Data Structures for Coding Interviews in C#/

...

/

Example 2: Time Complexity of an Algorithm With Nested Loops

Example 2: Time Complexity of an Algorithm With Nested Loops

This example is about computing the time complexity of an algorithm that involves nested for-loops.

We'll cover the following...

In the previous lesson, you learned how to calculate the time complexity of an algorithm that involves a loop. Now, you will extend the same idea to analyzing an algorithm with nested for-loops.

Nested for loop

Consider the following C# program:

Press + to interact
namespace Chapter_1
{
    class Example2
    {
        static void Main(string[] args)
        {
            int n = 5;
            int m = 7;
            int sum = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < m; j++)
                    sum += 1;
            }
            Console.Write(sum);
            return;
        }
    }
}

A simple piece of code prints the number of times the increment statement runs throughout the program. Compute its time complexity.

Time complexity

Take the training wheels off, and jump straight to line 10. As seen from the previous lesson, line 10 accounts for 6n+46n + 4 primitive operations: one for initialization, 3×(n+1)3\times(n + 1) for the comparison, and 3×n3\times n for the increment.

Move to line 12. Since this line is nested inside the for loop on line 10, it is repeated nn times. For a single iteration of the outer for loop, how many primitive operations does this line incur? You should be able to generalize from the last lesson that the answer is 6m+ ...