Suppose f(x):R rightarrow R be a function given by Find maximum and minimum of functional values using an algorithm with programming code. Find complexity of the algorithm.

**Step1 :** start

**Step2 :** function declaration of max

**Step3 :** function declaration of min

**Step4 :** array declaration

**Step5 :** for(x=0;x<8;x++)

**Step6 :** print the elements of the F

**Step7 :** calling function to max

**Step8 :** calling function to min

**Step9 :** print the maximum element of the F

**Step10 :** print the minimum element of the F

**Step11 :** called function of max

**Step12 :** maxInt=F[0];

**Step13 :** for(x=0; x<8; x++)

**Step14 :** temp=F[x];

**Step15 :** if(temp>maxInt)

**Step16 :** maxInt=temp;

**Step17 :** return maximum value

**Step18 :** called function of min

**Step19 :** minInt=F[0];

**Step20 :** for(x=0; x<8; x++)

**Step21 :** temp=F[x];

**Step22 :** if(temp<minInt)

**Step23 :** minInt=temp;

**Step24 :** return minimum value

**Step25 :** stop

**Program :**

#include <iostream>

using namespace std;

int findMax(int F[], int index); // function declaration

int findMin(int F[], int index); // function declaration

int main()

{

int F[8]={33,25,71,83,22,47,51,36}; // F declaration

int x,max,min;

for(x=0;x<8;x++)

{

cout<<“F[“<<x<<“] = “<<F[x]<<endl; // print the elements of the F

}

max=findMax(F,8); // calling function

min=findMin(F,8); // calling function

cout<<“The maximum element is “<<max<<endl; // print the maximum element of the F

cout<<“The minimum element is “<<min<<endl; // print the minimum element of the F

return 0;

}

int findMax(int F[], int index) // called function

{

int maxInt,temp,x;

maxInt=F[0];

for(x=0; x<8; x++) // loop to find maximum element of an F

{

temp=F[x]; // assign F element in temp

if(temp>maxInt) // if the F element is less than the maximum value

{

maxInt=temp; // change maximum value

}

}

return maxInt; // return maximum value

}

int findMin(int F[], int index) // called function

{

int minInt,temp,x;

minInt=F[0];

for(x=0; x<8; x++) // loop to find minimum element of an F

{

temp=F[x]; // assign F element in temp

if(temp<minInt) // if the F element is less than the minimum value

{

minInt=temp; // change minimum value

}

}

return minInt; // return minimum value

}

**Output :**

**Complexity of algorithm :**

- Here for loop for n times.
- The time complexity of
**for loop**is O(n). - Since the for loop consumes more time which is O(n) and remaining code consumes less than O(n).

**So Time complexity of algorithm is O(n).**

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