PLSQL Program to find Fibonacci Series

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. This sequence has numerous applications in mathematics and computer science. In this article, we will explore how to write a PL/SQL program to find the Fibonacci series efficiently.

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What is the Fibonacci Series?

The Fibonacci sequence follows this pattern:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Mathematically, the formula for Fibonacci numbers is:

F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = 1

PL/SQL provides an efficient way to generate this sequence using loops or recursion.

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PLSQL Program to Generate Fibonacci Series Using a Loop

Below is a PL/SQL program to generate Fibonacci numbers up to a given limit using a loop:

DECLARE
  num1 NUMBER := 0;
  num2 NUMBER := 1;
  temp NUMBER;
  counter NUMBER := 10; -- Change this to generate more terms
BEGIN
  DBMS_OUTPUT.PUT_LINE('Fibonacci Series:');
  DBMS_OUTPUT.PUT_LINE(num1);
  DBMS_OUTPUT.PUT_LINE(num2);
  
  FOR i IN 3..counter LOOP
    temp := num1 + num2;
    DBMS_OUTPUT.PUT_LINE(temp);
    num1 := num2;
    num2 := temp;
  END LOOP;
END;
/

Explanation:

• We initialize num1 as 0 and num2 as 1.
• A loop runs from 3 to the desired count.
• Inside the loop, we calculate the next Fibonacci number and update num1 and num2.

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PLSQL Program to Generate Fibonacci Series Using Recursion

CREATE OR REPLACE FUNCTION fibonacci(n IN NUMBER) RETURN NUMBER IS
BEGIN
  IF n = 0 THEN RETURN 0;
  ELSIF n = 1 THEN RETURN 1;
  ELSE RETURN fibonacci(n-1) + fibonacci(n-2);
  END IF;
END fibonacci;
/

DECLARE
  n NUMBER := 10; -- Change this for more terms
BEGIN
  FOR i IN 0..n-1 LOOP
    DBMS_OUTPUT.PUT_LINE(fibonacci(i));
  END LOOP;
END;
/

Explanation:

• The function fibonacci(n) calculates the Fibonacci number recursively.
• The anonymous block calls this function in a loop to print the sequence.

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Performance Considerations

• Loop-based approach is more efficient as recursion in PL/SQL can lead to stack overflow for large inputs.
• Using a table to store Fibonacci numbers can optimize performance.

CREATE TABLE fibonacci_numbers (term NUMBER, value NUMBER);

DECLARE
  num1 NUMBER := 0;
  num2 NUMBER := 1;
  temp NUMBER;
  counter NUMBER := 10;
BEGIN
  INSERT INTO fibonacci_numbers VALUES (1, num1);
  INSERT INTO fibonacci_numbers VALUES (2, num2);

  FOR i IN 3..counter LOOP
    temp := num1 + num2;
    INSERT INTO fibonacci_numbers VALUES (i, temp);
    num1 := num2;
    num2 := temp;
  END LOOP;
  COMMIT;
END;
/

This approach allows retrieving Fibonacci numbers from the database efficiently:

SELECT * FROM fibonacci_numbers;

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Applications of Fibonacci Series

• Algorithm design (Dynamic Programming, Divide and Conquer)
• Stock market analysis (Fibonacci Retracement)
• Computer graphics (Fractals, Recursive Patterns)
• Nature & science (Golden Ratio, Growth Patterns)

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Conclusion

We have explored multiple PL/SQL programs to find the Fibonacci series using loops, recursion, and database storage. The loop-based approach is optimal for performance, while recursion helps in understanding the logic. Using a database table provides a structured way to store and retrieve values.

Start implementing Fibonacci series in PL/SQL and enhance your SQL skills! 🚀

For more SQL-related discussions, visit our SQL Queries Community. Also, check out this comprehensive guide on Fibonacci Sequence – MathWorld to deepen your understanding of Fibonacci numbers.