Yadda kuke gano keken tare da Floyd's tu?

Question

Accepted Answer

**Floyd's ganan keken** yana samun kwara a cikin jeri (kamar jerin haɗi) ta amfani da maɓuɓɓu biyu da suke motsawa tare da sunan gudu. Idan keken akwai, maɓuɓɓun sauri na gida daga hankali kuma ya haɗu da jita mai laushi. Yana amfani da **O(1)** jiya mbalal.

## Tunani

Juyawa maɓuɓɓun **slow** tsake gida da maɓuɓɓun **fast** tsake biyu. A cikin keken, agwaci yana raguwa daya koli koli, don haka dole ne su ja, kaɗa babu keken, sauri yana kusan ƙarsheni.

## Tsarin

```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
```

## Haddi

- **Lokaci:** O(n). **Jiya:** O(1).

Hanyar hash-set kuma tana aiki amma tana ashe O(n) jiya; Floyd's tana amfani da jiya na jiya.

## Lokacin amfani / ɓataye

Aamfani don **ganan jerin haɗi na keken**, gano farkon keken, da ganan keken a cikin zane na aiki (koli koli yana da magajiya daya). Taba karɓar `fast.next` don kawar da daidai null. Ga zane na jita, yi amfani da DFS tare da jeri na maimaito maimakon.

## Dalilin ƙunsa mahimmanci

Ganan keken shine mahimmanci don suri mai aminci — keken da ba a gani ba yana nufin maimaiko ba tare da iyaka.

Algorithm na Floyd misali ne mai kyau na warware matsalar O(n)-jiya a O(1) jiya tare da lissafin da ke gyara.

Yana bayyana a jerin haɗi horo da ganan jerin dan lokaci a keken da jerin lambobi.