Data Structures for Coding Interviews in C#/

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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.

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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:

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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 ...