(Solved) : Consider Following Iterative Function Int Pentagonal Int N Int Result 0 Int 1 Target Retur Q30689739 . . .
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 usingrecursion and add preconditions and postconditions as comments.Then prove by induction that the recursive function you wrote iscorrect.
Suppose the number of steps required in the worst case for twoalgorithms are as follows:
Algorithm 1: f(n) = 10n2 + 6
Algorithm 2: g(n) = 21n + 7
Determine at what point algorithm 2becomes more efficient than algorithm 1.
Given the following function that evaluates a polynomial whosecoefficients are stored in an array:
double evaluate(double[] coefficients,double x)
{
double result = coefficients[0];double power = 1;
for (int i = 1; i <coefficients.length; i++)
{
power = power * x;
result = result + coefficients[i] *power;
}
return result;
}
Let n be the length of thearray. Determine the number of additions and multiplications thatare performed in the worst case as a function of n.
Given the following recursive binary search algorithm forfinding 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 thearray. Find the initial condition and recurrence equation thatexpresses the execution time for the worst case of this algorithmand then solve that recurrence.
Grading Rubric
Problem
Meets
Does Not Meet
Problem 1
10 points
0 points
Recursive version correctly written(3)
Recursive version not correctly written (0)
Precondition is correct (1)
Precondition is not correct (0)
Postcondition is correct (1)
Postcondition is not correct (0)
Base case is correct (1)
Base case is not correct (0)
Inductive case is correct (4)
Inductive case is not correct (0)
Problem 2
10 points
0 points
Determined correct value for n (5)
Did not determine correct value for n (0)
Show calculation for determining n (5)
Did not show calculation for determining n (0)
Problem 3
10 points
0 points
Provided correct formulas for additions (5)
Did not provide correct formulas for additions (0)
Provided correct formulas for multiplications (5)
Did not provide correct formulas for multiplications (0)
Problem 4
10 points
0 points
Provided correct initial condition (2)
Did not provide correct initial condition (0)
Provided correct recurrence equation (4)
Did not provide correct recurrence equation (0)
Provided correct solution torecurrence equation (4)
Did not provide correct solution torecurrence equation (0)
Expert Answer
Answer to Consider Following Iterative Function Int Pentagonal Int N Int Result 0 Int 1 Target Retur Q30689739 . . .
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