Question 3: a) Consider a recursive function to return the Number of Binary Digits in the Binary Representation of a Positive Decimal Integer (n) using a recursive algorithm. int Process (int n) { if (n == 1) return 1; else return (Extra() + Process (n/4) + Process (n/4)); } Given that Extra(n) is a function of O(n) 1) Find T(n) = number of arithmetic operations. 2) Calculate the complexity of this algorithm using Back Substitution. b) You are given an array A that contains n numbers, and you are also given a target valu T. The following algorithm is design for a specific purpose. SortX (A[1...n]) i= 1; j = n; while (i < j) { if (A[i]+A[j] < T) Il sort the array A) into ascending order i++; else if (A[i]+A[j] > T) j-- else // (A[i]+A[j] == T) return true; } return false; 1) Explain the purpose of the above algorithm 2) What is the complexity of such algorithm? Why?
Question 3: a) Consider a recursive function to return the Number of Binary Digits in the Binary Representation of a Positive Decimal Integer (n) using a recursive algorithm. int Process (int n) { if (n == 1) return 1; else return (Extra() + Process (n/4) + Process (n/4)); } Given that Extra(n) is a function of O(n) 1) Find T(n) = number of arithmetic operations. 2) Calculate the complexity of this algorithm using Back Substitution. b) You are given an array A that contains n numbers, and you are also given a target valu T. The following algorithm is design for a specific purpose. SortX (A[1...n]) i= 1; j = n; while (i < j) { if (A[i]+A[j] < T) Il sort the array A) into ascending order i++; else if (A[i]+A[j] > T) j-- else // (A[i]+A[j] == T) return true; } return false; 1) Explain the purpose of the above algorithm 2) What is the complexity of such algorithm? Why?
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Question 3:
a) Consider a recursive function to return the Number of Binary Digits in the Binary
Representation of a Positive Decimal Integer (n) using a recursive algorithm.
int Process (int n)
{ if (n == 1) return 1;
else return (Extra() + Process (n/4) + Process (n/4)); }
Given that Extra(n) is a function of O(n)
1) Find T(n) = number of arithmetic operations.
2) Calculate the complexity of this algorithm using Back Substitution.
b) You are given an array A that contains n numbers, and you are also given a target value
T. The following algorithm is design for a specific purpose.
SortX (A[1...n])
Il sort the array A[] into ascending order
i = 1;
j = n;
while (i < j) {
if (A[i]+A[j] < T)
i++;
else if (A[i]+A[j] > T)
j--;
else // (A[i)+A[j] == T)
return true;
}
return false;
1) Explain the purpose of the above algorithm
2) What is the complexity of such algorithm? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37c0efcd-6814-4ebb-a705-77be4ea670d6%2F24e2af9b-acc3-466a-a8e6-07be0eeb30c9%2Fmvpnj1l_processed.png&w=3840&q=75)
Transcribed Image Text:Question 3:
a) Consider a recursive function to return the Number of Binary Digits in the Binary
Representation of a Positive Decimal Integer (n) using a recursive algorithm.
int Process (int n)
{ if (n == 1) return 1;
else return (Extra() + Process (n/4) + Process (n/4)); }
Given that Extra(n) is a function of O(n)
1) Find T(n) = number of arithmetic operations.
2) Calculate the complexity of this algorithm using Back Substitution.
b) You are given an array A that contains n numbers, and you are also given a target value
T. The following algorithm is design for a specific purpose.
SortX (A[1...n])
Il sort the array A[] into ascending order
i = 1;
j = n;
while (i < j) {
if (A[i]+A[j] < T)
i++;
else if (A[i]+A[j] > T)
j--;
else // (A[i)+A[j] == T)
return true;
}
return false;
1) Explain the purpose of the above algorithm
2) What is the complexity of such algorithm? Why?
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