Divide and Conquer ExampleAssume you want to print a hollow square of “*”s with the length of each side read into the variable s.The square might look like* * * * ** ** ** ** * * * *In pseudo code this might bePrint a line of starsPrint the middle linesPrint a line of starsOne may want a mainline program that looks likeint main(){ int s;cout << " enter the length of a side ";cin >>s; //Read in length of sideprintstars(s); //do top lineprintmiddle(s); //call function printstars(s); //do bottom linereturn 0;}Writing subroutines with no return value:1Begin with function header:void printstars(int s)Continue with body:{// this subroutine prints a rows of *’sfor (int j = 1; j <=s; j++)cout << "*";cout << endl;}Similarly for the printmiddle function:void printmiddle(int s){for( int i=2; i <=s-1; i ++){ //print row icout << "*"; //print left hand *for ( int j=1; j <=s-2; j++)cout << " "; //print middle blankscout << "*" << endl; //print right hand *}}2Before int main() we need to tell the compiler what are the input and outputs of our function, we need a function prototype void printstars(int s); //function prototypevoid printmiddle(int s);The structure of the program would then be:void printstars(int s); //function prototypesvoid printmiddle(int s);int main(){ int s;cout << " enter the length of a side ";cin >>s;printstars(s); //do top lineprintmiddle(s);printstars(s); // do bottom line; return 0;}void printstars(int s){ for (int j=1;j <=s; j++)cout << "*";cout << endl;}void printmiddle(int s){ for(int i=2; i <=s-1; i ++){ cout << "*"; //print left hand *for (int j=1; j <=s-2; j++)cout << " "; //print middle blankscout << "*" << endl; //print right hand *}}3The inner loop of printmiddle looks like printstars with a ‘ ‘ rather than a ‘*’. Could we make another subroutine that makes whatevercharacter one wishes as invoid printchar(int s, char c){for (int j=1;j <=s; j++) //print a line of whatever iscout << c; //in c}The printmiddle would then bevoid printmiddle(int s){for(int i=2; i <=s-1;i ++){cout << "*"; //print left hand *printchar(s-2,' '); //print blankscout << "*" << endl; //print right hand *}}and prinstars would not be needed and the mainline would beint main(){ int s;cout << " enter the length of a side ";cin >>s;printchar(s,'*'); //do top linecout <<endl;printmiddle(s);printchar(s,'*'); // do bottom line;cout <<endl;return 0; }Exercises in interpreting and writing functions4For the following function headers, what is the type of the return value, and the number and types of the parameters1. double average(double a, double b, double c)2. double mpg(double miles, double gas)3. float getcelcius(float fahrenheit)4. int factorial(int n)5. void factorialprint(int n)6. void oddeven(int n)What are the function prototypes for the above headers?Sample bodies:1. double average(double a, double b, double c)double average(double a, double b, double c){return (a+b+c)/3.0;}2. double mpg(double miles, double gas)5double mpg(double miles, double gas){ if (gas!=0.0)return miles/gas;elsereturn 0;}3. double getcelcius(float fahrenheit)double getcelcius(float fahrenheit){return 5.0/9.0*(fahrenheit-32);}4. int factorial(int n);int factorial(int n){int prod=1;for (int i =1; i<=n); i++)prod=prod*i;return prod;}5. void factorialprint(int n);void factorialprint(int n){int prod=1;for (int i =1; i<=n; i++)prod=prod*i;cout << " the factorial is " <<prod;}6. void oddeven(int n)void oddeven(int n){6if(n%2 ==0)cout << n << " is even" << endl;elsecout << n << " is odd" << endl;}How these might be used:main(){cout << "average of 10 20 and 30 is "<< average(10.0,20.0,30.0);oddeven(23); cout << " 10 factorial is "<< factorial(n);factorialprint(9);cout << "miles per gallon is " <<mpg(250.0,10.4);return 0; }Write function headers for1. Findabs that accepts a double precision number and returns the numbers absolute value.2. mult that accepts two floating point numbers and returns their product.73. powfun that raises an integer passed to it to the power passed toit and returns the result4. table that produces a table of the squares and cubes of the numbers from 1 to 10.5. Sigma that returns the sum of the numbers from 1 to n, where n is passed to it.6. Totalamount that has four parameters: quarters, dimes, nickles, and pennies and returns the total amount of money in a piggy bank.7. max that computes the maximum of two numbers.max can be used to find the maximum of n values that are read in as follows:int a, maxn;cin >> maxn; //the first value is put into maxfor (int I=2, I<=n, I++){cin >>a;maxn=max(a,maxn)}Exercises for call by value and call by reference1.Consider the code:void swap(int &a, int & b){int temp;temp =a;a=b;b=temp; }8what does the following print ?a=2;b=4;swap(a, b);cout <<a<<b;What does this code do?cin >>a>>b>>c;if (a>b) swap(a,b);if(b>c) swap(b,c);if (a>b) swap(a,b);2.Consider the code:void sum(int a, int & b){ a=a+b;b=a+b;} what does the following print?:a=2;b=4;sum(a,b);cout <<a <<b;3. Consider the code:void sum(int &a, int & b){ a=a+b;b=a+b;} what does the following print?:a=2;b=4;sum(a,b);cout <<a <<b;94. Consider the code:void sum(int &a, int b){ a=a+b;b=a+b;} what does the following print?:a=2;b=4;sum(a,b);cout <<a <<b;5. Consider the code:int sum(int &a, int b){ a=a+b; return a+b;} what does the following print?:a=2;b=4;cout