3. (20 points) Write a C++ recursive function that finds the maximum value in an array (or vector) of integers without using any loops. (a) Test your function using different input arrays. Include the code. i. ii. (b) Write a recurrence relation that represents your algorithm. i. T(n) = T(n-1) + O(1) (c) Solve the recurrence relation and obtain the running time of the algorithm in Big-O notation.

Following are the code to this question:

In option (i):

#include <iostream>//defining header file

using namespace std;

int findMax(int B[], int x)//defining recursive method findMax

{

if (x == 1)//defining condition when value of n==1

return B[0];//return array first element

return max(B[x-1], findMax(B, x-1)); // calling recursive method inside max method and return value

}

int main() //defining main method  

{

int B[] = {12, 24, 55, 60, 50, 30, 29};//defining array B

int x= 7;//defining integer variable and assign a value

cout << "Maximum element value of the array is: "<<findMax(B, x)<<endl;//calling method findMax and print value

return 0;

}

Output:

Maximum element value of the array is: 60

In option (ii):

Explanation:

In the above-given program a recursive method "findMax" is defined, which accepts an array "B" and an integer variable "n" in its parameter, inside the method a conditional statement is used that, checks value of x equal to 1.

If the above condition is true it will return the first element of the array and find the max number. Inside the main method, an array B is declared that assigns some values and an integer variable is declared, that also assigns some values, in the last step print method is used that pass value in method and prints its return value. In the option (ii) we calculate the Big-O notation algorithm value.

Through the process of sedimentation,sediment is turned back to rock to form sedimentation.the process of sedimentation is: > deposition-where fragments were deposited into the river or sea under gravity or travelling agent such as wind or water. > sedimentation-the fragments deposited in the river sedimented and accumulate> compaction-the layers of fragments deposited undergoes compaction due to the weight if the upper layers> cementation-chemical substance of the fragments such as cement dissolved into the water and cement the other fragments together to form sedimentary rock.thus,cementation and compaction are the process.on the other hand, transformation only occur when a rock under goes metamorphism(compaction or extreme heat).while recrystillization occurs when a rock is melted and cooled down,which also requires metamorphism to take place.hope it !

Hypothesis: volumes of both figures are equal.the volume of  figure 1 is: .the volume of figure 2 is: .since , you can conclude that and . so, .volumes of figures are equal only when an angle in the basis is right (then figures will be the same), in another cases volume of figure 1 is less than volume of figure 2.the hypothesis was not correct in all cases.