Pseudocode Algorithm Sub(n) if n = 1 or n = 2 return n - 1 else...
Pseudocode
Algorithm Sub(n)
if n = 1 or n = 2
return n - 1
else
return Sub(n - 1) + Sub(n - 1)
Let Sub(n) be the number of "substraction operation" as the basic operation on input of size n.
what is the recurrence for Sub(n).
please show working.
Homework Answers
Recurrence for Sub(n:
T(n) = 2T(n-1) + 1
Basic case:
T(n) = 0
Solving recurrence is
T(n) = 2T(n-1) + 1
= 2(2T(n-2)+1) + 1
= 2^2T(n-2)+2 + 1
= 2^3T(n-3)+ 2^2 +2 + 1
.....
.....
= 2^nT(n-n)+ ... + 2^2 +2 + 1
= 2^nT(0)+ ... + 2^2 +2 + 1
= 2^n+ ... + 2^2 +2 + 1
= 2^(n+1)
= O(2^n)
ALGORITHM RecS(n) // Input: A nonnegative integer n ifn=0 return 0 else return RecS(n+ n n...
ALGORITHM RecS(n) // Input: A nonnegative integer n ifn=0 return 0 else return RecS(n+ n n n Determine what this algorithm computes. You must justify your answer. made by this algorithm and solve it. You must justify your answer. same thing using for/while loop(s) developed in (3). You must justify your answer. 1) 2) Set up the initial condition and recurrence relation for the number of multiplications 3) Write the pseudocode for the non-recursive version of this algorithm, i.e., compute...
pleas answer asap 3. (20 points) Algorithm Analysis and Recurrence There is a mystery function called Mystery(n) and the pseudocode of the algorithm own as below. Assume that n 3* for some positiv...
pleas answer asap
3. (20 points) Algorithm Analysis and Recurrence There is a mystery function called Mystery(n) and the pseudocode of the algorithm own as below. Assume that n 3* for some positive integer k21. Mystery (n) if n<4 3 for i1 to 9 5 for i-1 to n 2 return 1 Mystery (n/3) Print "hello" 6 (1) (5 points) Please analyze the worst-case asymptotic execution time of this algorithm. Express the execution time as a function of the input...
Given algorithm- procedure factorial (n: nonnegative integer) if n = 0 then return 1 else return...
Given algorithm- procedure factorial (n: nonnegative integer) if n = 0 then return 1 else return n*factorial(n-1) {output is n!} Trace the above algorithm when it is given n = 7 as input. That is, show all steps used by above algorithm to find 7!
Algorithm Riddle(A[0..n-1]) //Input: An array A[0..n-1] of real numbers if n=1 return A[0] else temp =...
Algorithm Riddle(A[0..n-1]) //Input: An array A[0..n-1] of real numbers if n=1 return A[0] else temp = Riddle(A[0..n-2]) if temp<=A[n-1] return temp else return A[n-1] what does it compute? explain please
urgent L. Consider the following pseudocode for finding binomial coefficients: Binom(n, r) Input: integers n and r Output: n choose r if r-0 or r-n thern return 1 end else return Binom(n-1, r-1) B...
urgent
L. Consider the following pseudocode for finding binomial coefficients: Binom(n, r) Input: integers n and r Output: n choose r if r-0 or r-n thern return 1 end else return Binom(n-1, r-1) Binom(n-1, r); end running time of this algorithm. Prove your bound for the upper bound. (5 points) Rewrite the above algorithm so that it is efficient. (You have 2 choices!) Analyze the worst case time of your new algorithm. (5 points) Find the edit distance between "SPOKE...
Using the pseudocode answer these questions Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do...
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 4. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a worst-case input of size n. Show your work. 5. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a best-case input of size n. Show your work.
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your...
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations. What is the time efficiency of your algorithm for the worst and best cases? Justify your answer. (The basic operation must be identified explicitly). Give one instance for the worst case and one instance for the best case respectively if there is any difference between the worst case and best case. Otherwise please indicate that...
Consider the following recursive algorithm for computing the sum of the first n cubes: S(n) =...
Consider the following recursive algorithm for computing the sum
of the first n cubes: S(n) = 13 +
23 + … + n3.
(a) Set up a recurrence relation for the number of
multiplications made by this algorithm.
(b) Provide an initial condition for the
recurrence relation you develop at the question (a).
(c) Solve the recurrence relation of the
question (a) and present the time complexity as described at the
question number 1.
Algorithm S n) Input: A positive...
Using the pseudocode answer these questions Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do...
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 6. Use limits to show that, for best case inputs, the asymptotic growth of the number of comparisons is (1). Show your work. 7. Use limits to show that, for worst case inputs, the asymptotic growth of the number of comparisons is O(n). Show your work.
Using the pseudocode answer these questions Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do...
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 1. Describe what it does and compute what value is returned when the input is the list {1, 2, 3, 4, 5}. (Hint: We're using 0-based array indexing, so 0 would represent the index of the first element, 1 the second element, etc.) 2. Identify and describe the worst-case input. 3. Identify and...
ALGORITHM RecS(n) // Input: A nonnegative integer n ifn=0 return 0 else return RecS(n+ n n n Determine what this algorithm computes. You must justify your answer. made by this algorithm and solve it. You must justify your answer. same thing using for/while loop(s) developed in (3). You must justify your answer. 1) 2) Set up the initial condition and recurrence relation for the number of multiplications 3) Write the pseudocode for the non-recursive version of this algorithm, i.e., compute...
pleas answer asap
3. (20 points) Algorithm Analysis and Recurrence There is a mystery function called Mystery(n) and the pseudocode of the algorithm own as below. Assume that n 3* for some positive integer k21. Mystery (n) if n<4 3 for i1 to 9 5 for i-1 to n 2 return 1 Mystery (n/3) Print "hello" 6 (1) (5 points) Please analyze the worst-case asymptotic execution time of this algorithm. Express the execution time as a function of the input...
urgent
L. Consider the following pseudocode for finding binomial coefficients: Binom(n, r) Input: integers n and r Output: n choose r if r-0 or r-n thern return 1 end else return Binom(n-1, r-1) Binom(n-1, r); end running time of this algorithm. Prove your bound for the upper bound. (5 points) Rewrite the above algorithm so that it is efficient. (You have 2 choices!) Analyze the worst case time of your new algorithm. (5 points) Find the edit distance between "SPOKE...
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 4. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a worst-case input of size n. Show your work. 5. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a best-case input of size n. Show your work.
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations. What is the time efficiency of your algorithm for the worst and best cases? Justify your answer. (The basic operation must be identified explicitly). Give one instance for the worst case and one instance for the best case respectively if there is any difference between the worst case and best case. Otherwise please indicate that...
Consider the following recursive algorithm for computing the sum
of the first n cubes: S(n) = 13 +
23 + … + n3.
(a) Set up a recurrence relation for the number of
multiplications made by this algorithm.
(b) Provide an initial condition for the
recurrence relation you develop at the question (a).
(c) Solve the recurrence relation of the
question (a) and present the time complexity as described at the
question number 1.
Algorithm S n) Input: A positive...
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 6. Use limits to show that, for best case inputs, the asymptotic growth of the number of comparisons is (1). Show your work. 7. Use limits to show that, for worst case inputs, the asymptotic growth of the number of comparisons is O(n). Show your work.
Using the pseudocode answer these questions
Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 1. Describe what it does and compute what value is returned when the input is the list {1, 2, 3, 4, 5}. (Hint: We're using 0-based array indexing, so 0 would represent the index of the first element, 1 the second element, etc.) 2. Identify and describe the worst-case input. 3. Identify and...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago