Friday, January 26, 2007

"One, demonstrations always crash.

And two, the probability of them crashing goes up exponentially

with the number of people watching."

- Steve Jobs

SELF TEST: Recursion

int factorial(int N){

int ans;

if (N<=1) return 1; //base case

ans=factorial(N-1)*N;

return ans;

}

int main() {

int answer=factorial(4);

cout<<answer;

return 0; }

Stack contents

Example: Binary Searchint BinarySearch(int no, int low,int high, int* iarray);int main(void) {

int num, i, size=15;

int* array=new int[size];

for (i=0; i<size; i++)

array[i]=13*i+4;

for (i=0; i<size; i++)

cout<<array[i]<<" ";

cout<<endl;

cin>>num;

if(BinarySearch(num, 0, size-1, array))

cout<<"found"<<endl;

else

cout<<"not found"<<endl;

return 0; }

Example: Binary Searchint BinarySearch(int no, int low,int high, int* iarray){

if (low>high){

return 0; }

int mid=low+(high-low)/2;

if (no==iarray[mid])

return 1;

else if (no>iarray[mid])

return BinarySearch(no, mid+1, high, iarray);

else

return BinarySearch(no, low, mid-1, iarray);

}

void recFunc(int i){if ((i/2)==0){

cout<<i%2;return;

}recFunc(i/2);cout<<i%2;

}int main(void){

int i;cin>>i;if (i<0){

cout<<"Sorry -ve nos not allowed"<<endl;

exit(1); }recFunc(i);return 0; }

Example Using Recursion: The Fibonacci Series

The Fibonacci series: 1,1,2,3,5,8,13,21,… begins with 0 and 1 and has the property that each subsequent Fibonacci number is the sum of the previous two.

The function to calculate the i-th Fibonacci looks like what?

What would the code for this would look like ?

Example Using Recursion: The Fibonacci Series

int fib(int n){int ans;

if (n<1)

ans= -1; //error condition

else if (1==n)

ans=1;

else if (2==n)

ans=1;

else

ans=fib(n-1)+fib(n-2);

return ans;

}

Recursionbool myFunction(int n, int k);

int main(void){

cout<<myFunction(5678, 4)<<endl;

cout<<myFunction(2359, 5)<<endl;

return 0;

}

bool myFunction(int n, int k){

if (n/10 == 0) return n==k;

else if (n%10 == k ) return true;

else return myFunction(n/10, k);

}

void RecLast(int *a, int i){

if(4==i) return;

*a *=2;

cout<<*a<<" ";

++i;

RecLast(a+1,i); }

int main() {

int i, index=0;

int array[]={1,2,3,4};

RecLast(array, index);

for (i=0; i<4; i++){

cout<<array[i]; }

return 0; }

SELF TEST

void RecFirst(int *a, int i){

if(i==4) return;

++i;

RecFirst(a+1,i);

*a *=2;

cout<<*a<<" "; }

int main() {

int i, index=0;

int array[]={1,2,3,4};

RecFirst(array, index);

for (i=0; i<4; i++){

cout<<array[i]; }

return 0; }

SELF TEST

SELF TEST: What is wrong here?

int fact(int N){

int ans;

ans=fact(N-1)*N;

return ans;

}

int main() {

cout<<fact(4);

return 0;

}

Recursionvoid output(char *s);

int main() {

char str[] = {“stay"};

output(str);

cout<<endl;

return 0; }

void output(char *s) {

if(*s)

output(s+1);

else

return;

cout << *s;

}

Recursion vs. IterationRecursion has many negativesIt repeatedly invokes the mechanism, and

consequently the overhead, of function calls.This can be expensive in both terms of processor

time and memory.

So Why use recursion?Some problems map very nicely to a recursive

solution. Thereby making code writing easier.

Recursion

void H(int topLeftX,int topLeftY,int bottomLeftY,int depth)

(0,0)

y

x

void H(int topLeftX,int topLeftY,int bottomLeftY,int depth)

{int bottomLeftX=topLeftX;int topRightX=topLeftX+(bottomLeftY-topLeftY);int topRightY=topLeftY;int bottomRightX=topRightX;int bottomRightY=bottomLeftY;

if (depth==0) return; //stopping condition

//Code for drawing lines

int oneFourth=(bottomLeftY-topLeftY)/4;

H(topLeftX-oneFourth, topLeftY-oneFourth, topLeftY+oneFourth, depth-1);

H(topRightX-oneFourth, topRightY-oneFourth, topRightY+oneFourth, depth-1);

H(bottomLeftX-oneFourth, bottomLeftY-oneFourth, bottomLeftY+oneFourth, depth-1);

H(bottomRightX-oneFourth, bottomRightY-oneFourth, bottomRightY+oneFourth, depth-1);

}

Defining a new name for existing type

typedef float balance;

balance over_due;

balance is another name for float.

typedef

char wordsb[11][80]={"Mechanics", "this", "help", "please", "is", "writing", "count", "natural", "select", "thought", "" };

int i=1;

while(strcmp(wordsb[i],"")) {

cout<<wordsb[i]<<" ";

i+=3;

}

char *words2[11]={"Mechanics", "this", "help", "please", "is", "writing", "count", "natural", "select", "thought", "" };

int i=1;

while(strcmp(words2[i],""))

{

cout<<words2[i]<<" ";

i+=3;

}

Memory Drawing!

char *words2[11]={"Mechanics", "this", "help", "please", "is", "writing", "count", "natural", "select", "thought", "" };

int i=1;

while(words2[i][0])

{

cout<<words2[i]<<" ";

i+=3;

}

char *words2[11]={"Mechanics", "this", "help", "please", "is", "writing", "count", "natural", "select", "thought", "" };

int i=1;

while(*words2[i])

{

cout<<words2[i]<<" ";

i+=3;

}