Question

1. You are running algorithm with squared complexity on data with 100 elements and it takes 10 seconds. How much time do you expect the algorithm will take when executed on data with 1000 elements?
2. Order the following: O(n²), O(12 + 7n), O(n log(n) + 300 n² + 1/125 n³)

Answer 1

Solutions:
1)  Given that the algorithm has squared complexity. This means that it takes (n2) time. Let the algorithm take cn2

time where n is the size of the input to the algorithm.Given n=100 and the time taken is 10s.

=> c (1002) = 10

=> c= 10/ 10000

=> c= 10-3

Now for n=1000 elements, the time taken is:

T= c (n2)

= 10-3 x 10002

= 1000 s

Hence tiume taken is 1000 seconds.

2) The decreasing order of the time complexities is:

O(n log(n) + 300 n2 + 1/125 n3) >  O(n2) > O(12 + 7n)

The lower order terms can be omitted and the terms reduce to O(n3) , O(n2) and O(n) respectively.