Prefix sum is pretty textbook but the part that tripped me up was thinking about initialization cost vs query cost.
Start by clarifying the requirements: the array is immutable, and the query function will be called many times, so preprocessing is worthwhile. Propose a prefix sum array that allows O(1) query time after O(n) preprocessing, and discuss the trade-off of using extra space. Then implement the class with a constructor that builds the prefix sum and a method that returns the sum of a range in constant time.
Pro tip: Mention that you would handle edge cases like empty array, invalid ranges, and integer overflow, and that you would consider using a 64-bit integer for the prefix sums to avoid overflow. Also, briefly note that if updates were allowed, a Fenwick tree or segment tree would be needed, showing awareness of alternatives.
Confirm that the array is immutable, queries are frequent, and determine the expected range of values and query indices. Ask about memory constraints and whether the array can be empty.
Select a prefix sum array (cumulative sum) because it provides O(1) query time after O(n) preprocessing, which is optimal for frequent queries on immutable data.
Define a constructor that takes the integer array and builds the prefix sum, and a method sumRange(i, j) that returns the sum of elements from index i to j inclusive.
Build an array where prefix[k] = sum of first k elements (prefix[0] = 0). Then sumRange(i, j) = prefix[j+1] - prefix[i]. Handle edge cases like i > j or out-of-bounds indices.
State that preprocessing takes O(n) time and O(n) space, and each query takes O(1) time. Mention that this is optimal for immutable arrays and compare with alternatives like segment trees for mutable arrays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the requirements and constraints, then propose a solution using two stacks: one for the main stack and one for tracking the maximum values. Discuss the trade-offs between time complexity for popMax and space complexity, and consider optimizations like using a doubly linked list with a tree map for O(log n) operations.
Pro tip: Demonstrate awareness of real-world constraints by discussing how to handle duplicate maximum values and the impact of frequent popMax calls on performance. Mention that in an interview, it's often better to start with a simple solution and then optimize based on feedback.
Ask about expected time complexity, frequency of operations, and whether the stack can contain duplicates. Confirm that popMax should remove the topmost maximum element if there are multiple.
Suggest using two stacks: one for all elements and one for tracking maximums. Explain how push, pop, top, and peekMax work in O(1) time, but popMax requires O(n) time to remove the maximum.
Compare the two-stack approach with more advanced solutions like a doubly linked list combined with a balanced BST (e.g., TreeMap) to achieve O(log n) for all operations. Discuss space and implementation complexity.
If needed, describe how to implement O(log n) popMax using a TreeMap mapping values to lists of nodes, and a doubly linked list to maintain stack order. Explain how to update the TreeMap on push and pop.
Walk through a sequence of operations, including duplicates and popMax, to verify correctness. Mention edge cases like popping from an empty stack.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.