![(2) Consider the following algorithm for the problem: for i = 1 to n do a binary search for -X[i] in Y[1 if found n] return true; return false; (a) (5 pts) What is the complexity of this algorithm? Briefly justify.](http://img.homeworklib.com/questions/43f00eb0-5263-11eb-a2c9-11b5f692b0c3.png?x-oss-process=image/resize,w_560)
Homework Answers
In the given snippet, there is a main for loop. For each iteration is is searching for some value in the array. Time complexity of binary search is log(N) and the same binary search is being performed n times. So, total complexity is O(NlogN)
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(2) Consider the following algorithm for the problem: for i = 1 to n do a...
Consider the following algorithm. ALGORITHM Enigma(A[0.n - 1]) //Input: An array A[0.n - 1] of integer...
Consider the following algorithm. ALGORITHM Enigma(A[0.n - 1]) //Input: An array A[0.n - 1] of integer numbers for i leftarrow 0 to n - 2 do for j leftarrow i +1 to n - 1 do if A[i] = = A[j] return false return true a) What does this algorithm do? b) Compute the running time of this algorithm.
Question 2 Consider the following algorithm Fun that takes array A and key Kas Fun(AO,...,n -...
Question 2 Consider the following algorithm Fun that takes array A and key Kas Fun(AO,...,n - 1], K) count = 0 for i = 0 ton - 1 do for j = i +1 to n - 1 do if A[i] + A[j] == K then count = count +1 end if end for end for return count What is the best case time complexity of the above algorithm?! (log(n)) O(1) (n) (na) Previous o H H 9
Consider an ordered array A of size n and the following ternary search algorithm for finding...
Consider an ordered array A of size n and the following ternary search algorithm for finding the index i such that A[i] = K. Divide the array into three parts. If A[n/3] > K. the first third of the array is searched recursively, else if A[2n/3] > K then the middle part of the array is searched recursively, else the last thud of the array is searched recursively. Provisions are also made in the algorithm to return n/3 if A[n/3]...
CAN SOMEONE HELP! The following problem is to design an algorithm which check if a binary tree is a binary search tree. The following code was given. There exists a bug in this code for the variable...
CAN SOMEONE HELP!
The following problem is to design an algorithm which check if a binary tree is a binary search tree. The following code was given. There exists a bug in this code for the variable last printed. (20 points) 6. Find the bug and provide a way to fix this bug: public static Integer last printed-null: public static boolean checkBST (TreeNode n) if (nnull) return true // check/ recurse left if (checkBST (n.left)) return false; /I check current...
What is the time-complexity of the algorithm abc? Procedure abc(n: integer) s := 0 i :=1...
What is the time-complexity of the algorithm abc? Procedure abc(n: integer) s := 0 i :=1 while i ≤ n s := s+1 i := 2*i return s consider the following algorithm: Procedure foo(n: integer) m := 1 for i := 1 to n for j :=1 to i2m:=m*1 return m c.) Find a formula that describes the number of operations the algorithm foo takes for every input n? d.)Express the running time complexity of foo using big-O/big-
Analysis of Algorithms Fall 2013 Do any (4) out of the following (5) problems 1. Assume n-3t is a...
Analysis of Algorithms Fall 2013 Do any (4) out of the following (5) problems 1. Assume n-3t is a power of 3 fork20. Solve accurately the following recursion. If you cannot find the exact solution, use the big-O notation. Tu) T(n)Tin/3)+2 2. Suppose that you have 2 differeut algorithms to solve a giveu probleen Algorithm A has worst-case time complexity e(n2) and Algorithm B has worst-case time complexity e(nlog n). Which of the following statements are true and which are...
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)...
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal...
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal integer n llOutput: The number of binary digits in "'s binary representation if n1 return 1 else return BinRec(ln/2)) +1 ALGORITHM 2 Binary(n) tive decimal integer nt io 's binary representation //Output: The number of binary digits in i's binary representation count ←1 while n >1 do count ← count + 1 return count a. Analyze the two algorithms and find the efficiency for...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a and b are integers while (a>0) B- a/2 A a-2 end while return b; i. What is the time complexity of the IterativeFunction pseudocode shown above? ii. What is the space complexity of the IterativeFunction pseudocode shown above? 2. What is the time complexity of the following algorithm (Note that n(n+1) 2,2 n(n+1)(2n+1) 2 and ): Provide both T(n) and order, e(f(n)). int A=0;...
Suppose we are given two sorted arrays (nondecreasing from index 1 to index n) X[1] ·...
Suppose we are given two sorted arrays (nondecreasing from index 1 to index n) X[1] · · · X[n] and Y [1] · · · Y [n] of integers. For simplicity, assume that n is a power of 2. Problem is to design an algorithm that determines if there is a number p in X and a number q in Y such that p + q is zero. If such numbers exist, the algorithm returns true; otherwise, it returns false....
Consider the following algorithm. ALGORITHM Enigma(A[0.n - 1]) //Input: An array A[0.n - 1] of integer numbers for i leftarrow 0 to n - 2 do for j leftarrow i +1 to n - 1 do if A[i] = = A[j] return false return true a) What does this algorithm do? b) Compute the running time of this algorithm.
Question 2 Consider the following algorithm Fun that takes array A and key Kas Fun(AO,...,n - 1], K) count = 0 for i = 0 ton - 1 do for j = i +1 to n - 1 do if A[i] + A[j] == K then count = count +1 end if end for end for return count What is the best case time complexity of the above algorithm?! (log(n)) O(1) (n) (na) Previous o H H 9
Consider an ordered array A of size n and the following ternary search algorithm for finding the index i such that A[i] = K. Divide the array into three parts. If A[n/3] > K. the first third of the array is searched recursively, else if A[2n/3] > K then the middle part of the array is searched recursively, else the last thud of the array is searched recursively. Provisions are also made in the algorithm to return n/3 if A[n/3]...
CAN SOMEONE HELP!
The following problem is to design an algorithm which check if a binary tree is a binary search tree. The following code was given. There exists a bug in this code for the variable last printed. (20 points) 6. Find the bug and provide a way to fix this bug: public static Integer last printed-null: public static boolean checkBST (TreeNode n) if (nnull) return true // check/ recurse left if (checkBST (n.left)) return false; /I check current...
Analysis of Algorithms Fall 2013 Do any (4) out of the following (5) problems 1. Assume n-3t is a power of 3 fork20. Solve accurately the following recursion. If you cannot find the exact solution, use the big-O notation. Tu) T(n)Tin/3)+2 2. Suppose that you have 2 differeut algorithms to solve a giveu probleen Algorithm A has worst-case time complexity e(n2) and Algorithm B has worst-case time complexity e(nlog n). Which of the following statements are true and which are...
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)...
Q4) [5 points] Consider the following two algorithms: ALGORITHM 1 Bin Rec(n) //Input: A positive decimal integer n llOutput: The number of binary digits in "'s binary representation if n1 return 1 else return BinRec(ln/2)) +1 ALGORITHM 2 Binary(n) tive decimal integer nt io 's binary representation //Output: The number of binary digits in i's binary representation count ←1 while n >1 do count ← count + 1 return count a. Analyze the two algorithms and find the efficiency for...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a and b are integers while (a>0) B- a/2 A a-2 end while return b; i. What is the time complexity of the IterativeFunction pseudocode shown above? ii. What is the space complexity of the IterativeFunction pseudocode shown above? 2. What is the time complexity of the following algorithm (Note that n(n+1) 2,2 n(n+1)(2n+1) 2 and ): Provide both T(n) and order, e(f(n)). int A=0;...
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