Menene fasahar alamomiyi biyu?

Question

Accepted Answer

Fasahar **alamomiyi biyu** tana amfani da alamomi biyu waɗanda suke tafiya ta jeri don warware matsaloli a jira gida — cikakken samar da warware brute-force O(n²) gidajiya zuwa **O(n)**.

## Tunanin

Ńi alamomiyi biyu (sau da yawa a ƙarshen, ko jiya yayyaki da ɗaya cikin sauri) kuma jigya su dangane da yanayi, raguwa aiki ba tare da sake bincike ba.

## Misali: jiga alamar tafiya a iyakar jeri da aka bugi

```python
def two_sum_sorted(arr, target):
    lo, hi = 0, len(arr) - 1
    while lo < hi:
        s = arr[lo] + arr[hi]
        if s == target:
            return (lo, hi)       # found the pair
        elif s < target:
            lo += 1               # need a bigger sum
        else:
            hi -= 1               # need a smaller sum
    return None

two_sum_sorted([1, 3, 4, 6, 9], 10)   # -> (1, 3) for 4 + 6
```

## Alaƙa

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

## Yaushe za a yi amfani / makabe

Walau sosai don **jeri da aka bugi**, bincike palindrome, juyawa, da cire muhammama a wuri. Jeri yakan bugi sau da yawa don nau'i mai haɗiya-alamar. Kula da iyakokin alamar da yanayin madauki (`lo < hi`).

## Yaushe ya kamata

Alamomiyi biyu ɗaya daga cikin manyan misalai na bincike: yana fara hani manyan gadewa cikin sicar layi mai tsarki.

Yana koyar maka samun amfani da tsari (kamar bugi) maimakon ƙarfi mai faɗi.

Tunani iri ɗaya ya bugi haɗi, ɓucewar, da mataki haɗin haɗin ɓucewar.