![(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.
6.3.1 [10] <§6.2> Consider the following binary search algorithm (a classic divide and conquer algorithm) that...
6.3.1 [10] <§6.2> Consider the following binary search algorithm (a classic divide and conquer algorithm) that searches for a value X in a sorted N-element array A and returns the index of matched entry: BinarySearch(A[0..N−1], X) { low = 0 high = N −1 while (low <= high) { mid = (low + high) / 2 if (A[mid] >X) high = mid −1 else if (A[mid] <X) low = mid + 1 else return mid // found } return −1...
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...
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...
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