Algorithms for Coding Interviews in C++/

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Example: Measuring Time Complexity of a Single Loop Algorithm

Example: Measuring Time Complexity of a Single Loop Algorithm

In this lesson, we are going to learn how to compute the time complexity of an algorithm that involves a for loop.

We'll cover the following...

A For Loop With n Iterations

Let’s consider what happens when a loop is involved. Consider the following C++ program::

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#include <iostream>
using namespace std;
int main(){
  int n = 10;
  int sum = 0;
  for (int i = 0; i < n; i++)
    sum += 2;
  cout << sum;
  return 0;
}

Let’s count the number of primitive operations in the above program. We skip the non-executable lines and come to lines 4 and 5 where variable initializations are taking place, which account for one primitive operation, each.

Line 6 is a loop statement. To count the number of primitive operations on that line, we must dissect it into its constituents: the initialization, the increment, and the test. The initialization occurs only once and is counted as one primitive operation. The increment ( ...

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