NW| 26-Jul-SDC | Ahmad Hmedan | Sprint 2 | Improve code with precomputing

[AhmadHmedann]

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Task code

CYF-1183

Changelist

Speed up the solutions by introducing precomputing

[cjyuan]

Can you use complexity to explain how the new implementation is better than the original implementation?

[AhmadHmedann]

Original:

• Time Complexity: O(N² × K)
• Space Complexity: O(N + K)

New:

• Time Complexity: O(N × K²)
• Space Complexity: O(N × K)

Where:

• N is the number of strings in the list.
• K is the maximum length of a string.

[cjyuan]

The time complexity analyses are correct.

Both the original and the refactored code require more space. If string length, $K$, is to be taken into consideration, an array of strings would need O(Nk) space.

[AhmadHmedann]

Do you mean the input space complexity?

I was calculating the auxiliary space complexity, excluding the input memory. Should I make that clear in my analysis?

I also realised that because of prefix = string[:i] and storing all the prefixes in a set, the auxiliary space complexity of the new implementation should be O(N × K²), not O(N × K).

Is my understanding correct?

[cjyuan]

Do you mean the input space complexity?

Yes

Should I make that clear in my analysis?

No need. Since your space complexity analyses were wrong. I was just trying to clarify.

I also realised that because of prefix = string[:i] and storing all the prefixes in a set, the auxiliary space complexity of the new implementation should be O(N × K²), not O(N × K).

Is my understanding correct?

Correct.