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How much time does the following "algorithm" require as a function Problem 4.1. of n? for...
3) How much time does the following “algorithm” require as a function of n? l=0 for...
3) How much time does the following “algorithm” require as a function of n? l=0 for i=1 to n do for j=1 to i do for k=j to n do l = l + 1
Problem 1: Let W(n) be the number of times "whatsup" is printed by Algorithm WHATSUP (see below) ...
Problem 1: Let W(n) be the number of times "whatsup" is printed by Algorithm WHATSUP (see below) on input n. Determine the asymptotic value of W(n). Algorithm WHATSUP (n: integer) fori1 to 2n do for j 1 to (i+1)2 do print("whatsup") Your solution must consist of the following steps: (a) First express W(n) using summation notation Σ (b) Next, give a closed-form formula for W(n). (A "closed-form formula" should be a simple arithmetio expression without any summation symbols.) (c) Finally,...
Perform the following to the algorithm below: - - Express T(n) as a function of n...
Perform the following to the algorithm below: - - Express T(n) as a function of n Find a best approximation for the Big O function for T(n) Perform a time complexity analysis Define the basic operation of the algorithm Correctness Efficiency - - Procedure maxMin (n, A, I, h) integer h, I, A (1:n), n integer j j-2 IA (1) hS (1) while (i <=n) do if (Ali) < 1) then TEA (0) if(Ali) >h) then h A() j+į+1 repeat...
4.1 4.1 Insertion Sort 4. Design 137 the a algorithm for generating the power set of...
4.1 4.1 Insertion Sort 4. Design 137 the a algorithm for generating the power set of a set of n elements. (The power set of a set s is the set of all the subsets of S,including empty set and S itself.) 5. Consider the following algorithm to check connectivity of graph defined by adjacency a ALGORITHM Connected (A 0...n-1, 0..n ij) Input: Adjacency matrix Alo..n 1,0. n -1) of an undirected graph G //Output: 1 (true) if G is...
Analyze the running time of the following algorithms asymptotically. (a) Algorithm for-loop(n): P = 1 for...
Analyze the running time of the following algorithms asymptotically. (a) Algorithm for-loop(n): P = 1 for i = 1 to 5n^2 do p = p times i return p (b) Algorithm for-loop(n): s = 0 for i = 1 to n do for j = I to n do s = s + i return s (c) Algorithm WhileLoop(n): x = 0; j = 2; while (j = n){x = x+ 1; j =j times 2;}
Need to find number of elementary expressions in terms of n, not looking for Big O...
Need to find number of elementary expressions in terms
of n, not looking for Big O complexity.
4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
6. Consider the following algorithm, where P is an array containing random numbers. The function swap(v1,v2)...
6. Consider the following algorithm, where P is an array containing random numbers. The function swap(v1,v2) will swap the values stored in the variables v1 and v2. Note that % is the modulus operation, and will return the integer remainder r of a/b, i.e., r-a%b Require: Array P with n > 0 values 1: i-1, j-n-l 2: while i<=j do for a=i to j by i do 4: 5: 6: 7: if Pla>Pat 11 and Pla]%2--0 then swap(Plal, Pla+1l) end...
(V). Given the following algorithm, answer relevant questions. Algorithm 1 An algorithm 1: procedure WHATISTHIS(21,22,...,n: a...
(V). Given the following algorithm, answer relevant questions. Algorithm 1 An algorithm 1: procedure WHATISTHIS(21,22,...,n: a list of n integers) for i = 2 to n do c= j=i-1 while (j > 0) do if ra; then break end if 4j+1 = a; j= j-1 end while j+1 = 1 end for 14: return 0.02. 1, 15: end procedure Answer the following questions: (1) Run the algorithm with input (41, 02, 03, 04) = (3, 0, 1,6). Record the values...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
Analyze the time complexity of the following algorithm. You may assume that the floor function in...
Analyze the time complexity of the following algorithm. You may assume that the floor function in line 2 takes Theta (1) time. Please show your work. Input: data: array of integers Input: n: size of data Output: median of data 1 Algorithm: MedianSelect 2 lim = [n/2] + 1 3 min = - infinity 4 for i = 1 to lim do 5 prev = min 6 min = infinity 7 for j = 1 to n do 8 if...
Problem 1: Let W(n) be the number of times "whatsup" is printed by Algorithm WHATSUP (see below) on input n. Determine the asymptotic value of W(n). Algorithm WHATSUP (n: integer) fori1 to 2n do for j 1 to (i+1)2 do print("whatsup") Your solution must consist of the following steps: (a) First express W(n) using summation notation Σ (b) Next, give a closed-form formula for W(n). (A "closed-form formula" should be a simple arithmetio expression without any summation symbols.) (c) Finally,...
Perform the following to the algorithm below: - - Express T(n) as a function of n Find a best approximation for the Big O function for T(n) Perform a time complexity analysis Define the basic operation of the algorithm Correctness Efficiency - - Procedure maxMin (n, A, I, h) integer h, I, A (1:n), n integer j j-2 IA (1) hS (1) while (i <=n) do if (Ali) < 1) then TEA (0) if(Ali) >h) then h A() j+į+1 repeat...
4.1 4.1 Insertion Sort 4. Design 137 the a algorithm for generating the power set of a set of n elements. (The power set of a set s is the set of all the subsets of S,including empty set and S itself.) 5. Consider the following algorithm to check connectivity of graph defined by adjacency a ALGORITHM Connected (A 0...n-1, 0..n ij) Input: Adjacency matrix Alo..n 1,0. n -1) of an undirected graph G //Output: 1 (true) if G is...
Analyze the running time of the following algorithms asymptotically. (a) Algorithm for-loop(n): P = 1 for i = 1 to 5n^2 do p = p times i return p (b) Algorithm for-loop(n): s = 0 for i = 1 to n do for j = I to n do s = s + i return s (c) Algorithm WhileLoop(n): x = 0; j = 2; while (j = n){x = x+ 1; j =j times 2;}
Need to find number of elementary expressions in terms
of n, not looking for Big O complexity.
4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
6. Consider the following algorithm, where P is an array containing random numbers. The function swap(v1,v2) will swap the values stored in the variables v1 and v2. Note that % is the modulus operation, and will return the integer remainder r of a/b, i.e., r-a%b Require: Array P with n > 0 values 1: i-1, j-n-l 2: while i<=j do for a=i to j by i do 4: 5: 6: 7: if Pla>Pat 11 and Pla]%2--0 then swap(Plal, Pla+1l) end...
(V). Given the following algorithm, answer relevant questions. Algorithm 1 An algorithm 1: procedure WHATISTHIS(21,22,...,n: a list of n integers) for i = 2 to n do c= j=i-1 while (j > 0) do if ra; then break end if 4j+1 = a; j= j-1 end while j+1 = 1 end for 14: return 0.02. 1, 15: end procedure Answer the following questions: (1) Run the algorithm with input (41, 02, 03, 04) = (3, 0, 1,6). Record the values...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
Analyze the time complexity of the following algorithm. You may assume that the floor function in line 2 takes Theta (1) time. Please show your work. Input: data: array of integers Input: n: size of data Output: median of data 1 Algorithm: MedianSelect 2 lim = [n/2] + 1 3 min = - infinity 4 for i = 1 to lim do 5 prev = min 6 min = infinity 7 for j = 1 to n do 8 if...
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