Question 3: Given the following two code fragments [2 Marks] (i)Find T(n), the time complexity (as...
Question 3: Given the following two
code fragments [2 Marks]
(i)Find T(n), the time complexity (as operations count) in the worst case?
(ii)Express the growth rate of the function in asymptotic notation in the closest bound possible.
(iii)Prove that T(n) is Big O (g(n)) by the definition of Big O
(iv)Prove that T(n) is (g(n)) by using limits
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Question 3: Given the following two
code fragments [2 Marks]
(i)Find T(n), the time complexity (as...
Question 1 (25 pts) Find the running time complexity for the following code fragments. Express yo...
Question 1 (25 pts)
Find the running time complexity for the following code
fragments. Express your answers using either the Big-O or Big-Θ
notations, and the tightest bound possible. Justify your
answers.
for(int count O , i -0; i < n* n; i++) for(int i0 ; j <i; j++) count++
for(int count O , i -0; i
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
Show your work Count the number of operations and the big-O time complexity in the worst-case...
Show your work Count the number of operations and the big-O time complexity in the worst-case and best-case for the following code int small for ( i n t i = 0 ; i < n ; i ++) { i f ( a [ i ] < a [ 0 ] ) { small = a [ i ] ; } } Show Work Calculate the Big-O time complexity for the following code and explain your answer by showing...
Which big-O expression best characterizes the worst case time complexity of the following code? public static...
Which big-O expression best characterizes the worst case time complexity of the following code? public static int foo(int N) ( int count = 0; int i1; while (i <N) C for (int j = 1; j < N; j=j+2) { count++ i=i+2; return count; A. O(log log N) B. O(log N2) C. O(N log N) D. O(N2)
(10') 6. For each of the following code blocks, write the best (tightest) big-o time complexity...
(10') 6. For each of the following code blocks, write the best (tightest) big-o time complexity i) for (int i = 0; ǐ < n/2; i++) for (int j -0: ni j++) count++ i) for (int í = 0; i < n; i++) for (int ni j0 - for (int k j k ni kt+) count++ İİİ) for (int í ー 0; i < n; i++) for(int j = n; j > 0; j--) for (int k = 0; k...
For questions 10-12, refer to the following iterative code computes values for the table t. 1 pub...
For questions 10-12, refer to the following iterative code computes values for the table t. 1 public int [] tIterative (int [C A)1 2 3 4 int n - A.length; int [] t = new int [n]; int j; for (inti-0; i 0) while (j > 0 && A[j] [1] A[i] [O]) 12 13 14 15 16 t[i]Math.max( t[i-1] , A[i][i] - A[i] [o] + t[j] ); return t; 10. Does the code for tIterative use dynamic programming? 11. What...
For each problems segment given below, do the following: Create an algorithm to solve the problem...
For each problems segment given below, do the following: Create an algorithm to solve the problem Identify the factors that would influence the running time, and which can be known before the algorithm or code is executed. Assign names (such as n) to each factor. Identify the operations that must be counted. You need not count every statement separately. If a group of statements always executes together, treat the group as a single unit. If a method is called, and...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n into 3 subproblems of sizes n/2 , n/4 , n/8 , respectively with O(n) time; Recursively call on these subproblems; and then combine the results in O(n) time. The recursive call returns when the problems become of size 1 and the time in this case is constant." (a) Let T(n) denote the worst-case running time of this approach on the problem of size n....
Exercise 1 Use Top-Down Design to “design” a set of instructions to write an algorithm for...
Exercise 1 Use Top-Down Design to “design” a set of instructions to write an algorithm for “travel arrangement”. For example, at a high level of abstraction, the algorithm for “travel arrangement” is: book a hotel buy a plane ticket rent a car Using the principle of stepwise refinement, write more detailed pseudocode for each of these three steps at a lower level of abstraction. Exercise 2 Asymptotic Complexity (3 pts) Determine the Big-O notation for the following growth functions: 1....
Question 1. (1 marks) The following procedure has an input array A[1..n] with n > 2...
Question 1. (1 marks) The following procedure has an input array A[1..n] with n > 2 arbitrary integers. In the pseudo-code, "return” means immediately erit the procedure and then halt. Note that the indices of array A starts at 1. NOTHING(A) 1 n = A. size 2 for i = 1 ton // i=1,2,..., n (including n) 3 for j = 1 ton // j = 1,2,...,n (including n) 4. if A[n - j +1] + j then return 5...
Question 1 (25 pts)
Find the running time complexity for the following code
fragments. Express your answers using either the Big-O or Big-Θ
notations, and the tightest bound possible. Justify your
answers.
for(int count O , i -0; i < n* n; i++) for(int i0 ; j <i; j++) count++
for(int count O , i -0; i
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
Which big-O expression best characterizes the worst case time complexity of the following code? public static int foo(int N) ( int count = 0; int i1; while (i <N) C for (int j = 1; j < N; j=j+2) { count++ i=i+2; return count; A. O(log log N) B. O(log N2) C. O(N log N) D. O(N2)
(10') 6. For each of the following code blocks, write the best (tightest) big-o time complexity i) for (int i = 0; ǐ < n/2; i++) for (int j -0: ni j++) count++ i) for (int í = 0; i < n; i++) for (int ni j0 - for (int k j k ni kt+) count++ İİİ) for (int í ー 0; i < n; i++) for(int j = n; j > 0; j--) for (int k = 0; k...
For questions 10-12, refer to the following iterative code computes values for the table t. 1 public int [] tIterative (int [C A)1 2 3 4 int n - A.length; int [] t = new int [n]; int j; for (inti-0; i 0) while (j > 0 && A[j] [1] A[i] [O]) 12 13 14 15 16 t[i]Math.max( t[i-1] , A[i][i] - A[i] [o] + t[j] ); return t; 10. Does the code for tIterative use dynamic programming? 11. What...
For each problems segment given below, do the following: Create an algorithm to solve the problem Identify the factors that would influence the running time, and which can be known before the algorithm or code is executed. Assign names (such as n) to each factor. Identify the operations that must be counted. You need not count every statement separately. If a group of statements always executes together, treat the group as a single unit. If a method is called, and...
Question 1. (1 marks) The following procedure has an input array A[1..n] with n > 2 arbitrary integers. In the pseudo-code, "return” means immediately erit the procedure and then halt. Note that the indices of array A starts at 1. NOTHING(A) 1 n = A. size 2 for i = 1 ton // i=1,2,..., n (including n) 3 for j = 1 ton // j = 1,2,...,n (including n) 4. if A[n - j +1] + j then return 5...
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