EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Write a version of bottom-up mergesort that takes advantage of order in the array by proceeding as follows each time it needs to find two arrays to merge: find a sorted subarray (by incrementing a pointer until finding an entry thatis smaller than its predecessor in the array), then find the next, then merge them. Analyze the running time of this algorithm in terms of the array size and the number of maximal increasing sequences in the array.
Make and implement a mergesort variation that gives an int[] array perm, where perm[i] is the index of the array's i th smallest element, rather than rearranges the array's elements.
You are given an array of integers nums and an integer target. Return the indices of two numbers in the array such that they add up to target. You may assume that each input would have exactly one solution, and you may not use the same element twice. Implement a function in Java to solve this problem using a hash map, and explain the time and space complexity of your solution.
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- Using Java implementations presented in the algorithms below.Practice Mergesort algorithm with Comparable Java objects whose class definition implements Java's Comparable interface. For example, using sample Comparable Student objects or Comparable Java class objects of your own implementation. Algorithm: void mergesort(E[] A, E[] temp, int l, int r) { int i, j, k, mid = (l+r)/2; if (l == r) return; // List has one element if ((mid-l) >= THRESHOLD) mergesort(A, temp, l, mid); else inssort(A, l, mid-l+1); if ((r-mid) > THRESHOLD) mergesort(A, temp, mid+1, r); else inssort(A, mid+1, r-mid); // Do merge. First, copy 2 halves to temp. for (i=l; i<=mid; i++) temp[i] = A[i]; for (j=1; j<=r-mid; j++) temp[r-j+1] = A[j+mid]; // Merge sublists back to array for (i=l,j=r,k=l; k<=r; k++) if (temp[i].compareTo(temp[j])<0) A[k] = temp[i++]; else A[k] = temp[j--];}arrow_forwardwe have proven that the computational time complexity of mergesort is O(n * log2n). Perhaps the time complexity of mergesort can be improved further by separating the array into three parts instead of two. Start by implementing a method called merge3. This method should take three sorted arrays as inputs and return a sorted array consisting of all elements of the three input arrays. public static int[] merge3(int[] a, int[] b, int[] c) { return new int[] {-1}; } * must be done in this format and in javaarrow_forward) Implement a quicksort based on using a sample of size 2k 1. First, sort the sample, then arrange to have the recursiveroutine partition on the median of the sample and to move the two halves of the rest ofthe sample to each subarray, such that they can be used in the subarrays, without havingto be sorted again. This algorithm is called samplesort.arrow_forward
- Implement a quicksort based on partitioning on the median of a random sample of five items from the subarray. Put the items of the sample at the appropriate ends of the array so that only the median participates in partitioning. Run doubling tests to determine the effectiveness of the change, in comparison both to the standard algorithm and to median-of-3 partitioning (see the previous exercise). Extra credit : Devise a median-of-5 algorithm that uses fewer than seven compares on any input.arrow_forwardUsing an unsorted array to implement a map would allow an O(log2N) get operation (where N is the number of elements in the map). Group of answer choices True False also explain why?arrow_forwardimplement merge-sort multithreadA is an array and p and q indexes of the array such as you gonna sort the sub-array A[p..r]. B is a sub-array which willbe populated by the sort.A call to p-merge-sort(A,p,r,B,s) sorts elements from A[p..r] and put them in B[s..s+r-p]arrow_forward
- 2.) Consider an input array A of size n in which n − 1 of the elements have identical values and the remaining one value is smaller than the n − 1 identical values. What is the running time of Heapsort with input A?arrow_forwardDevelop a topological sort implementation thatmaintains a vertex-indexed array that keeps track of the indegree of each vertex. Initialize the array and a queue of sources in a single pass through all the edges. Then, perform the following operations until the source queue is empty:■ Remove a source from the queue and label it.■ Decrement the entries in the indegree array corresponding to the destination vertex of each of the removed vertex’s edges If decrementing any entry causes it to become 0, insert the corresponding vertex onto the source queue.arrow_forwardImplement a quicksort based on partitioning on themedian of a random sample of five items from the subarray. Put the items of the sampleat the appropriate ends of the array so that only the median participates in partitioning.Run doubling tests to determine the effectiveness of the change, in comparison bothto the standard algorithm and to median-of-3 partitioning (see the previous exercise).Extra credit : Devise a median-of-5 algorithm that uses fewer than seven compares onany input.arrow_forward
- 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. botharrow_forwardImplement a natural mergesort for linked lists.Since it doesn't take up extra space and is certain to be linearithmic, this approach is the one used to sort linked lists.arrow_forwardImplement a city database using ordered lists by using java. Each database record contains the name of the city (a string of arbitrary length) and the coordinates of the city expressed as integer x and y coordinates. Your database should allow records to be inserted, deleted by name, and searched by name. Another operation that should be supported is to print all records within a given distance of a specified point/coordinate. The order of cities should be alphabetically by city name. Implement the database using both: an arraybased list implementation, and a circular single linked list implementation.Use may the following node, SLL implementations to implement an ordered circular single linked listarrow_forward
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