Unit 2.9: Developing Algorithms Using Selection and Iteration

Developing algorithms is a core skill in computer science. By combining selection (if statements) and iteration (loops), you can solve a wide variety of complex problems.

Standard Algorithms

The AP CSA framework identifies several "standard" algorithms that every student should be able to implement.

These are the building blocks for more advanced programming.

1. Divisibility and Frequency

This algorithm uses the remainder operator (%) to check if a number is divisible by another and uses a counter variable to track how often a condition is met.

Task: Counting frequencies using the remainder operator.

public class DivisibilityCount {
    public static void main(String[] args) {
        int count = 0;
        // Goal: Count how many numbers between 1 and 100 are divisible by 7
        for (int i = 1; i <= 100; i++) {
            if (i % 7 == 0) {
                count++; // Increment count when the condition is true
            }
        }
        System.out.println("Frequency of numbers divisible by 7: " + count);
    }
}

2. Digit Processing

To process individual digits of an integer, we use % 10 to peel off the last digit and / 10 to remove it. This typically requires a while loop because we continue until the number becomes 0.

Task: Extracting and processing individual digits of a number.

public class DigitProcessor {
    public static void main(String[] args) {
        int number = 12345;
        
        while (number > 0) {
            int digit = number % 10; // 1. Isolate the rightmost digit
            System.out.println("Processing digit: " + digit);
            
            number /= 10; // 2. Remove the processed digit from the number
        }
    }
}

3. Finding a Minimum or Maximum

To find the largest or smallest value in a sequence, initialize a variable to a starting value (like the first input or Integer.MIN_VALUE/MAX_VALUE) and update it whenever a "better" value is found.

Task: Finding the maximum value in a sequence of user inputs.

import java.util.Scanner;

public class MaxFinder {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        // Initialize max to the smallest possible integer 
        int max = Integer.MIN_VALUE; 
        
        for (int i = 0; i < 5; i++) {
            System.out.print("Enter a number: ");
            int num = input.nextInt();
            
            if (num > max) {
                max = num; // Found a new maximum! Update the variable.
            }
        }
        System.out.println("The largest number entered was: " + max);
    }
}

4. Sum and Average

This algorithm uses an accumulator variable to keep a running total. To find the average, divide the total sum by the number of items, ensuring you use type casting to avoid integer division.

Task: Calculating the sum and average of multiple values.

import java.util.Scanner;

public class AverageCalculator {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int sum = 0;
        int count = 5;
        
        for (int i = 0; i < count; i++) {
            System.out.print("Enter a value: ");
            sum += input.nextInt(); // Accumulate the sum
        }
        
        // Use (double) to ensure decimal precision in the result
        double average = (double) sum / count;
        
        System.out.println("Total Sum: " + sum);
        System.out.println("Calculated Average: " + average);
    }
}