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1. Consider the following iterative function: int pentagonal(int-(Answered)

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Please help me answer. Homework 1. Please see attached?


1. Consider the following iterative function:

 

int pentagonal(int n)

 

{

 

int result = 0;

 

for (int i = 1; i <= n; i++)

 

result += 3 * i - 2;

 

return result;

 

}

 


 

Rewrite the function pentagonal using recursion and add preconditions and

 

postconditions as comments. Then prove by induction that the recursive function you

 

wrote is correct.

 


 

2. Suppose the number of steps required in the worst case for two algorithms are as follows:

 


 


 


 

Algorithm 1: f(n) = 10n2 + 6

 

Algorithm 2: g(n) = 21n + 7

 


 

Determine at what point algorithm 2 becomes more efficient than algorithm 1.

 

3. Given the following function that evaluates a polynomial whose coefficients are stored in

 

an array:

 

double evaluate(double coefficients, double x)

 

{

 

double result = coefficients[0];

 

double power = 1;

 

for (int i = 1; i < array.length; i++)

 

{

 

power = power * x;

 

result = result + coefficients[i] * power;

 

}

 

return result;

 

}

 


 

Let n be the length of the array. Determine the number of additions and multiplications

 

that are performed in the worst case as a function of n.

 

4. Given the following recursive binary search algorithm for finding an element in a sorted

 

array of integers:

 

int recursiveBinarySearch(int array, int target, int left, int right)

 

{

 

if (left > right)

 

return -1;

 

int middle = (left + right) / 2;

 

if (array[middle] == target)

 

return middle;

 

if (array[middle] > target)

 


 

return recursiveBinarySearch(array, target, left, middle - 1);

 

return recursiveBinarySearch(array, target, middle + 1, right);

 

}

 


 

Assume n is the length of the array. Find the initial condition and recurrence equation that

 

expresses the execution time for the worst case of this algorithm and then solve that

 

recurrence.

 


 

 

Paper#9255892 | Written in 27-Jul-2016

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