Related Coding / DSA
Longest Strictly Increasing Subsequence
Given a sequence of integers, find the length of the longest subsequence (not necessarily contiguous) whose elements are strictly increasing.
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
- 1Contract clarification (empty input, all-negative, empty selection allowed)
- 2Recurrence derivation and DP table
- 3Space optimisation to O(1)
- 4Edge cases: empty list, single element, two elements
- 5Follow-up: return chosen indices
4. What Strong Candidates Should Demonstrate
- ✓Clarify the adjacency constraint, empty selection behaviour, and all-negative edge case.
- ✓Derive the DP recurrence: best[i] = max(best[i-1], best[i-2] + nums[i]).
- ✓Reduce from O(n) space to O(1) space using two rolling variables.
- ✓Trace the recurrence on concrete examples including all-negative and single-element inputs.
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