Define a class to overload the method generate() with the following variations:

1. void generate(int n, char ch) — Prints a pattern of n rows based on the value of ch:

   • If ch is '*', print a pattern of stars (*).
     n = 5

   *
   * *
   * * *
   * * * *
   * * * * *
   

   • If ch is 'N', print a pattern of numbers.
     n = 5

   1
   2 2
   3 3 3
   4 4 4 4
   5 5 5 5 5
   

   • For any other value of ch print Invalid Input.

2. double generate(int n) — Calculates and returns the sum of the following series:
   1 - $\dfrac{1}{2}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ ….. to n terms

3. double generate(double p, double q, double r) — Calculates and returns the value of z, where:
   z = p² + q² - r²

public class KboatOverload
{
    _______(1)_________ {
        if (ch != '*'
            && Character.toLowerCase(ch) != 'n') {
            System.out.println("Invalid Input");
        }
        else {
            _______(2)_________
                _______(3)_________
                    _______(4)_________
                        System.out.print("* ");
                    }
                    else {
                        System.out.print(i + " ");
                    }
                }
                System.out.println();
            }
        }
    }
    
    double generate(int n) {
        int a = 1;
        double sum = 0;
        _______(5)_________
            double t = _______(6)_________
            t *= a;
            _______(7)_________
            a *= -1;
        }
        return sum;
    }
    
    _______(8)_________ {
        double z = _______(9)_________
        _______(10)_________
    }
}

1. void generate(int n, char ch)
2. for (int i = 1; i <= n; i++) {
3. for (int j = 1; j <= i; j++) {
4. if (ch == '*') {
5. for (int i = 1; i <= n; i++) {
6. 1.0 / i;
7. sum += t;
8. double generate(double p, double q, double r)
9. (p * p) + (q * q) - (r * r);
10. return z;

Explanation

public class KboatOverload
{
    void generate(int n, char ch) {
        if (ch != '*'
            && Character.toLowerCase(ch) != 'n') {
            System.out.println("Invalid Input");
        }
        else {
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= i; j++) {
                    if (ch == '*') {
                        System.out.print("* ");
                    }
                    else {
                        System.out.print(i + " ");
                    }
                }
                System.out.println();
            }
        }
    }
    
    double generate(int n) {
        int a = 1;
        double sum = 0;
        for (int i = 1; i <= n; i++) {
            double t = 1.0 / i;
            t *= a;
            sum += t;
            a *= -1;
        }
        return sum;
    }
    
    double generate(double p, double q, double r) {
        double z = (p * p) + (q * q) - (r * r);
        return z;
    }
}

Variable Description Table

Method: void generate(int n, char ch)

Method: double generate(int n)

Method: double generate(double p, double q, double r)

Program Explanation

Let's go through the Java program step by step to understand how it works:

Method 1: generate(int n, char ch)

1. Input Validation:

• The method takes two parameters: an integer n (the number of rows) and a character ch (which determines the type of pattern).
• The method initially checks if the character ch is neither an asterisk ('*') nor the letter 'N'.
  • This condition is evaluated using if (ch != '*' && Character.toLowerCase(ch) != 'n').
  • If the character ch does not match '*' or 'n', it prints "Invalid Input" and exits the method because the patterns are defined only for these characters.

2. Pattern Generation:

• If ch is '*' or 'N', the method proceeds to generate a pattern involving multiple rows, based on the number n.

3. Nested Loop Construction:

• Outer Loop:

  • for (int i = 1; i <= n; i++) iterates from 1 through n, each iteration representing a new row of the pattern.
  • The value of i signifies the current row number and dictates how many elements will be printed in that row.

• Inner Loop:

  • for (int j = 1; j <= i; j++) iterates from 1 to i, determining the number of characters to be printed in the i-th row.
  • The inner loop runs precisely i times for each iteration of the outer loop, allowing for the growing number of elements in the pattern across consecutive rows.

4. Pattern Decision:

• Star Pattern (ch == '*'):

  • If ch is an asterisk ('*'), the inner loop prints a star followed by a space ("* "), using System.out.print("* ");.
  • This creates a symmetric triangular pattern of stars with each row i having i stars.

• Number Pattern (ch == 'N'):

  • If ch is the letter 'N' (case-insensitive check is performed with Character.toLowerCase(ch)), the inner loop prints the current row number i repeatedly, i times, followed by a space.
  • Each element in the row is generated using System.out.print(i + " ");. This creates a symmetric triangular pattern of numbers.

5. Row Termination:

• After the inner loop completes its cycles for one row, System.out.println(); is used to move the cursor to the next line before continuing to the next iteration of the outer loop, presenting each row on a new line.

Method 2: generate(int n)

1. Initialization:

• The method initializes an integer variable a to 1. This variable is used to alternate the sign of each term in the series.
• A double variable sum is initialized to 0. This will hold the accumulated sum of the series.

2. Iteration Over Terms:

• for (int i = 1; i <= n; i++): The loop iterates from 1 to n. Each iteration corresponds to computing one term of the series.
• The variable i represents the current term index in the series.

3. Term Calculation:

• double t = 1.0 / i;: This calculates the reciprocal of the current index i, which is the base value of the current term in the series.
• t *= a;: Multiplies the base value by a, effectively alternating the sign of t:
  • When a is 1, the term remains positive.
  • When a is -1, the term becomes negative.
• The alternation in signs achieves the series' structure of alternating addition and subtraction.

4. Accumulation of the Series:

• sum += t;: Adds the current term t to the cumulative sum. Since the terms alternate between positive and negative based on a, the overall effect is an accumulation according to the series pattern.

5. Prepare for the Next Term:

• a *= -1;: Flips the sign of a for the next term. This ensures the alternation continues correctly through the iterations.

6. Return the Result:

• After the loop completes, return sum; provides the final computed sum of the series to n terms.

Method 3: generate(double p, double q, double r)

• This method calculates the expression (p * p) + (q * q) - (r * r).
• It squares p and q, adds these squares together, and subtracts the square of r from this sum.
• The result of this calculation is stored in the variable z, which is then returned as the output.

Output