INFSCI 0015 Data Structures Lecture 24: Recursion

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INFSCI 0015 - Data StructuresLecture 24
Recursion

• Peter Brusilovsky
• http//www2.sis.pitt.edu/peterb/0015-011/

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Recursive Definitions

• Factorial function can be defined recursively
  (function definition use this function as a part
  of definition)

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Recursive Calculations

• Recursive definition can be used to calculate
  factorial

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Recursive factorial (24.1)

• void main()
• int i
• printf("Enter an integer (non-negative) ")
• scanf("d", i)
• if(i gt 0) printf("d! d\n", i,
  factorial(i))
• int factorial(int n)
• if(n 0)
• return 1
• else
• return (n factorial(n-1))

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How it works? Power Case
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Power C code (Example 24.2)

• void main()
• int a, b
• printf("Enter a and b ")
• scanf("d d", a, b)
• if(b gt 0)
• printf("d power d d\n", a, b, power(a,
  b))
• int power(int base, int exp)
• if(exp 0)
• return 1
• else
• return (base power(base, exp-1))

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Stackframe and system stack

• When one function calls another function in C all
  parameters and return value are transferred via
  system stack
• At each call a stackframe is placed into stack
• Parameters of the call
• Local variable of calling function
• Next statement in the calling function
• Place for a return value

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The process of calling a function

• Calling function pushes stackframe
• Called function
• Gets parameters from the stack
• Performs calculations
• Places return value to the stack
• Transfers control to the next statement
• Calling function
• Restores local variables from the stack
• Uses return value from the stack

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Figure 6-6
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Rules for writing using recursion

• Every recursive call must either solve the
  problem or reduce its size
• Terminal case solving (no calls)
• Base case reducing size (recursive call)
• To make a recursive program
• Identify base case(s) and terminal case(s)
• Combine them (usually with if-else)

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Working with recursive data

• Recursive functions is a good way to work with
  recursive data structures
• struct node
• int data
• struct node link

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PrintReverse and PrintList

• void printList(NODE l)
• / nothing to do with an empty list /
• if(l NULL)
• return
• printf("c ", l-gtdata)
• printList(l-gtlink)
• return
• void printReverse(NODE l)
• / nothing to do with an empty list /
• if(l NULL)
• return
• printReverse(l-gtlink)
• printf("c ", l-gtdata)
• return

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The Towers of Hanoi
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Solution for two disks
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Solution for three disks
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Recursive algorithm

• Algorithm
• Move n-1 disks from source to auxilary
• Move one disk from source to destination
• Move n-1 disks from auxilary to destination
• Function towers(disks, sour, dest, aux)
• towers(n-1, sour, aux, dest)
• move one disk from sour to dest
• tovers(n-1, aux, dest, sour)

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Calls Output Towers (3, A, C, B) Towers
(2, A, B, C) Towers (1, A, C, B) Step 1 Move
from A to C Step 2 Move from A to B Towers
(1, C, B, A) Step 3 Move from C to
B Step 4 Move from A to C Towers (2, B, C,
A) Towers (1, B, A, C) Step 5 Move from B to
A Step 6 Move from B to C Towers (1, A, C,
B) Step 7 Move from A to C
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Homework find greatest common divisor of two
numbers

• Use Euclids algorithm below and write a program
  that inputs two integers and returns their GCD
  using recursive function int gcd(int x, int y)