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- 1. See through C Module 1 Stack and Recursion Tushar B Kute http://tusharkute.com
- 2. Overview Subjects: • Stacks – Structure – Methods – Stacks and Method – Calls • Recursion – Principle – Recursion and Stacks – Examples
- 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. Stacks: Properties Possible actions: • PUSH an object (e.g. a plate) onto dispenser • POP object out of dispenser
- 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. 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. 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. 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. 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. 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. Applications using a Stack Examples: • Finding Palindromes • Bracket Parsing • RPN • RECURSION !
- 12. RecursionRecursion
- 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. RecursionRecursion When you turn that into a program, you end up with functions that call themselves: Recursive Functions
- 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. 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. int factorial(int a){ if (a==0) return(1); else return(a * factorial( a-1)); } Tracing the example
- 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 !
- 19. int factorial(int a){ if (a==1) return(1); else return(a * factorial( a-1)); } Watching the Stack a = 5 Return to L4 a = 4 Return to L4 a = 3 Return to L4 a = 2 Return to L4 a = 1 After 4th recursion a = 5 Return to L4 a = 4 Return to L4 a = 3 Return to L4 a = 2*1 = 2 a = 5 Return to L4 a = 4 Return to L4 a = 3*2 = 6 a = 5 Return to L4 a = 4*6 = 24 a = 5*24 = 120 Result
- 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. 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. Recursion does not terminate properly: Stack Overflow ! Common Programming Error
- 23. Examples: Fractal Tree http://id.mind.net/~zona/mmts/geometrySection/fractals/tree/treeFractal.html
- 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. Thank you This presentation is created using LibreOffice Impress 3.6.2.2

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