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# Module 01 Stack and Recursion

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The presentation given at PCCOE, Nigdi, Pune by Prof. Tushar B Kute in workshop on "See through C".
http://tusharkute.com

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### Module 01 Stack and Recursion

1. 1. See through C Module 1 Stack and Recursion Tushar B Kute http://tusharkute.com
2. 2. Overview Subjects: • Stacks – Structure – Methods – Stacks and Method – Calls • Recursion – Principle – Recursion and Stacks – Examples
3. 3. Stack: Properties Answer: They both provide LIFO (last in first out) Structures 1 2 3 4 5 6 1 2 3 4 5 6
4. 4. Stacks: Properties Possible actions: • PUSH an object (e.g. a plate) onto dispenser • POP object out of dispenser
5. 5. Stacks: Definition Stacks are LIFO structures, providing • Add Item (=PUSH) Methods • Remove Item (=POP) Methods They are a simple way to build a collection • No indexing necessary • Size of collection must not be predefined • But: extremely reduced accessibility
6. 6. A look into the JVM 1 int main( ) { 2 int a = 3; 3 int b = times(a); 4 printf(“%d“, b); 5 } 6 int times(int a) { 7 int b = 5; 8 int c = a * b; 9 return (c); 10 } a = 3 a = 3 b Return to LINE 3 b = 5 c = 15
7. 7. A look into the compiler ... 9 return (c); 10 ... a = 3 a = 3 b Return to LINE 3 b = 5 c = 15 15 a = 3 b Return to LINE 3 a = 3 b c = 15 Return to LINE 3 Temporary storage Clear Stack
8. 8. A look into the CompilerA look into the 1 int main() { 2 int a = 3; 3 int b = times(a); 4 printf(“%d“, b); 5 } a = 3 b c = 15 Temporary storage a = 3 b = 15
9. 9. A look into the CompilerA look into the 1 int main() { 2 int a = 3; 3 int b = times(a); 4 printf(“%d“, b); 5 } clear stack from local variables
10. 10. A look into the CompilerA look into the Important: Every call to a function creates a new set of local variables ! These Variables are created on the stack and deleted when the function returns
11. 11. Applications using a Stack Examples: • Finding Palindromes • Bracket Parsing • RPN • RECURSION !
12. 12. RecursionRecursion
13. 13. RecursionRecursion • Sometimes, the best way to solve a problem is by solving a smaller version of the exact same problem first • Recursion is a technique that solves a problem by solving a smaller problem of the same type • A function that is defined in terms of itself
14. 14. RecursionRecursion When you turn that into a program, you end up with functions that call themselves: Recursive Functions
15. 15. RecursionRecursion int fact (int a) { if (a==1) return(1); else return (a * fact( a-1)); } It computes f! (factorial) What’s behind this function ?
16. 16. Factorial: a! = 1 * 2 * 3 * ... * (a-1) * a Note: a! = a * (a-1)! remember: ...splitting up the problem into a smaller problem of the same type... a! a * (a-1)! Factorial
17. 17. int factorial(int a){ if (a==0) return(1); else return(a * factorial( a-1)); } Tracing the example
18. 18. int factorial (int a){ if (a==1) return(1); else return(a * factorial( a-1)); } Watching the Stack a = 5 a = 5 a = 5 Return to L4 a = 4 Return to L4 a = 4 Return to L4 a = 3 Return to L4 a = 2 Return to L4 a = 1 Initial After 1 recursion After 4th recursion … Every call to the method creates a new set of local variables !
20. 20. Problems that can be solved by recursion have these characteristics: • One or more stopping cases have a simple, nonrecursive solution • The other cases of the problem can be reduced (using recursion) to problems that are closer to stopping cases • Eventually the problem can be reduced to only stopping cases, which are relatively easy to solve Follow these steps to solve a recursive problem: • Try to express the problem as a simpler version of itself • Determine the stopping cases • Determine the recursive steps Properties of Recursive Functions
21. 21. The recursive algorithms we write generally consist of an if statement: IF the stopping case is reached solve it ELSE split the problem into simpler cases using recursion Solution Solution on stack Solution on stack Solution on stack
22. 22. Recursion does not terminate properly: Stack Overflow ! Common Programming Error
23. 23. Examples: Fractal Tree http://id.mind.net/~zona/mmts/geometrySection/fractals/tree/treeFractal.html
24. 24. Examples: The 8 Queens Problem http://mossie.cs.und.ac.za/~murrellh/javademos/queens/queens.html Eight queens are to be placed on a chess board in such a way that no queen checks against any other queen
25. 25. Thank you This presentation is created using LibreOffice Impress 3.6.2.2
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