How do you find the maximum sum subarray with no consecutive elements?
This variation of the maximum subarray problem adds a constraint prohibiting adjacent selections. It tests dynamic programming intuition.
Why Interviewers Ask This
This problem evaluates the ability to define state transitions in dynamic programming where choices affect future possibilities. It distinguishes candidates who understand DP from those who only know Kadane's algorithm.
How to Answer This Question
Define two states for each position: the maximum sum including the current element and the maximum sum excluding it. If including the current element, add it to the max sum excluding the previous element. If excluding, take the max of the previous include/exclude states.
Key Points to Cover
- Define include and exclude states
- Update states iteratively
- No adjacency allowed
- Space optimization to O(1)
Sample Answer
I can use dynamic programming with two variables: incl representing the max sum including the current element, and excl representing the max sum excluding it. For each element, the new incl is excl + current element. The new excl is the max of the old incl and excl. The final answer is the max of incl and excl.
Common Mistakes to Avoid
- Using standard Kadane's algorithm
- Forgetting the exclusion case
- Incorrect state transition logic
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