimal.
  • State the time and auxiliary-space complexity of the final solution.
  • Validate with your own examples, including all-negative and single-element inputs, stating expected outputs first.

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Practice this problem in the live coding workspace while the interviewer probes your clarification, implementation, trade-offs, and validation.

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Core Concepts

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Dynamic ProgrammingArraysGreedy Thinking

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