RECURSION IN DSA OR RECURSIVE FUNCTIONS, Slides of Data Structures and Algorithms

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Data Structure & Algorithms

Lecture 8

Recursion

Introduction

• In C++, any function can call another function.
• A function can even call itself.
• When a function call itself, it is making a recursive call. - Recursive Call - A function call in which the function being called is the same as the one making the call.
• Recursion is a powerful technique that can be used in

the place of iteration(looping).

- Recursion

Recursive Definition

- A definition in which something is defined in terms

of smaller versions of itself.

• To do recursion we should know the followings - Base Case: - The case for which the solution can be stated non-recursively - The case for which the answer is explicitly known. - General Case: - The case for which the solution is expressed in smaller version of itself. Also known as recursive case.

Example (Recursive Power Function)

• Now lets suppose that X=3 and N=
• Now we can simplify the above equation as
• So the base case in this equation is

int Power ( int x , int n ) { if ( n == 1 ) return x; //Base case else return x * Power (x, n-1); // recursive call }

Factorial- a simple recursion

Recursive function: when we write a function in a simpler form of itself

Example 2 (Recursive Factorial Function)

- Factorial definition

n! = n × n-1 × n-2 × n-3 × … × 3 × 2 × 1 0! = 1

- To calculate factorial of n - Base case - If n = 0, return 1 - Recursive step - Calculate the factorial of n- - Return n × (the factorial of n-1)

Evaluation of Factorial Example

To evaluate Factorial(3) evaluate 3 * Factorial(2) To evaluate Factorial(2) evaluate 2 * Factorial(1) To evaluate Factorial(1) evaluate 1 * Factorial(0) Factorial(0) is 1 Return 1 Evaluate 1 * 1 Return 1 Evaluate 2 * 1 Return 2 Evaluate 3 * 2 Return 6

Recursive Programming

The Runtime Stack during Recursion

• To understand how recursion works at run time, we need to understand what happens when a function is called.
• Whenever a function is called, a block of memory is allocated to it in a run-time structure called the stack.
• This block of memory will contain
  • the function’s local variables,
  • local copies of the function’s call-by-value parameters,
  • pointers to its call-by-reference parameters , and
  • a return address, in other words where in the program the function was called from. When the function finishes, the program will continue to execute from that point.

Stack Frames

*** .This is how recursion is implemented ***

int main() { cout << factorial(4); return 0; }

int factorial(int n) { int result; if ((n == 1) || (n == 0)) return 1; else { result = n * factorial(n-1); return result; } {

General System Stack

stack

stack

main frame

Fact: return=

200 n=4,result=

General System Stack

stack

stack

main frame

Fact: return=

200 n=4,result=

Fact: return=

300 n=3,result=

General System Stack

stack

stack

main frame

Fact: return=

200 n=4,result=

Fact: return=

300 n=3,result=

Fact: return=

400 n=2,result=

Fact: return=

500 n=1,result=

()int main } ;cout << factorial(4) ;return 0 {

int factorial(int n) } ;int result if ((n == 1) || (n == 0)) ;return 1 } else ;result = n * factorial(n-1) ;return result