Proof that for T(n)=2T(n/2)+n^2, the worst case complexity will be n^2.
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- Exercise on Big-Oh Analysis. Answer True or False whether a function with growth rate is a member of the set of algorithms that grow with a certain complexity. Draw also the graph. n3/2 = O (n2); if n = 500 4n2+5n+2 = Ω (n2); if n = 150 2n3+8n2+6n+7 = ω (2n); if n = 500 (n+1)(n-1)/ 3 = o (logn); if n = 200 5n + 3 = O (nlogn); if n = 1000 int[] arr = {2,4,6,8,10,12,14,16}; for(int i= 0; i<arr.length; i++){ System.out.println(arr[i]); } = o (n) 7. for(int row= 1; row<=5; row++){ for(int col=1; col<=3; col++){ System.out.print(“*”); } System.out.println(); } = Ω (n2) 8. 2n = ω (n); if n = 20 9. 6n2+2n+5 = O (n!); if n = 50 10. 2n + 10 = ϴ (nlogn); if n = 200(a) What “better-known”/simpler complexity class is equivalent to O(N log N2); briefly explain why. (b) Explain under what conditions sorted(set(l)) runs faster than set(sorted(l)) for a list l (they both produce the same answer); state the worst-case complexity class of each.Calculate Cyclomatic complexity for the given code for (i=0 ; i<=N ; i++)p[i] = 1;for (i=2 ; i<=N ; i++){k = p[i]; j=1;while (a[p[j-1]] > a[k] {p[j] = p[j-1];j--;}p[j]=k;}
- The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps. 2. The time complexity equation of merger-sort T(n) = 3* T(n/3) + n, where T(1)=T(2)=C, what would be T(n)? Please do the 2 question only, thanksSuppose we are to sort a set of 'n' integers using an algorithm with time complexity O (log2 n) that takes 0.5 ms (milliseconds) in the worst case when n = 20,000. How large an element can the algorithm then handle in 1 ms? (Note that only numeric answers can be provided.)Answer the given question with a proper explanation and step-by-step solution. Question 1 What is the worst time complexity for inserting an arbitrary item into a AVL tree? 0(n) 0 (log2 (n)) 0(1) 0(n^2) 0 (n log2 (n)) Question 2 What is the worst time complexity for inserting an arbitrary item into a binary search tree? 0(n) 0 (log2(n)) 0(1) 0 (n^2) 0 (n log2 (n)) Question 13 What is the time complexity for efficiently ordering elements (sorting) from a binary search tree? 0 (n) 0 (Log2 (n)) 0(1) 0(n^2) 0 (n log2 (n)) Question 11 The average Big O runtime to find an arbitrary element in an arbitrary AVL tree is roughly equal to the element in which other data structure or structures? Queue Hash Table Sorted Array LinkedList None of the above Question 13 What is the time complexity for efficiently ordering elements (sorting) from a binary search tree? 0 (n) 0 (log2 (n)) 0(1) 0 (n^2) 0 (n log2 (n)) Question 23 What is the time complexity of the most time efficient algorithm for…
- The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps. If you have an equation like the following T(n) = 3* T(n/3) + n, where T(1)=T(2)=C, what would be T(n)?Complexity in Big-O notation -- first line should be let mem = [0;n+1]a certain divide and conquer algorithm splits a problem into 16 sub-instances each of which is about one half of the original size it performs 3n^2 characteristic operations to do the splitting and combining. Let T(n) be the time complexity of the algorithm as a function of its input size n a) Determine a recurrence relation for T(n) b) Determine T's Big-0 complexity class using the master theorem.
- Suppose we are to sort a set of 'n' integers using an algorithm with time complexity O (n) that takes 1 ms (milliseconds) in the worst case when n = 50,000. How large an element can the algorithm then handle at least 0.2 ms?Suppose we are to sort a set of 'n' integers using an algorithm with time complexity O(n) that takes 1 ms (milliseconds) in the worst case when n = 5000. How large an element can the algorithm then handle at least 0.2 ms?Find the close form complexity function of T(n)= 3T(n-1)+1, while T(1)=1