Introduction
Analysis complexity is an important concept in computer science, as it helps to determine the efficiency of algorithms. In particular, the analysis of complexity in a for inside for loop is important, as the complexity of the second for loop depends on the first one. This article will discuss the analysis of complexity in a for inside for loop, and how the complexity of the second for loop is affected by the first one.
Solution
The complexity of a nested for loop is O(n^2), where n is the number of iterations of the outer loop. This is because the inner loop will run n times for each iteration of the outer loop, resulting in n*n total iterations.
You will have to use some mathematics here. Lets talk about your 2nd and 3rd loop:
No of iterations in 3rd loop(for c) for each iteration of 2nd loop(for b):
1 = 2^0 ( for b < 1)
2 = 2^1 ( for b < 2)
4 = 2^2 ( for b < 4)
.
.
n = 2^(logn base 2)
sum of above iterations is GP series sum which comes down to :
2((2 ^ logn) -1) / (2-1) which gives n.
now first loop runs n times.
So overall your code runs in order of n^2.
Hope this answers your question.
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solved Analysis complexity, in for inside for, the 2nd for depeneds from the first one [closed]
When analyzing the complexity of a for-in-for loop, it is important to consider the fact that the second for loop depends on the first one. This means that the number of iterations of the second loop is determined by the number of iterations of the first loop. Therefore, the complexity of the loop is determined by the number of iterations of the first loop multiplied by the number of iterations of the second loop. For example, if the first loop iterates 10 times and the second loop iterates 5 times, then the complexity of the loop is 10 x 5 = 50.
It is also important to consider the complexity of the code inside the loop. If the code inside the loop is complex, then the overall complexity of the loop will be higher. For example, if the code inside the loop is a nested loop, then the complexity of the loop will be the number of iterations of the first loop multiplied by the number of iterations of the nested loop.
In conclusion, the complexity of a for-in-for loop depends on the number of iterations of the first loop and the complexity of the code inside the loop. If the code inside the loop is complex, then the overall complexity of the loop will be higher.