Amortized analysis tana auna matsakaici kashi a gaban aikin akan jerin, kodai lokacin da wasu ayyukan daban-daban sukan kasko da yawa. Yana bayyana dalilin da yasa append na susuwan keɓaɓɓu ya zama "O(1) amortized" duk da sake gyara O(n) na lokaci-lokaci.
Lokacin da susuwan keɓaɓɓu ya cika, yana rantsar wani sabon susi (galibi ) kuma yana kwafin duk abubuwan - wani O(n) mataki. Amma saboda iko ya , girke-girke masu tsada suna zama kaɗa-kaɗa mara mahimmanci.
Appending into a doubling array (cap shown):
ops: 1 2 3 4 5 6 7 8 9
cap: 1 2 4 4 8 8 8 8 16
copy: * * * * * <- copies at 1,2,4,8,16...
To insert n elements, total copy work =
1 + 2 + 4 + ... + n ≈ 2n (geometric series)
Total cost for n inserts = O(n)
Amortized cost per insert = O(n)/n = O(1)
arr = []
for i in range(1_000_000):
arr.append(i) # almost always O(1); rarely O(n) during a resize
| Aiki | Mafi mungu daya | Amortized |
|---|---|---|
| append (ninka) | O(n) | O(1) |
Kasua ta adadin tsiri zai saukar zuwa girke a kowane saki, jiya O(n) amortized. Adadi mai ninka shine abin da ke yaɗa farashi.
Amortized analysis tana ba da hoto mabambanci, ainihi na aikin — ba tare da ta ba, zai yi zaman da kowa append ko hash-table saki shine O(n).
Hari kuma yana tabbatar da wata muhimmin kanun tsari: kasua iko mai ninka, wanda ya ciza susuwan keɓaɓɓu, teburin hash, da gida mai ure a ko'ina.