Programming Discrete Math Concepts for Beginners/

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Introduction to Time Complexity

Introduction to Time Complexity

Learn the basics of time complexity and its calculation.

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Time complexity calculation

We’ve learned that data structures are discrete structures. So, algorithms are all about discrete structures.

Let’s consider a simple Java program where we simultaneously iterate over two loops. These outer and inner loops are connected, and they finally give us an output.

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class Main {
    static int i, j, totalOne, totalTwo;
    public static void main(String[] args) {
        for (i = 0; i <= 5; i++){
            totalOne += i;
            System.out.print("i = " + i);
            System.out.println("--------");
            for (j = 0; j <= 5; j++){
                totalTwo += j;
                System.out.println("j = " + j);
            }
        }
        System.out.println("The total of the outer loop: " + totalOne);
        System.out.println("The total of the inner loop: " + totalTwo);
    }
}

And from this elementary program, we get the following output:

i = 0--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
i = 1--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
i = 2--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
i = 3--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
i = 4--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
i = 5--------
j = 0
j = 1
j = 2
j = 3
j = 4
j = 5
The total of the outer loop: 15
The total of the inner loop: 90

Time complexity of only one loop

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