Piye carane nggawe struktur data kanthi prasyarat O(1)/O(log n) tartamtu?

Question

Accepted Answer

Nggawe struktur khusus tegese **nggabung struktur sing wis ana** supaya saben operasi sing dibutuhake tekan sasaran kompleksitase, lan siji struktur bisa nutupi kalemahan struktur liyane. Teknik klasik yaiku pasangan **hash map** karo **array, heap, utawa linked list**.

## Tuladha sing wis ditindakake: insert, delete, getRandom — kabeh O(1)

Prasyarat: `insert(x)`, `remove(x)`, lan `getRandom()` saben-saben O(1). Hash map piyambak ora bisa nggawe random O(1); array piyambak ora bisa nggawe remove O(1). **Goyok keduane**.

```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)
```

## Resep desain umum

```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.
```

| Pola | Struktur sing digabung | Ngaktifake |
|---|---|---|
| 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 |

## Mengapa iku penting

Sistem nyata jarang butuh struktur siji saka buku teks — butuh komposit sing disetel kanggo pola akses spesifik, apa sing persis ditaleni dening desain iki.

Surveysor nggunakake masalah-masalah iki kanggo ngeji apa sampeyan bisa mikir saka **biaya operasi menyang komposisi**, keahlian pokok ing mburi desain sistem berkinerja tinggi.

Pola	Struktur sing digabung	Ngaktifake
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