Nested Loops and Mathematical Programming in Java

Course Information and Lesson Overview

Institution: Sulaimani Polytechnic University (SPU) / زانكوى بولى ءة كنى كى سلى مانى
College: Technical College of Informatics
Department: Database Technology Department
Lesson: Lesson 4: Nested Loops in Programming
Instructor: Askandar H. Amin
Date: April, 2026

Content Areas

Creating games using logic
Performing mathematics using loops
Distinction between Print and Print-line (println)
Utilization of the Math Function library
Structural implementation of Nested Loops
Integrating conditions inside loops
Matrix conceptualization and representation
Useful practical exercises

Interactive Logic: Guessing Game Loop

This section challenges the student to identify loop types and modify behavior:

What is the type of loop?: The provided code uses a for(; ; ) structure, which is an infinite loop unless terminated by a break statement.
Variable Inclusion: A challenge is posed to add a variable specifically to count the number of trials the user takes to guess the number.

Guessing Game Code Example

import java.util.Scanner;

public class nestedLoop {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Try guessing the number: ");
        int input;
        for (; ; ) {
            input = sc.nextInt();
            if (input == 27) {
                System.out.println("Correct!");
                break;
            }
            System.out.print("Try again: ");
        }
    }
}

Mathematical Operations Using Loops

Loops are highly effective for calculating sums. Using the example where $n=5$ , the total sum from 1 to 5 is calculated as $1+2+3+4+5=15$ .

Mathematical Formulas

The general equation for the sum of the first $n$ integers is: $\frac{n(n+1)}{2}$
Example 1 ( $n=5$ ): $\frac{5(6)}{2} = 15$
Example 2 ( $n=100$ ): While calculating $1+2+3+\dots+100$ manually is difficult, the formula provides the answer immediately: $\frac{100(101)}{2} = 5050$
Exercise for $n=1000$ : Construct a loop to calculate the sum when $n=1000$ :

for (int i = 1; i < 1000; i++) {
    // Implementation of sum logic goes here
}

Loop Control and Variable Tracking

Understanding the output of different loop configurations is vital for mastering flow control.

Standard Increment Loop:

for (int i = 0; i <= 10; i++) {
    System.out.println(i);
}

Standard Decrement Loop:

for (int i = 10; i >= 0; i--) {
    System.out.println(i);
}

Multi-Variable Loop:

for (int i = 0, j = 10; i <= 10; i++, j--) {
    System.out.println("i=" + i + "  j=" + j);
}

Logic Challenge: Determine the output if the loop condition is changed from $i \leq 10$ to $i == j$ .

Print and PrintLine Management

Proper use of System.out.print() versus System.out.println() is necessary for formatting.

User Input within Loops

Example code for entering names:

Scanner sc = new Scanner(System.in);
System.out.println("Enter five names:");
for (int i = 1; i <= 5; i++) {
    System.out.print("name " + i + " is: ");
    sc.next();
}

Execution Results:

Enter five names:
name $1$ is: Ali
name $2$ is: Basan
name $3$ is: Kurdonia
name $4$ is: Sazy
name $5$ is: Sarbast

Critical Warning: Using a Scanner inside a loop can be effective but requires care. Specifically, note that if the scanned value is not assigned to a variable (or if the variable is overwritten in every iteration), the data is not stored and will be lost.

Java Math Library Functions

The Math class provides several built-in methods for complex operations:

Minimum and Maximum:
- Math.max(5, 10) returns $10$
- Math.min(5, 10) returns $5$
Roots and Exponents:
- Math.sqrt(64) returns $8.0$
- Math.pow(2, 8) returns $256.0$
Absolute Values:
- Math.abs(-4.7) returns $4.7$
- Math.abs(4.7) returns $4.7$
Rounding and Approximations:
- Math.round(4.4) returns $4$
- Math.round(4.5) returns $5$
- Math.round(4.6) returns $5$
- Math.ceil(4.1) returns $5.0$
- Math.ceil(4.7) returns $5.0$
- Math.floor(4.1) returns $4.0$
- Math.floor(4.9) returns $4.0$
Random Number Generation:
- Math.random() returns a double between $0.0$ and $1.0$ (e.g., $0.5547975775921309$ ).
- To get a range from $0$ to $10$ , use: (int)(Math.random() * 11).

Educational Note: It is considered good practice to attempt writing the logic for these functions (especially max, min, sqrt, pow, round, and random) yourself to understand the underlying algorithms.

Nested Loop Structure and Syntax

A nested loop is a loop inside another loop.

Syntax

for (initialization; condition; update) {
    for (initialization; condition; update) {
        // loop's body
    }
}

Iteration Calculation

Example:

for (int i = 0; i <= 5; i++) {
    for (int j = 0; j <= 5; j++) {
        System.out.println(i + " " + j);
    }
}

Analysis: Consider how many total iterations occur (outer iterations $\times$ inner iterations) and how the placement of code inside or outside the inner loop affects the output.

Variations in Other Loop Types

While-While:

while (condition) {
    while (condition) {
        // your code
    }
}

Do-While-Do-While:

do {
    do {
        // your code
    } while (condition);
} while (condition);

Nested Loop Output Formats

Different println placements result in different visual structures.

Row-Based Printing Example

for (int i = 0; i < 5; i++) {
    System.out.println("row: " + i);
    for (int j = 0; j < 5; j++) {
        System.out.print(j + " ");
    }
    System.out.println();
}

Output:

row: 0
0 1 2 3 4
row: 1
0 1 2 3 4
… (repeated for rows 2, 3, and 4)

Column-Labeled Printing Example

for (int i = 0; i <= 5; i++) {
    System.out.print("row " + i + ":");
    for (int j = 0; j <= 5; j++) {
        System.out.print("Column:" + j + " ");
    }
    System.out.println();
}

Matrix Conceptualization

Matrices are vital for understanding coordinates in programming.

Coordinate Matrix Code

for (int i = 0; i < 5; i++) {
    for (int j = 0; j < 5; j++) {
        System.out.print("(" + i + ", " + j + ") ");
    }
    System.out.println();
}

Visual Matrix Layout (5x5):

(0,0) (0,1) (0,2) (0,3) (0,4)
(1,0) (1,1) (1,2) (1,3) (1,4)
(2,0) (2,1) (2,2) (2,3) (2,4)
(3,0) (3,1) (3,2) (3,3) (3,4)
(4,0) (4,1) (4,2) (4,3) (4,4)

Key Matrix Insights:

Understand the role of brackets (or lack thereof) in loop bodies.
A matrix allows you to select specific angles (diagonals) and data points.
You can create different matrices by initializing $i$ and $j$ with different starting values.

Conditional Logic Within Loops

By inserting conditions like if(i == j), you can isolate specific patterns within a matrix.

Pattern Matching Example

for (int i = 0; i <= 5; i++) {
    for (int j = 0; j <= 5; j++) {
        if (i == j) {
            System.out.print(i);
        } else {
            System.out.print(" ");
        }
    }
    System.out.println("");
}

Comparison of Loops and Conditions:

Both execute exactly one statement immediately following them (unless a block {} is used).
This specific code prints the value of $i$ only along the diagonal from top-left to bottom-right.

Matrix Pattern Challenges

Students are encouraged to find patterns in coordinate grids.

Example Matrix Grid:

row 0: [0,0 0,1 0,2 0,3 0,4 0,5]
row 1: [1,0 1,1 1,2 1,3 1,4 1,5]
row 2: [2,0 2,1 2,2 2,3 2,4 2,5]
row 3: [3,0 3,1 3,2 3,3 3,4 3,5]
row 4: [4,0 4,1 4,2 4,3 4,4 4,5]
row 5: [5,0 5,1 5,2 5,3 5,4 5,5]

Exercises for Nested Loops

Tasks to practice loop logic by printing star patterns:

Inverse Triangle (Right-aligned): ****** ***** **** *** ** *     
Incrementing Stars per Row: * ** *** **** ***** ******
Spaced Single Stars: * * * * * * (Horizontal or vertical distribution logic)
Standard Right-Angled Triangle: * ** *** **** ***** ******     
Descending Blocks: ***** **** *** ** *
Diagonal/Spaced Alignment: * * * * * *