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Recursion. Functions – reminder A function can call other functions. Return causes the execution...

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Page 1: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursion

Page 2: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Functions – reminder

A function can call other functions. Return causes the execution of the function to

terminate and returns a value to the calling function.

The type of the value returned must be the same as the return-type defined for the function.

return-type name(argType1 arg1, argType2 arg2, …) {function body;return value;

}

Page 3: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

A recursive definition

C functions can also call themselves! However, usually not with the same

parameters (why?) Some functions can be defined using

smaller occurrences of themselves.Such a definition is called a “recursive

definition” of a function.

Page 4: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive calling

Example:void func(int n){

putchar(`*`);func(n);

}Infinite series of *What is the problem ?Look for other problem …

Page 5: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Factorial

By definition : n! = 1*2*3*… *(n-1)*n

Thus, we can also define factorial the following way: 0! = 1 n! = n*(n-1)! for n>0

(n-1)!

*n

Page 6: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Example - factorial

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);

}

int factorial(int n){ int fact = 1; while (n >= 1) {

fact *=n; n--;

} return fact;}

Page 7: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Conclusions for Recursive calling

Every recursive function has a “boundary condition”. The function stops calling itself when it is satisfied.

Page 8: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

Page 9: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…4*…

Page 10: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

Page 11: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

Page 12: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…3*…

Page 13: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…

Page 14: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…

Page 15: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…2*…

Page 16: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…

FactRec(1)n

1

Returns…

Page 17: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…

FactRec(1)n

1

Returns…

Page 18: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…

FactRec(1)n

1

Returns…1

Page 19: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…

FactRec(2)n

2

Returns…2*1

Page 20: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…

FactRec(3)n

3

Returns…3*2

Page 21: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive factorial – step by step

int factRec(int n){ if (n==0 || n==1) return 1;

return n*factRec(n-1);}

FactRec(4)n

4

Returns…4*6

Page 22: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

1הדפסת מספרים- דוגמא

#include <stdio.h>void print1(int n){

if (n>=0){printf("%d

",n);print1(n-1);

{{void main(){

int i = 3;print1(i);putchar('\n');

{

3 2 1 0

Page 23: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

2הדפסת מספרים- דוגמא

#include <stdio.h>void print2(int n){

if (n>=0){print2(n-1);printf("%d

",n);{

{void main(){

int i = 3;print2(i);putchar('\n');

{

0 1 2 3

Page 24: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

3הדפסת מספרים- דוגמא

#include <stdio.h>void print3(int n){

if (n>=0){printf("%d ",n);print3(n-1);printf("%d ",n);

{{void main(){

int i = 3;print3(i);putchar('\n');

{

3 2 1 0 0 1 2 3

Page 25: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

4הדפסת מספרים- דוגמא

#include <stdio.h>void print4(int n){

if (n>=0){print4(n-1);printf("%d ",n);print4(n-1);

{{void main(){

int i = 3;print4(i);putchar('\n');

{

0 1 0 2 0 1 0 3 0 1 0 2 0 1 0

Page 26: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Another example - power

Xy = x*x*…*x

Recursive definitions (assume non-negative y):

Base: x0=11. Xy = X*(Xy-1)

2. Xy = (Xy/2)2 (for even y’s only)

y times

Page 27: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Fibonacci Series

Fibonacci definition: n0 = 0

n1 = 1

nn = nn-1 + nn-2

0 1 1 2 3 5 8 13 21 34 55 …

Page 28: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Fibonacci Iterative

void fibonacci(int n) { int Fn, Fn1, Fn2, ind;  Fn2 = 0 ;

Fn1 = 1 ; Fn = 0 ;

if ( n == 1 )Fn = 1 ;

for (ind=2 ; ind <= n ; ind++){ Fn = Fn1 + Fn2; Fn2 = Fn1;

Fn1 = Fn;}

printf("F(%d) = %d \n", n, Fn);} 

Page 29: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Fibonacci Recursive

fibonacci(1)

fibonacci(5)

fibonacci(4) fibonacci(3)

fibonacci(3) fibonacci(2) fibonacci(2)

fibonacci(1)

fibonacci(2) fibonacci(1) fibonacci(1)

fibonacci(0)

fibonacci(0) fibonacci(1) fibonacci(0)

int fibonacci(int n) { if (n==0)

return 0; if (n==1)

return 1; return fibonacci(n-1) + fibonacci(n-2);}

Page 30: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

Page 31: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

Page 32: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

Page 33: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

Page 34: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

2*…

y

5

Page 35: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

y

4

Page 36: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

y

4

Page 37: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

y

4

Page 38: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

Page 39: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

y

2

Page 40: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

y

2

Page 41: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

y

2

Page 42: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

Page 43: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

y

1

Page 44: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

y

1

Page 45: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

y

1

Page 46: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

y

1

Page 47: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

2*…

y

1

Page 48: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

2*…

y

1

rec_pow(2, 0)x

2

Returns…

y

0

Page 49: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

2*…

y

1

rec_pow(2, 0)x

2

Returns…

y

0

Page 50: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

2*…

y

1

rec_pow(2, 0)x

2

Returns…

1

y

0

Page 51: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(…)

y

2

rec_pow(2, 1)x

2

Returns…

2*1

y

1

Page 52: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(…)

y

4

rec_pow(2, 2)x

2

Returns…

square(2)

y

2

Page 53: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

y

5

rec_pow(2, 4)x

2

Returns…

square(4)

y

4

Page 54: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

rec_pow – step by step

int rec_pow(int x, int y){if (y == 0)

return 1;if (y%2 == 0)

return square(rec_pow(x,y/2));else

return x*rec_pow(x,y-1);}

rec_pow(2, 5)x

2

Returns…

2*16

y

5

Page 55: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Exercise

Write a program that receives two non-negative integers and computes their product recursively.

Not * multiple operator !!

Hint: Notice that the product a*b is actually a+a+…+a (b times).

Page 56: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Solution

int recMult( int x, int y ) {if( x == 0)

return 0;return y + recMult( x-1,y);

{

Page 57: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Exercise

Given the following iterative version of sum-of-digits calculation

Find the recursive definition of this function

(don’t forget the base case!)

int sum_digits(int n){int sum = 0;while (n > 0) {

sum += n%10;n = n/10;}return sum;

}

Page 58: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Solution

int sumOfDigits( int x ) {if( x < 0)

x *= -1;if( x == 0 )

return 0;else

return x % 10 + sumOfDigits( x / 10 );

}

Page 59: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

More uses

Recursion is a general approach to programming functions.

Its uses are not confined to calculating mathematical expressions!

For example : write a function that finds the max member in an array of integer.

Page 60: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Solution

int rec_max(int arr[ ], int size){int rest;if (size == 1)

return arr[0];else {

rest = rec_max(arr+1, size-1); if (arr[0] > rest) return arr[0];else return rest;

}}

Page 61: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

חיפוש בינארי

int BinarySearch(int arr[],int x, int left, int right) { int middle;if(left>right) return -1; else { middle=(left+right)/2); if(arr[middle]==x)

return middle; else if(x < arr[middle])

return BinarySearch(arr,x,left,middle-1); else return

BinarySearch(arr,x,middle+1,right); }

}

Page 62: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Towers of Hanoi

The Towers of Hanoi problem consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following rules: Only one disk may be moved at a time. Each move consists of taking the upper disk from

one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.

No disk may be placed on top of a smaller disk.

Page 63: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Towers of Hanoi

Page 64: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive Solution

To move n disks from peg A to peg C: move n−1 disks from A to B. This leaves disk

#n alone on peg A move disk #n from A to C move n−1 disks from B to C so they sit on

disk #n

Page 65: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Recursive Solution - Function

void hanoi(int x, char from, char to, char aux){ if(x==1){

printf("Move Disk From %c to %c\n", from, to);

}else {

hanoi(x-1,from,aux,to);printf("Move Disk From %c to %c\n",

from, to);hanoi(x-1,aux,to,from);

}}

Page 66: Recursion. Functions – reminder A function can call other functions. Return causes the execution of the function to terminate and returns a value to the.

Scope of variables - reminder

A variable declared within a function is unrelated to variables declared elsewhere.

A function cannot access variables that are declared in other functions.


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