Designing Data Structures for Efficient Operations

Design picks primitives (array, hash map, heap) and composes invariants—e.g. min-stack stores pairs (value, current_min) so get_min stays O(1). Document operations and their complexities.

Why this shows up in the real world

LRU caches combine hash map with doubly linked list order. Undo buffers pair stacks for redo.

Core idea (explained for students)

List required operations, choose backing stores, prove each op meets its budget. Prototype with Python collections then swap hot paths to tighter structures if needed.

Try this in Python

class MinStack:
    def __init__(self) -> None:
        self.st: list[tuple[int, int]] = []

    def push(self, x: int) -> None:
        m = x if not self.st else min(x, self.st[-1][1])
        self.st.append((x, m))

    def pop(self) -> None:
        self.st.pop()

    def get_min(self) -> int:
        return self.st[-1][1]


ms = MinStack()
ms.push(3)
ms.push(1)
ms.push(2)
print(ms.get_min())

Common mistakes

• Optimizing before the API is stable—rewrites cascade.
• Hidden linear scans inside pop(0) on a Python list masquerading as a queue.

Key takeaways

• Start with correctness + clarity, then profile.
• Encode invariants as assertions in tests during development.