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The time complexity of the  following code snippet isc=0; while (n>=1) {for(i=1;i<=n;i++){ c++;}n=n/2;}

Question

The time complexity of the  following code snippet isc=0; while (n>=1) {for(i=1;i<=n;i++){ c++;}n=n/2;}

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Solution 1

The given code snippet consists of a while loop and a nested for loop. The outer while loop runs as long as n is greater than or equal to 1, and in each iteration, n is halved. The inner for loop runs from 1 to n.

The time complexity of this code can be calculated as follows:

  1. In the first iteration of the while loop, the for loop runs n times.
  2. In the second iteration, n is halved, so the for loop runs n/2 times.
  3. In the third iteration, n is halved again, so the for loop runs n/4 times.
  4. This continues until n is less than 1.

So, the total number of iterations is n + n/2 + n/4 + n/8 + ... until n < 1. This is a geometric series, and the sum of this series is less than 2n.

Therefore, the time complexity of the code is O(n), where n is the initial value of n.

This problem has been solved

Solution 2

The given code snippet consists of a while loop and a nested for loop. The outer while loop runs as long as n is greater than or equal to 1, and in each iteration, n is halved. The inner for loop runs from 1 to n.

Let's break down the time complexity:

  1. The outer while loop: This loop runs until n becomes less than 1. Since n is halved in each iteration, the number of iterations will be log(n) base 2. So, the time complexity of the outer loop is O(log n).

  2. The inner for loop: This loop runs n times. So, its time complexity is O(n).

Since the for loop is nested inside the while loop, we multiply their time complexities to get the overall time complexity. Therefore, the time complexity of the given code snippet is O(n log n).

This problem has been solved

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