thursday, january 25, 2007

Thursday, January 25, 2007

"To define recursion, we must first define recursion."

- Anonymous

Remaining Lectures Schedule

Thursday January 25 (Today)Friday January 26Thursday February 1Friday February 2Saturday February 3Tuesday February 6

What is wrong here?

int* function_returns_ptr(void){

int array[8]={1,2,3,4,5,6,7,8};

int *ptrArray=array;

return (ptrArray+4);

}

int main(void){

int *result=function_returns_ptr();

cout<<*result<<endl;

return 0;

}

References

Safer and simpler use of memory addresses are references

When a reference parameter is used, the address of an argument is automatically passed to the function.

Within the function the operations on reference parameter are automatically de-referenced.

With call by reference, the caller gives the called function the ability to directly access the caller’s data and to modify that data if the called function so chooses.

To indicate that a function parameter is passed by reference, simply follow the parameter’s type in the function prototype by an ampersand &.

e.g. void myFunction( int &x);

Calling Functions

int squareByValue(int a);

void squareByReference(int &aref);

Calling Functions

int main() {

int x = 2, z = 4;

cout << "x = " << x << " before squareByValue" ;

squareByValue(x) ;

cout<< "x = " << x << " after squareByValue" ;

cout << "z = " << z << "before squareByReference”;

squareByReference(z);

cout << "z = " << z << " after squareByReference";

return 0;

}

Calling Functions

int squareByValue(int a)

{

return a *= a; //caller's argument not modified

}

void squareByReference(int &cRef)

{

cRef *= cRef; // caller's argument modified

}

Calling Functions

Function to swap two numbers

void swap(int &sa, int &sb){

int temp=sa;

sa=sb;

sb=temp; }

int main() {

int a=3;

int b=5;

cout<<a<<" "<<b<<endl;

swap(a, b);

cout<<a<<" "<<b<<endl;

return 0; }

Calling Functions -II

void f1(int *num) {

cout<<*num<<endl;

num++;

num++;

cout<<*num<<endl;}

int main(void){

int a[8]={1,2,3,4,5,6,7,8};

int *aptr=a;

f1(aptr);

cout<<*aptr<<endl;return 0;} //OUTPUT?

Calling Functions with pointers

1

3

1

Calling Functions with pointers

void f1(int* &num) {

cout<<*num<<endl;

num++;

num++;

cout<<*num<<endl;}

int main(void){

int a[8]={1,2,3,4,5,6,7,8};

int *aptr=a;

f1(aptr);

cout<<*aptr<<endl;return 0;} //OUTPUT?

1

3

3

The most common use of references is in function parameters.

int a=6;

int &b =a;

cout<<b<<" "<<a<<endl;

b=3;


References must be initialized

Reference variables

6 6

3 3

Reference variables

What is wrong here?

int a=6;

int &b=a+4;


Reference variables

A function call ends when Return statement is executed. The closing } brace of the end of

function is reached.

At the end of function call, flow of control returns back to the calling function.

void X() {

int a = 1;

int b = 2;

// T1

Y(a);

// T3

Y(b);

// T5

}

void Y(int p) {

int q;

q = p + 2;

// T2 (first time through), T4 (second time through)

}

Remember the even odd question?

RecursionA recursive function is one that calls itself.

Recursive functions have two partsStopping Condition(s) -- solving the base

case(s).Recursive call -- breaking the problem

down.

Recursion

When a function calls itself, new local variables and parameters are allocated storage on stack and the function is executed with these new variables from the beginning of function.

void PrintFunc(int x){ int y=x-1;if (x<=0)

return;cout<<"In Print Func before recursive call. x="<<x<<endl;PrintFunc(y);cout<<"In Print Func after recursive call. x="<<x<<endl;

}

int main(void){PrintFunc(3);

//...}

Focus on the flow of control

void PrintFunc(int x){ int y=x-1;

if (x<=0) return;cout<<"In Print Func before recursive call. x="<<x<<endl;PrintFunc(y);cout<<"In Print Func after recursive call. x="<<x<<endl;}

x is 3





x is 3

x is 2







x is 3

x is 2

x is 1









x is 3

x is 2

x is 1

x is 0







x is 3

x is 2

x is 1





x is 3

x is 2



x is 3

In Print Func before recursive call. x=3In Print Func before recursive call. x=2In Print Func before recursive call. x=1In Print Func after recursive call. x=1In Print Func after recursive call. x=2In Print Func after recursive call. x=3

int RecFunc(int x){int sum;if(x<=1)

return 1;sum = x*x + RecFunc(x-1);cout<<sum<<endl;return sum;

}

int main(void){int ans;ans=RecFunc(5);cout<<"ans="<<ans<<endl;//...

}

5

14

30

55

ans=55

Recursion vs. IterationSimilarities:

Both iteration and recursion involve repetition:Iteration explicitly uses a repetition structure;recursion achieves repetition through repeated

function calls.

Iteration and recursion each involve a

termination test iteration terminates when the loop condition fails recursion terminates when a base case is

recognized.

Recursion vs. IterationSimilarities:

Both iteration and recursion can occur

infinitely:An infinite loop can occur with iteration,Infinite recursion can occur when the base case is

not reached.

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);

}

thursday, january 25, 2007

Documents

int recfuncint x

int temp

int qq

int sb

int mainvoid

int sumifx5143055ans

int array8

void x