Spent the first few minutes just trying to understand what the alternating sign pattern was actually doing.
First, clarify the problem constraints and edge cases (e.g., empty array, negative numbers, cuts at boundaries). Then, derive an efficient algorithm, likely using dynamic programming or prefix sums, and analyze its time and space complexity. Finally, walk through a small example to validate the approach and discuss potential optimizations.
Pro tip: Emphasize that the problem allows cuts to coincide or fall at boundaries, which means segments can be empty; this simplifies the DP state transitions and avoids special-case handling.
Confirm the definition of cut points, segment sums, and the objective. Ask about constraints (array size, value ranges) and edge cases like empty array or all negative numbers.
Let dp[i][k] be the maximum value for the first i elements split into k segments with alternating signs. Derive the transition by considering the last cut point j.
Use prefix sums to compute segment sums in O(1). The naive DP is O(n^3) for 4 segments, but can be optimized to O(n) or O(n^2) by maintaining running maxima.
State the time and space complexity of your solution. For 4 segments, an O(n) solution exists by iterating once and keeping track of best values for each segment count.
Walk through a small array (e.g., [1, -2, 3, -4]) to verify the recurrence and edge cases like empty segments.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by sorting developers by skill level to simplify counting lower/higher teammates. Then, for each possible team size, check if there exists a contiguous window of that size where every member's constraints are satisfied. Use binary search on team size or two-pointer to find the maximum efficiently.
Pro tip: Emphasize that sorting is key to reducing the problem to checking contiguous subarrays, and mention that constraints can be verified in O(1) with prefix sums or sliding window. This shows you can optimize from brute force to O(n log n) or O(n).
Confirm the problem: each developer has a lower-skill tolerance L_i and higher-skill tolerance H_i. In a valid team, for each member, the number of selected teammates with lower skill ≤ L_i and with higher skill ≤ H_i. Ask about input format and constraints.
Sort developers by skill. In any valid team, the selected members form a contiguous block in sorted order. For a member at position i in the block, the number of lower-skill teammates is i - start, and higher-skill is end - i. So constraints become: i - start ≤ L_i and end - i ≤ H_i.
For a fixed team size k, we need to find a contiguous window [s, s+k-1] such that for all i in window: i - s ≤ L_i and (s+k-1) - i ≤ H_i. This can be checked in O(n) per k using sliding window or prefix maxima/minima.
Use binary search on k (from 1 to n) to find the maximum valid team size. For each mid, check feasibility in O(n). Total O(n log n). Alternatively, use two pointers to maintain a valid window and expand/shrink, achieving O(n).
Discuss time/space complexity: O(n log n) with binary search, O(n) with two pointers. Mention that sorting is O(n log n) anyway. Consider edge cases: all developers can be in team, no valid team (return 0), etc.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.