Find the maximum sum subarray such that no elements are consecutive.
A dynamic programming problem where you must select non-adjacent elements to maximize the total sum.
Why Interviewers Ask This
This tests your grasp of dynamic programming and the ability to define states for inclusion/exclusion decisions. It is a variation of the House Robber problem, common in Amazon interviews.
How to Answer This Question
Define the recurrence relation: max_sum[i] = max(max_sum[i-1], arr[i] + max_sum[i-2]). Explain that at each step, you either skip the current element or include it (plus the best sum from two steps back). Discuss base cases for the first two elements. Mention space optimization to use variables instead of an array.
Key Points to Cover
- Define recurrence relation clearly
- Choose between including or excluding current element
- Handle base cases correctly
- Optimize space to O(1)
Sample Answer
This is a classic dynamic programming problem. Let dp[i] represent the maximum sum up to index i. At each step, I have two choices: either include the current element and add it to the max sum from two steps ago, or excl…
Common Mistakes to Avoid
- Confusing with standard Kadane's algorithm
- Incorrect recurrence relation
- Failing to handle negative numbers correctly
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