Unit 4¶
4.1 While Loops¶
Goals
Represent iterative processes using while loops.
Use Boolean expressions to determine if a loop body is executed and when the iteration should cease.
Write a program code to satisfy method specifications using expressions, conditional statements, and iterative statements.
In programming, loops are used to repeat a block of code x
amount of times. With some loop programs, the expression is evaluated (Is the condition true or not?) before each iteration of the loop body. When the expression evaluates to true
, the loop body is executed. This continues until the expression evaluates to false, where the loop ends.
Note: While Java is flexible with spacing around conditional expressions, between keywords, before and after operators, it is not however flexible with spacing around the dot operator. The following statements are not equivalent.
str.substring(i, i+1);
str. substring(i, i+1); // syntax error
str .substring(i, i+1); // syntax error
One more thing, An infinite loop is an instruction sequence that loops endlessly when a terminating condition isn’t met. An infinite loop might be a programming error, but may also be intentional.
Within Unit 4, we will explore different keyword loop terms and how they are utilized.
Take a look at the program below:
public class Main {
public static void main(String[] args) {
int i=1;
while(i<=10){ // use of a Boolean to create a loop
System.out.println(i);
i++;
}
}
}
Another example using the while
loop.
public class Main {
public static void main(String[] args) {
int i = 1;
int n = 10; // use of a second variable to create a loop
while(i <= n) {
System.out.println(i);
i++;
}
}
}
Using .equals
within a while
loop.
import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter your input (q to quit): ");
String input = sc.nextLine();
while (!input.equals("q")) // use of a while loop using .equals
{
System.out.println("Enter your input (q to quit): ");
input = sc.nextLine();
}
System.out.println("Goodbye.");
}
}
Click Here
import java.util.*;
public class Main{
public static void main(String[] args)
{
int i=0;
int n;
Scanner sc=new Scanner(System.in);
System.out.print("Enter the number of elements you want to store: ");
n = sc.nextInt(); // storing the number of elements that you want to store.
int[] array = new int[n]; // defining the number of inputs for the array
System.out.println("Enter the elements of the array: ");
while (i < n){
//reading array elements from the user
array[i] = sc.nextInt();
i++;
}
System.out.println("Contents of the array are: " + Arrays.toString(array));
// printing the stored elements within the array.
}
}
Activity 4.1.1¶
Must use a
while
loopYou may use Arrays for this assignment
Use a
scanner
class to recievex
amount ofint
inputsOrganize the inputted numbers into a traditional grade structure:
A = 90 - 100
B = 80 - 90
C = 70 - 79
D = 60 - 69
F = 0 - 59
Return
the total number of A’s, B’s, C’s, D’s, and F’s
Activity 4.1.2¶
1. Is a Factor?
Write an algorithm that determines whether divisor is a factor of number.
Do not use the modulo or division operators.
Sample Ouput:
Enter the number:
104
Enter the divisor:
13
13 is a factor of 104
Enter the number:
52
Enter the divisor:
3
3 is not a factor of 52
2. Extract Digits
Using a while loop, create an algorithm extractDigits that prints the
individual digits of a positive integer.
For instance, extractDigits(54321); would create the output:
1
2
3
4
5
Hint: The % and the / operators are going to be very useful in this program.
How can you use these to extract the last digit of the given number?
3. SumAverage
Write an algorithm that will ask the user for a number until they enter 'q'.
Then calculate the sum and everage of those numbers.
Sample Output:
Enter a number, or the letter 'q' to end the sequence:
25
Enter a number, or the letter 'q' to end the sequence:
78
Enter a number, or the letter 'q' to end the sequence:
16
Enter a number, or the letter 'q' to end the sequence:
14
Enter a number, or the letter 'q' to end the sequence:
q
The sum is: 133
The average is: 33.25
4.1a Do While Loops - Oracle¶
The do-while
loop will not be assessed for the AP CSA exam, it can be a useful tool when writing programs.
A do-while
loop in Java is a type of loop where the code block is executed at least once before checking the loop condition.
This is in contrast to a while
loop, which checks the condition before entering the loop. Here’s a Java program that
demonstrates and explains a do-while
loop:
//Do While Example
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner posNum = new Scanner(System.in);
int number;
// Prompt the user to enter a positive number
do { //keyword do
System.out.print("Enter a positive number: ");
number = posNum.nextInt();
// Check if the number is positive
if (number <= 0) {
System.out.println("Please enter a positive number.");
}
} while (number <= 0); // Loop continues as long as the number is not positive
// Now, we have a positive number
System.out.println("You entered a positive number: " + number);
}
}
Inside the “do” block, we use a do-while
loop to repeatedly prompt the user for input until they enter a positive number. The loop will always execute at least once because the condition is checked at the end of the loop. Within the loop, a message asks the user to enter a positive number and read their input using the scanner class. The program then checks if the entered number is less than or equal to 0. If it is, a message asks the user to enter a positive number again. The loop will continue to execute as long as the condition (number <= 0) is true. Once the user enters a positive number, the loop ends, and a message is printed indicating that they entered a positive number.
This program demonstrates a simple “do-while” loop to ensure that the user provides valid input before proceeding with the program.
4.1a - Classwork Guessing Game¶
Directions: Write a java program that will ask the user to pick a number between 1 - 100. Use a do
while loop that will compare the random number generated with Math.random()
method with the choice of the user. If the user inputs the correct number, end the game with a congratulatory message. If the user inputs the number wrong, tell the user how close they are to the actual number and give them another chance to pick the number. Program ends when the number is selected.
Click Here
import java.util.Scanner;
public class Name {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int randomNumber = (int) (Math.random() * 100) + 1;
int userGuess;
System.out.println("Welcome to the Number Guessing Game!");
System.out.println("I've picked a number between 1 and 100. Try to guess it!");
do {
System.out.print("Enter your guess: ");
userGuess = scanner.nextInt();
if (userGuess == randomNumber) {
System.out.println("Congratulations! You guessed the correct number: " + randomNumber);
break;
} else {
int difference = Math.abs(randomNumber - userGuess);
if (difference <= 10) {
System.out.println("You're very close! Try again.");
} else if (difference <= 20) {
System.out.println("You're close! Try again.");
} else if (difference <= 30) {
System.out.println("You're getting warmer! Try again.");
} else {
System.out.println("You're far away! Try again.");
}
}
} while (true);
scanner.close();
}
}
Activity 4.1b - convert program¶
Directions: Convert Program A and Program B from a for
loop to a do-while
loop.
//Program A
import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter a String with at least 3 characters: ");
String input = sc.nextLine();
String pattern = "aaa";
int howMany = 0;
for (int i = 0; i < input.length() - pattern.length() + 1; i++)
{
String currSeq = input.substring(i, i + pattern.length());
if (currSeq.equals(pattern))
howMany++;
}
System.out.println("There were " + howMany +
" substrings matching " + pattern);
}
}
// Program B
import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter a String: ");
String input = sc.nextLine();
String output = "";
for (int i = input.length(); i > 0; i--)
output += input.substring(i - 1, i);
System.out.println(output);
}
}
Activity 4.1c¶
Directions: Write a program using a do-while
loop that does the following:
Write a do-while loop that asks a user for their name, which must be at least four characters long.
Write another do-while that asks for the user’s age, which must be between 18 and 65, inclusive. Recall the nextIntmethod Scanner class.
Sample Output
What is your first name?
Jon
Your name needs to be at least 4 characters long.
What is your first name?
Jonathan
What is your current age?
50
Jonathan is 50 years old.
You have learned about primitive data types like int
, double
, and boolean
. Java has a char
data type that stores a single character. When using a char
data type, use single quotes to assign a character to your char
variable. For example:
char reply = 'y';
Java chars and strings are closely related. A String is a sequence of chararcters that reference an object. Using a new method, you can find individual characters in a String. Remember, a char
is a primitive data type, you can compare primitive data types with == in conditionals.
Assignment char
- Oracle¶
Directions: Using a do-while, validate the input so the user types only one character. Write a switch
statement to show the character “is a vowel” or “ is a consonant.”
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter a letter");
String str = sc.nextLine();
}
}
Sample Output
Enter a letter
b
b is a consonant.
Break and Continue Keywords in Java - Oracle¶
Break and Continue keywords in Java
The Break
statement in Java is used most often in one of the two cases below.
Break quits the loop and jumps out of it (both for and while).
Break statement exits a case in the switch statement.
Example 1
public class Main {
public static void main(String[] args) {
// Testing break statement in while loop
System.out.println("Test Break statement in While loop");
int i = 0;
while (i < 5) {
if (i == 2) {
break;
}
System.out.println(i++);
}
}
}
Sample Output
Test Break statement in While loop
0
1
The continue
statement in Java is most often used in one of the two cases below.
It skips the following statements and moves to the next iteration in the for loop.
Continue in while loops hop the following statements and jump to the conditional statement.
Example 2
public class Main {
public static void main(String[] args) {
// Testing continue statement in while loop
System.out.println("Test Continue in While loop");
int i = 0;
while (i < 5) {
if (i == 2) {
i++;
continue;
}
System.out.println(i++);
}
}
}
Sample Output
Test Continue in While loop
0
1
3
4
Differences between continue and break The considerable difference between break and continue is that the break exits a loop at once. Once a break statement is executed, the loop will not run again. However, after executing the continue statement, the following lines of code will be skipped for the current iteration only. The loop will begin to execute again.
Break and Continue in While Loop
Both Break
and Continue
can be used in a while
loop.
Example 1
public class Main {
public static void main(String[] args) {
// Testing both break and continue statements side by side
String [] weekdays = { "Sunday", "Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday" };
System.out.println("Test Break statement in While loop");
System.out.println("\nWorking Days:\n");
int i = 0;
while (i < weekdays.length ) {
if (weekdays[i].equals("Saturday") || weekdays[i].equals("Sunday")) {
i++;
break;
// Not any working day will be printed
// because the loop breaks on Sunday
// once the loop breaks it moves out of the loop
}
System.out.println(weekdays[i++]);
}
System.out.println("\nTest Continue statement in While loop");
System.out.println("\nWorking Days:\n");
int j = 0;
while (j < weekdays.length ) {
if (weekdays[i].equals("Saturday") || weekdays[i].equals("Sunday")) {
j++;
continue;
// All the working/business days will be printed
// when the loop encounters Saturday or Sunday
// it skips that iteration and continues to the next iteration
}
System.out.println(weekdays[i++]);
}
}
}
Sample Output
Test Break statement in While loop
Working Days:
Test Continue statement in While loop
Working Days:
Monday
Tuesday
Wednesday
Thursday
Friday
The break
and continue
keywords can be a valuable tool when writing Java programs.
Activity Break and Continue - Oracle¶
Directions Modify the selection sort
program below by using the break and continue keywords.
Use a
break
statement to stop the selection sort when it encounters a negative value.Show a message that the sort was aborted.
Use a
continue
statement to continue the sort when the next value is a positive value.
import java.util.ArrayList;
public class Main
{
public static void main(String[] args)
{
ArrayList<Integer> ratings = new ArrayList<Integer>();
ratings.add(5);
ratings.add(4);
ratings.add(8);
ratings.add(9);
ratings.add(2);
ratings.add(-3);
ratings.add(1);
ratings.add(4);
// Iterate through all the values in the list.
for (int i = 0; i < ratings.size() - 1; i++)
{
// Keep track of the index of the smallest number.
int minIndex = i;
// Iterate from the next index up to the end of the array
for (int j = i + 1; j < ratings.size(); j++)
{
// If the current element is smaller than the minimum, we have a new
// smallest element, so set minIndex to the index of the current element.
if(ratings.get(j) < ratings.get(minIndex))
{
minIndex = j;
}
}
// Swap current with minimum element if they're different
if(ratings.get(i) != ratings.get(minIndex))
{
// Swap current with minimum element
int temp = ratings.get(i);
ratings.set(i, ratings.get(minIndex));
ratings.set(minIndex, temp);
}
}
// Print all the elements of the list
System.out.println(ratings);
}
}
4.2 For Loops¶
Goals
Write for loops.
For
and while
loops are, for the most part, interchangable. From my personal experience, I prefer for
loops because it is easier to read within your program. The main difference between for
and while
loops is that a for
loop is finite. If you look at the modifier of a for
loop, you will know how many loops will be executed. With a while
loop, it can be infinite. Another difference between the two loops is that initialization variable of a for
loop cannot be changed; whereas, a while loop’s initialization variable is outside of the while
loop. There are four components that are used to create the syntax of a for
loop:
Keyword
initialization
Boolean expression
modifier
Take a look at the program below.
public class Main {
public static void main(String[] args) {
for (int i = 0; i <= 10; i++) {
System.out.println(i);
}
}
}
// The syntax of a for loop:
// keyword (intialization; boolean expression; modifier){ /*Body of the loop*/ }
// for (int i = 0; i <=10; i++ ){ System.out.println(i);}
Notice the initialization variable location. It is located outside of the while loop. Observe the program below.
int i = 0;
while (i < 11)
{
System.out.println(i);
i++;
}
Now, observe an equivalent for loop.
for (int i = 0; i < 11; i++)
{
System.out.println(i);
}
The scope of the intialization variable, i, is within the for
loop; any attempt to access it outside of the for
loop results in an error.
IMPORTANT off-by-one error – Must Read –> Click Here
An off-by-one error occurs when a loop iterates one time too many or one time too few due to incorrect initialization, termination, or increment/decrement logic. This is a common logical error in programming.
Example of an Off-by-One Error Consider a scenario where you want to iterate through an array of integers and print each element.
Incorrect Code (with an Off-by-One Error)
public class Main {
public static void main(String[] args) {
int[] numbers = {10, 20, 30, 40, 50};
// Off-by-one error in loop condition
for (int i = 0; i <= numbers.length; i++) {
System.out.println(numbers[i]);
}
}
}
Rationale:
Initialization (
int i = 0
): Correct, starts at the first index of the array.Condition (
i <= numbers.length
): Incorrect, asnumbers.length
is 5, but the last valid index of the array is 4 (0-based indexing).Result: The loop runs one extra iteration (when
i == 5
), causing an ArrayIndexOutOfBoundsException.
Correct Code (Fixing the Error)
public class Main {
public static void main(String[] args) {
int[] numbers = {10, 20, 30, 40, 50};
// Correct loop condition
for (int i = 0; i < numbers.length; i++) {
System.out.println(numbers[i]);
}
}
}
Fix:
The loop condition is updated to
i < numbers.length
to ensure that the loop stops beforei
reachesnumbers.length
.
Common Scenarios of Off-by-One Errors
Iterating through arrays:
Mistaking
<=
for<
in the loop condition.
Using ranges in loops:
for (int i = 1; i <= 10; i++) // Correct (includes 1 through 10) for (int i = 1; i < 10; i++) // Correct (includes 1 through 9)
Accidentally swapping the two could lead to unintended behavior.
String indexing: When processing a string character by character, forgetting that string indices start at
0
can cause off-by-one errors.
Activity 4.2.1¶
Task 1: Using a for
loop, write a program where you ask the user for a number
and print out the number
of perfect squares up until that number
.
Enter the number of squares:
10
1 squared = 1
2 squared = 4
3 squared = 9
4 squared = 16
5 squared = 25
6 squared = 36
7 squared = 49
8 squared = 64
9 squared = 81
10 squared = 100
Task 2: Repeatly ask the for a number
. When the user is done, report back the number
of odd numbers
. Decide whether to use a while
loop or a for
loop.
Enter a number (type "done" when complete):
4
Enter a number (type "done" when complete):
9
Enter a number (type "done" when complete):
12
Enter a number (type "done" when complete):
11
Enter a number (type "done" when complete):
15
Enter a number (type "done" when complete):
3
Enter a number (type "done" when complete):
done
You had 4 odd numbers.
Activity 4.2.2¶
Factorial Implement a program which calculates the factorial of a number given by the user. The factorial of a number is found by multiplying itself by all positive integers less than it (excluding 0).
For example, 4 factorial, written as 4!, can be computed as follows:
4! == 4 * 3 * 2 * 1 == 24 Additionally, it has been specified that the factorial of 0 is 1, so 0! = 1.
Multiplication Table Implement a program which will display a multiplication table. Ask the user for a number and how many mutiples to display.
Example Output:
Enter an integer:
4
Enter the number of mulltiples:
10
4 * 1 = 4
4 * 2 = 8
4 * 3 = 12
4 * 4 = 16
4 * 5 = 20
4 * 6 = 24
4 * 7 = 28
4 * 8 = 32
4 * 9 = 36
4 * 10 = 40
Activity 4.2.3¶
Given the array below, loop through the array and print out all odd numbers on a separate line. Order is not important! Do not print any numbers that come after 894 in the sequence. Hint: One way you will need to use .length
public class Main {
public static void main(String[] args) {
int[] numbers = {
951, 402, 984, 651, 360, 169, 408, 319, 601, 485, 980, 507, 725, 547, 544, 941,
615, 83, 165, 141, 501, 263, 617, 865, 575, 219, 390, 984, 592, 236, 105, 942,
386, 462, 47, 418, 907, 344, 236, 375, 823, 566, 597, 978, 328, 615, 953, 345,
399, 162, 758, 219, 918, 237, 412, 566, 826, 248, 866, 950, 626, 949, 687, 217,
815, 67, 104, 58, 512, 24, 892, 894, 767, 553, 81, 379, 843, 831, 445, 742, 717,
958, 609, 842, 451, 688, 753, 854, 685, 93, 857, 440, 380, 126, 721, 328, 753, 470,
743, 527};
/* your code goes here */
}
}
Example output for even numbers:
402
984
360
408
980
544
390
984
592
236
4.3 Developing Algorithms Using Strings¶
Goals
Manipulate Strings using loops
In this activity, you will observe, modify, and implement some standard String algorithms using traversals.
import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter a String: ");
String input = sc.nextLine();
String pattern = "aaa";
int howMany = 0;
for (int i = 0; i < input.length() - pattern.length() + 1; i++)
{
String currSeq = input.substring(i, i + pattern.length());
if (currSeq.equals(pattern))
{
howMany++;
}
}
System.out.println("There were " + howMany +
" substrings matching " + pattern);
}
}
Predict what is going to happen when you type aaaaa
.
Look at the program below. What do you think is going to happen when you type a string
?
import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter a String: ");
String input = sc.nextLine();
String output = "";
for (int i = input.length(); i > 0; i--)
{
output += input.substring(i - 1, i);
}
System.out.println(output);
}
}
There are standard algorithms that utilize String traversals to:
Find if one or more substring has a particular property.
Determine the number of substrings that meet specific criteria.
Create a new String with the characters reversed.
Activity 4.3.1¶
You will write 3 programs that will do the following:
Write a program that will remove every other letter within a string.
Write a second program that will remove vowels from a String.
Write a third program that will replace every instance of d,b,p and q with a random d,b, p or q.
Activity 4.3.2¶
wordCount and vowelCount Write an algorithm that will ask the user for a phrase and return the number of words and vowels. HINT: the number of words is the number of spaces + 1.
Sample Output:
Enter a phrase:
This phrase has eight words and twelve vowels.
Words: 8
Vowels: 12
Hexidecimal The hexadecimal (hex) number system uses 16 symbols, 0-9 and A-F (or a-f). Write a program to verify a hex string. The program shall prompt user for a hex string; and decide if the input string is a valid hex string.
Sample Output:
Enter a hex string:
123aBc
"123aBc" is a hex string
Enter a hex string:
123aBcx
"123aBcx" is NOT a hex string
4.4 Nested Iteration¶
Goals
Represent nested iterative processes.
Determine code that would be used to complete code segments.
A nested iteration occurs when we have a loop inside of another loop, similar to nested conditional statements back in Unit 3. Here is the general structure:
//nested iteration with three loops
loopOne {
do something
loopTwo {
do something
loopThree {
do something
}
}
}
/* The outer loop is a for loop that increments whenever a prime number is
found until we get to n prime numbers. The middle loop is a while loop that
increments the number being checked until it becomes a prime number. Finally,
the inner loop is a for loop that checks all possible divisors to see if the
number is a prime number or not. */
When a loop is nested inside another loop, all of the iterations of the inner loop must be completed until the next iteration of the outer loop starts. If there is a break statement inside the inner loop, then it only takes effect in the current iteration of the outer loop. When the next iteration of the outer loop starts, the inner loop starts all over again. If there are two nested for loops without break statements, and the outer loop runs x times, and the inner loop runs y times for every iteration of the outer loop, then the inner loop will run x*y times. This can be extended to situations where there are more than 2 nested loops. The total number of times the innermost loop is run is the product of the number of times that each loop runs per iteration.
In the while loop, we assume that the number is prime, but once the number is found to be not prime in the for loop, the for loop breaks and the boolean notPrime is set to true. If the number is actually not prime, notPrime remains false and the while loop exits.
Example: Printing a Triangle using asterisks
public static void main(String[] args) {
int n = 5;
for (int outer = 0; outer < n; outer++) {
for (int inner = outer; inner < n; inner++) {
System.out.print("*");
}
System.out.println();
}
Sample Output:
*****
****
***
**
*
Explanation of Code
This is a nested iteration with two loops. In the first loop, we go from 0 to n in order to have n rows in the output. In the second loop, we start from the row number and print n-row number of stars for the row. Once we exit the second loop, we print an empty line, i is incremented by one, and we enter the second loop to print the stars for the next line.
Example: Printing a Number Triangle
public static void main(String [] args) {
int n = 5;
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
System.out.print(i+j);
}
System.out.println();
}
Sample Output:
01234
2345
456
67
8
Explanation of Code
This is essentially the same code as earlier, except now we print out the sum of the row and column indices. This will allow us to demonstrate the use of break and continue in the next two examples.
Example: Break in Nested Loops
public static void main(String [] args) {
int n = 5;
for (int outer = 0; outer < n; outer++) {
for (int inner = outer; inner < n; inner++) {
if (outer == 3 && inner == 3) {
break;
}
System.out.print(outer+inner);
}
System.out.println();
}
Sample Output:
01234
2345
456
8
Explanation of Code
Notice that this time, because we told the program to break when it reaches the fourth row (when i = 3, since Java uses zero-based indexing) and tries to print the first number on that row (since j is always set to the row index when we start a new row), it completely breaks out of the second loop so nothing is printed in the fourth row. Once the program breaks out of the second loop, the first loop iterates by one and the program prints the fifth row the same way it did in the example above.
Example: Continue in Nested Loops
public static void main(String [] args) {
int n = 5;
for (int outer = 0; outer < n; outer++) {
for (int inner = outer; inner < n; inner++) {
if (outer == 3 && inner == 3) {
continue;
}
System.out.print(outer+inner);
}
System.out.println();
}
Sample Output:
01234
2345
456
7
8
Explanation of Code
This time, instead of using a break, we used a continue. This means that we didn’t completely break out of the second loop. We just skipped the iteration that happens when j is 3. (It doesn’t print 6.) The second loop continues, iterating j to 4 and printing the 7. Then j is incremented again to be 5, but since that is not less than n (which is also 5), we exit the second loop normally. Once we exit the second loop, we move on to the fifth row, which is printed normally. Pay careful attention to the Break in Nested Loops example and the Continue in Nested Loops example, since they illustrate the important difference between break and continue. Break completely exits the loop it is called in; continue just skips the current iteration of the loop it is called in.
4.5 Informal Code Analysis¶
Goal
Determine the number of times a code segment will execute.
What is Informal Code Analysis?
Informal code analysis is a process where you will manually check your program line by line. You may also know this as code tracing. Successful code tracing requires you to go through the code line by line, notating of how many times the code is executed, all variable values, and what is output produced to the console. This is a very important skill to learn!
Debugging
Another part of code tracing is debugging. Debugging are syntax or logic errors that prevents your code from executing as intended. With debugging, you have a panel (located in Tools in replit and Debug Console in VSCode) that displays the program values running in real-time as the program is being executed. When we use the debugging panel, you can even sometimes change the variable values to see what may happen to the code as well. We can also have breakpoints in debugging as well. These breakpoints are points allow you to stop at given sections of the program. This is useful when you want to see the values at a certain points in the code. After, you go line-by-line through the code you will see how the variables change or see how the variables change after every iteration of a loop.
Hand-Tracing Tool