2. Recursion Function calling itself

3. Introduction
Recursive functions are those function which are call themselves repetitively.
The function call themselves repetitively until certain condition is satisfied.
The recursive function have following types of statements:
A statement or condition to determine if the function is calling itself again.
Function call which should have argument
Conditional statement(if-else)
A return statement.

4. Simple Example
main() { int i=2; printf(“%d”,i); main(); }

5. Non-Recursive Function for Factorial

6. Computing Factorial Using Recursion
factorial(0) = 1; //Basis or Base case
factorial(n) = n*factorial(n-1); // Inductive Step

7. Computing Factorial factorial(3) factorial(0) = 1;
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3)

8. Computing Factorial factorial(3) = 3 * factorial(2) factorial(0) = 1;
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)

9. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))

10. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))
= 3 * ( 2 * (1 * factorial(0)))

11. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))
= 3 * ( 2 * (1 * factorial(0)))
= 3 * ( 2 * ( 1 * 1)))

12. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))
= 3 * ( 2 * (1 * factorial(0)))
= 3 * ( 2 * ( 1 * 1)))
= 3 * ( 2 * 1)

13. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))
= 3 * ( 2 * (1 * factorial(0)))
= 3 * ( 2 * ( 1 * 1)))
= 3 * ( 2 * 1)
= 3 * 2

14. Computing Factorial factorial(3) = 3 * factorial(2)
animation
Computing Factorial
factorial(0) = 1;
factorial(n) = n*factorial(n-1);
factorial(3) = 3 * factorial(2)
= 3 * (2 * factorial(1))
= 3 * ( 2 * (1 * factorial(0)))
= 3 * ( 2 * ( 1 * 1)))
= 3 * ( 2 * 1)
= 3 * 2
= 6

15. Trace Recursive factorial
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Trace Recursive factorial
Executes factorial(4)

16. Trace Recursive factorial
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Trace Recursive factorial
Executes factorial(3)

17. Trace Recursive factorial
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Trace Recursive factorial
Executes factorial(2)

18. Trace Recursive factorial
animation
Trace Recursive factorial
Executes factorial(1)

19. Trace Recursive factorial
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Trace Recursive factorial
Executes factorial(0)

20. Trace Recursive factorial
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Trace Recursive factorial
returns 1

21. Trace Recursive factorial
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Trace Recursive factorial
returns factorial(0)

22. Trace Recursive factorial
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Trace Recursive factorial
returns factorial(1)

23. Trace Recursive factorial
animation
Trace Recursive factorial
returns factorial(2)

24. Trace Recursive factorial
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Trace Recursive factorial
returns factorial(3)

25. Trace Recursive factorial
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Trace Recursive factorial
returns factorial(4)

26. factorial(4) Stack Trace

27. Fibonacci Numbers
Finonacci series: …
indices:
fib(0) = 0;
fib(1) = 1;
fib(index) = fib(index -1) + fib(index -2); index >=2
fib(3) = fib(2) + fib(1) = (fib(1) + fib(0)) + fib(1) = (1 + 0) +fib(1) = 1 + fib(1) = = 2