Paano ngayon nggunakan Floyd tortoise lan hare kanggo ndeteksi cycle?

Question

Accepted Answer

**Floyd's cycle detection** nemokaken loop ing sequence (kaya linked list) nggunakaken rong pointer sing obah ing beda kecepetan. Yen cycle ana, pointer cepet eventually nemuin pointer adem. Nggunakaken **O(1)** spasi tambah.

## Ideane

Obah pointer **slow** siji langkah lan pointer **fast** rong langkah. Ing cycle, gap nyusut siji per langkah, dadi kudu adu; tanpa cycle, fast nggayuh duwur.

## Conto

```python
def has_cycle(head):
    slow = fast = head
    while fast and fast.next:
        slow = slow.next            # +1 step
        fast = fast.next.next       # +2 steps
        if slow is fast:            # pointers met -> cycle
            return True
    return False                    # fast hit the end -> no cycle
```

## Kerumitan

- **Wektu:** O(n). **Spasi:** O(1).

Pendekatan hash-set uga kerja nanging butuh O(n) spasi; Floyd's nggunakaken spasi konstans.

## Kapan monggo / celakane

Gunakaken kanggo **deteksi loop linked-list**, nemokaken simpen cycle, lan nemokaken cycle ing functional graph (saben node duwe successor siji). Tansah lindungi `fast.next` kanggo ngindari null dereference. Kanggo graph umum, gunakaken DFS karo recursion stack.

## Apa penting

Nemokaken cycle penting kanggo traversal aman — loop sing ora ketemu terus iterasi tanpa pedhot.

Floyd algorithm conto ayu solusine O(n)-space problem ing O(1) spasi karo invariant clever.

Kulonuwun ing linked-list interview lan nemokaken loop tanpa pedhot ing state machine lan number sequence.