The following algorithm:for i in range(n): # from 0 to n-1 for j in range(i) # from 0 to i-1 s += i * log(j)has a complexity inSelect one:a. O( n log(n) )b. O(n)c. O(n^2)d. O(1)e. O(n/2)
Question
The following algorithm:for i in range(n): # from 0 to n-1 for j in range(i) # from 0 to i-1 s += i * log(j)has a complexity inSelect one:a. O( n log(n) )b. O(n)c. O(n^2)d. O(1)e. O(n/2)
Solution
The complexity of the given algorithm is O(n^2).
Here's why:
The outer loop runs n times, and for each iteration of the outer loop, the inner loop runs i times (where i is the current iteration of the outer loop).
In the worst-case scenario, the inner loop will run n times (when i=n). Therefore, the total number of operations is the sum of the first n integers, which is (n*(n+1))/2.
This is a well-known formula that simplifies to O(n^2) in Big O notation.
So, the correct answer is c. O(n^2).
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