How do you design a data structure with specific O(1)/O(log n) requirements?

Question

IT Interview Practice · Accepted Answer

Designing a custom structure means **composing existing structures** so that each required operation hits its target complexity, letting one structure cover another's weakness. The classic technique is pairing a **hash map** with an **array, heap, or linked list**.

## A worked example: insert, delete, getRandom — all O(1)

Requirements: `insert(x)`, `remove(x)`, and `getRandom()` each in O(1). A hash map alone can't do O(1) random; an array alone can't do O(1) remove. **Combine them**.

```python
import random
class RandomizedSet:
    def __init__(self):
        self.idx = {}      # value -> index in list
        self.vals = []     # values for O(1) random pick
    def insert(self, x):                    # O(1)
        if x in self.idx: return False
        self.idx[x] = len(self.vals)
        self.vals.append(x)
        return True
    def remove(self, x):                    # O(1): swap with last, pop
        if x not in self.idx: return False
        i, last = self.idx[x], self.vals[-1]
        self.vals[i] = last                 # move last into the hole
        self.idx[last] = i
        self.vals.pop()
        del self.idx[x]
        return True
    def getRandom(self):                    # O(1)
        return random.choice(self.vals)
```

## A general design recipe

```text
1. List every required operation + its target complexity.
2. For each, name a structure that hits it:
     by key O(1)      -> hash map
     by index O(1)    -> array
     min/max O(log n) -> heap
     ordered O(log n) -> balanced tree / skip list
     O(1) splice      -> doubly linked list
3. COMBINE them; use the hash map to map keys -> positions/nodes
   in the other structure so updates stay O(1).
4. Verify each operation against its target.
```

| Pattern | Structures combined | Enables |
|---|---|---|
| LRU cache | hash map + doubly linked list | O(1) get/put |
| O(1) randomized set | hash map + array | O(1) insert/remove/random |
| Min in O(1) on a stack | stack + auxiliary min-stack | O(1) getMin |

## Why it matters

Real systems rarely need a single textbook structure — they need a composite tuned to a specific access pattern, which is exactly what these designs deliver.

Interviewers use these problems to test whether you can reason from **operation costs to a composition**, the core skill behind high-performance system design.

Pattern	Structures combined	Enables
LRU cache	hash map + doubly linked list	O(1) get/put
O(1) randomized set	hash map + array	O(1) insert/remove/random
Min in O(1) on a stack	stack + auxiliary min-stack	O(1) getMin

A worked example: insert, delete, getRandom — all O(1)

A general design recipe

Why it matters

Related questions