Exercise 2. We have seen that Dijkstra's algorithm can be implemented in two ways: Variant (a) uses an array to store the dist] values of the unknown nodes, and Variant (b) uses a MIN-HEAP to store these values. (a) Suppose in your application m <3n. Which variant gives a faster runtime? Justify your answer. (b) Suppose in your application m2 n²/3. Which variant gives a faster runtime? Justify your answer.

Exercise 2. We have seen that Dijkstra's algorithm can be implemented in two ways: Variant (a) uses an array to store the dist] values of the unknown nodes, and Variant (b) uses a MIN-HEAP to store these values. (a) Suppose in your application m <3n. Which variant gives a faster runtime? Justify your answer. (b) Suppose in your application m2 n²/3. Which variant gives a faster runtime? Justify your answer.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Given a BST, which traversal method would allow you to turn it into a min heap using N heap insertions calls in O(N) worst case runtime? Draw an example of this process. First, draw a BST with 4 nodes and height of 3. You can pick the integer values in your BST. Then show the resulting traversal order, and a drawing of the values inserted into a min heap using N heap insertions. Redraw the heap after each insertion.
Consider the following vector: { 1, 2, 3, 6, 9, 5, 10, 14}(1) Give me the vector version of the binary heap that results when you call Pop() on this heap (vector) (2) You would like to sort this specific vector/heap. Which is better to divide and conquer: quick sort using the first element as a pivot or merge sort? Please explain your answer in your own words your decision and the reasons why
Write a procedure that, given parameters A, n, and i, where A is the array representation of an n-element heap, and 1 ≤ i ≤ n, deletes the element A[i] from the heap in O(log n) tim e.
Please assume that you have been given an implementation of a stack that supports both push and pop in O(1) time. With this information, you would like to implement a queue with these stacks. (a) In what way can you efficiently implement a queue using two of these stacks? “Efficiently” in this case means in a way which will allow you to do part B. (b) Please prove that the amortized cost of each dequeue and enqueue operation is O(1) for your stack-based queue by using the aggregate amortized analysis technique.
For this given code, please help me create a recursive case for transpose of matrix using the cache oblivious algorithm. for ( size_t i=0; i<n; i += block ) { for ( size_t j=0; j<n; j++ ) { for ( size_t b = 0; b < block && i + b < n; ++b){ b[ j*n + i ] = a[ i*n + j ]; } } else { recursMatTranspose ( n, n, a, 0, 0, b, 0, 0 ); //recursive case using cache-oblivious algo } }
Let S1 and S2 be two stacks. 1. Is it possible to keep two stacks in a single array? If so, explain how. Otherwise, why not? Show your work step by step. Otherwise, your solution is incorrect. 2. If your answer is “Yes” for the above question, write a procedure Push(x, S) that pushes element x onto stack S, where S is one or the other of these two stacks. Include all necessary error checks in your procedure. Show your work step by step. Otherwise, your solution is incorrect.
QuickSort is run for an array A in a manner that PARTITION consistently produces a 5:1 split for the (sub)arrays to be sorted (recursively) next. Picture the recurrence tree for this scenario ... What will be the length of the longest path from the root to a leaf (= deepest depth)in this tree? Group of answer choices log_5/6 (n) ... "log of n with base 5/6" log_6/5 (n) ... "log of n with base 6/5" log_6 (n) ... "log n with base 6" n^log_5(6) ... "n to the power of log_5(6)"
Consider the following vector: { 1, 2, 3, 6, 9, 5, 10, 14}(1) Give me the vector version of the binary heap that results when you call Pop() on this heap (vector) (no code needed, just the 7 numbers in order)(2) You would like to sort this specific vector/heap. Which is better to divide and conquer: quick sort using the first element as a pivot or merge sort? Please explain your answer in your own words your decision and the reasons why
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Given a max-priority queue A = <8, 5, 7, 3, 2, 4, 1>, consider calling Max-Heap-Insert(A, 6). Note: Array index starts from 1. (1) What will be the resulting max-priority queue A? Please write your answer as a sequence of numbers separated by ", ". For example: 1, 2, 3, 4, 5, 6, 7, 8
Using the provided MinHeap implementation & helper functions, build two sorted arrays as follows: Option 1:Given an unsorted array, build a sorted array in ascending order utilizing a minheap. Hint: this one is quite easy.. Load a minheap with your unsorted array. From there you can get the min element from the minheap & build your sorted array. Option 2:Given your unsorted array loaded into a maxheap.. Using this max-heap, in which the root node contains the largest element, build a sorted array in ascending order. To achieve this you’ll ‘Float’ the max to the front and build the sorted list from the back. The basic idea is to sort in place. - Every time the algorithm polls from the heap, the heaps size shrinks by one. - Hence, the next place at the end of the array is not part of the heap anymore. - At this index the n-th smallest number is placed. Final Solution should look like: Array to be sorted by MinHeap: [5, 3, 17, 10, 84, 19, 6, 22,…
Using heapsort to sort [10,5,10,5] and [5,10,5,10], on which of the two arrays, the relative order of all the elements of the same values will be preserved? Can you show a working behind your answer? Options are: 1. only [10,5,10,5] 2. only [5,10,5,10] 3. none 4. both