If an algorithm has a time complexity of O(n^3), how will the running time change if the input size is doubled?It will doubleIt will tripleIt will increase by a factor of 8It will increase by a factor of 4
Question
If an algorithm has a time complexity of O(n^3), how will the running time change if the input size is doubled?It will doubleIt will tripleIt will increase by a factor of 8It will increase by a factor of 4
Solution
It will increase by a factor of 8.
Here's why:
The time complexity of an algorithm, O(n^3), means that the running time of the algorithm is proportional to the cube of the size of the input.
So, if you double the size of the input (i.e., if n becomes 2n), the running time will be proportional to (2n)^3 = 8n^3.
This is 8 times the original running time when the input size was n (which was n^3).
So, the running time increases by a factor of 8 when the input size is doubled.
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