Optimisation - Merge Sort can be optimised to perform better. The method uses the merge sort technique and * must be recursive. In this tutorial, we'll have a look at the Merge Sort algorithm and its implementation in Java. Bubble sort is the simplest sorting algorithm. In this tutorial we will learn about Merge sort algorithm. Merge Sort using Java with program code In computer science, merge sort or mergesort is a sorting algorithm for rearranging lists (or any such linear sequential data storage structure) into a specified order. Tracing Sort and Merge 70. Iterative Destructive Merge 65. Join Raghavendra Dixit for an in-depth discussion in this video, Introduction, part of Introduction to Data Structures & Algorithms in Java. Click here for Java MergeSort Recursive Algorithm. Returns a Set view of the keys contained in this map. Both return a bracket from the head of the sorted list until item past the end of the sorted list. 21 Time Complexity of Recursive functions_TS_Output_28. Whatever I git commit to Master is built and deployed to the running instance. This property helps us to deduce a threaded version of merge sort algorithm where, we can really solve the left and right sub-portion of a range in a parallel fashion by. Having gone through and re-read sections of the CIRCULARSTRING code, it is amazing how much easier the code is to read without the confusion of a curve being either a CIRCULARSTRING or LINESTRING as per the SQL-MM spec. In terms of space complexity, Mergesort takes O(n) amount of space, worst case (this is due to the size of the array itself, the array is "n" amount of elements, we need to store the elements somewhere after sorting). The algorithm is encapsulated in a class OddEvenMergeSorter. * Generic List class with merge-sort implementation * @author Drew Braden. reference P 21. Partition algorithm is important per se, therefore it may be carried out as a separate function. Contribute to HSatwick/ProgrammersCorner development by creating an account on GitHub. It only takes a minute to sign up. Sorting the remaining two sub-arrays takes 2* O(n/2). The next two codes are merge sort and bubble sort. Another fast algorithm, Merge Sort starts sorting from small pieces and repeatedly merges the sorted pieces together until the whole array is. Dividing a List 68. Contribute to WWaldo/Sorting-Algorithms development by creating an account on GitHub. Java implementers also think so; that's why a lot of the sorting thingies are already built in! JDK 1. The following procedure uses recursion to calculate the factorial of its original argument. Define divide and conquer approach to algorithm design ; Describe and answer questions about example divide and conquer algorithms. Geomagnetic field modeling by optimal recursive filtering. mergesort recursion. Merge sort's most common implementation does not sort in place, meaning memory the size of the input must be allocated for the sorted output to be stored in. how will it then return and take new arguments(a,mid+1,j) if it already broke to recurse at first place?. The entire code could be found over on GitHub. It is possible to sort in constant. Merge Sort is a Divide and Conquer algorithm. Firstly a quick recap on the merge sort. In such an algorithm, we divide the data into smaller pieces, recursively conquer each piece, and then combine the results into a final result. Background : Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order. For example, to sort a Vector, all we need to do is call a sort() method of the java. Merge-sort is based on an algorithmic design pattern called divide-and-conquer. Contrary to what many other CS printed textbooks usually show (as textbooks are static), the actual execution of Merge Sort does not split to two subarrays level by level, but it will recursively sort the left subarray first before dealing with the right subarray. Tracing recursion in merge sort java. Bubble Sort (Basic idea, example, code, brief analysis) 5. Non recursive merge sort - Answered by a verified Programmer We use cookies to give you the best possible experience on our website. Given the two sorted singly linked lists. Let's say merge sort has its worst case and quick sort its best. Merge sort is preferred algorithm for sorting a linked list, lets see why, The way linked list is structured which doesn't allow random access makes some other algorithms like Quicksort perform poorly, So Merge sort is often preferred algorithm for sorting linked list. Bottom-up merge sort. The copy back step is avoided with alternating the direction of the merge with each level of recursion. Java Program Insertion Sort. Conceptually, a merge sort works as follows: If the list is of length 0 or 1, then it is already sorted. It can only be used for sorted arrays, but it's fast as compared to linear search. Here is a simple explanation about merge sort on how to it will divide and merge elements. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. It is efficient, comparison based sorting algorithm. (It's implemented below in the merge() method. Now, so that's the Merge Sort algorithm. sort() (remember how JavaScript behaves differently in different browsers?). Quick Sort Algorithm. Learning through experience is the reason I created this post about the implementation of the Merge Sort algorithm in Java. To split an array, Mergesort wi. Below is the syntax highlighted version of Merge. This is known as the base case. // mergeSort. I personally think this video is great at explaining the merge sort algorithm and its underlying logic. Introduction - [Instructor] Now we will learn another sorting algorithm called merge sort. Recursively sort each half. Start the Stopwatch. In this method, we split the given list into two halves. In order to sort A[1 n], we recursively sort A[1 n-1] and then insert A[n] into the sorted array A[1 n-1]. Given the abundance of built-in libraries that perform tasks like sorting and binary search, we often become forgetful of exactly how these tasks are accomplished. If we closely look at the merge sort tree structure, it becomes very clear that, int the recursive call tree, parent nodes depend on children, but siblings are independent. Merge sort is a sorting technique based on divide and conquer technique. Merge Sort is a Divide and Conquer algorithm. What is Recursion In Java programming - Here we cover in-depth article to know more about Java Recursion with proper examples. As you can see in the implementation example that is given here it needs an extra temporary array called : mergedSortedArray to store the temp sorted element. Divide and Conquer is an algorithm paradigm based on multi branched recursion. On small inputs, insertion sort may be faster. 10 Unbundled Product: JavaSE Unbundled Release: 8 Xref: This patch available for x86, 64bit, as patch 152928 Topic. Finally Merge the two sub lists back into one sorted list. Create MergeSort Method Without Using Recursion Nov 6, 2014. In this post we’ll see how to write merge sort program in Java. For example, to sort a Vector, all we need to do is call a sort() method of the java. file streams) into a specified order. Since this is a recursion based algorithm, we have a recurrence relation for it. Best Answer: Just replace the arrays in this code with a java. It seems as though it is breaking down the lists and sorting them correctly but is not carrying over those sorted lists into the next recursive call. For example: You want to sort list of numbers into ascending order or list of names into lexicographical order. Suppose you have some data that's close to sorted -- it forms two sorted lists. 6, for primitive types, it uses an optimized (tuned) quicksort, and for objects (with a comparator) it uses a recursive, stable mergesort. An implementation of odd-even mergesort in Java is given in the following. datastructures, which forms a coherent library of data structures and algorithms in Java specifically designed for educational purposes in a way that is complementary with the Java Collections Framework. The naive version of the merge sort algorithm creates many arrays during its execution:. You should have to never write one because you'd be silly to do that when a standard library class already will already do it for you. This property helps us to deduce a threaded version of merge sort algorithm where, we can really solve the left and right sub-portion of a range in a parallel fashion by. The code I have is meant to read in information from accounts. It is efficient, comparison based sorting algorithm. This operation immediately lends itself to a simple recursive sort method known as mergesort: to sort an array, divide it into two halves, sort the two halves (recursively), and then merge the results. Function oddEvenMergeSort recursively sorts the two halves of the array. Sort the two subsequences recursively by re-applying merge sort. Constructive Merge 65. Binary Search. The command line interface is of little relevance nowadays (please don'. sort() or Collections. With the worst-case time complexity being Ο(n log n), it is one of the most respected algorithms. Join Raghavendra Dixit for an in-depth discussion in this video, Selection sort: Pseudocode, part of Introduction to Data Structures & Algorithms in Java. Especial if the problem size is measured by the level of the recursive tree and the operation count is total number of nodes. The method starts by sorting elements far apart from each other and progressively reducing the gap between them. Concise presentations of java programming practices, tasks, and conventions, amply illustrated with syntax highlighted code examples. The code shown below uses a second array the same size as the original array for merging the values in order. Selection Sort (Basic idea, example, code, brief analysis) 6. One drawback is that it requires an additional array along with the original array that is sorted. Merge sort is much more efficient than the simple sort algorithms like bubble sort and insertion sort. Function Factorial(n As Integer) As Integer If n <= 1 Then Return 1 End If Return Factorial(n - 1) * n End Function Considerations with Recursive Procedures. In Java, the key points in the recursion are exactly the same as in C or C++. Quick Sort (Basic idea, example, comparative analysis only) 7. The base case would be when the array has only one element in it, in which case it is already sorted. Merge sort is an example of a divide-and-conquer algorithm. nio package is integrated with the virtual memory manager of the operating system. As these calls are made the problem gets simpler until you reach a condition that leads to the method no longer making calls upon itself. Finally Merge the two sub lists back into one sorted list. Firstly a quick recap on the merge sort. Merge Sort Implementation in Java Print In computer science, merge sort or mergesort is a sorting algorithm for rearranging lists (or any other data structure that can only be accessed sequentially, e. Destructive Merge Function 64. how will it then return and take new arguments(a,mid+1,j) if it already broke to recurse at first place?. Initial analysis was performed on minibatch field model recovery. List and then use the List's iterator in the for-loops. Go through the following example which uses Merge Sort to sort the unsorted list (7,5,3,1,2,6,2,4) Merge Sort Code Starts. Constructive Merge 65. Studies are being performed to examine the convergence. In merge sort the array is firstly divided into two halves, and then further sub-arrays are recursively divided into two halves till we get N sub-arrays, each containing 1 element. I'm studying algorithms now and I'm trying to do a merge sort on a list of 100000 numbers, the merge sort is recursive and when I execute this code I get the following, File "inversion_count. In this lesson we will learn how to write a source code in Java programming language for doing simple Merge sort using array in ascending order. Java merge sort solution. I feel like I'm almost there but, It's not sorting the last part of my array. We can sort the array values using heap sorting algorithm. This sorting algorithm is known as merge sort. This is accomplished through recursive templates and template meta-programming. If a given array A has zero or one element, simply return; it is already. These are sorted using one comparison and one swap operation (if required), then are merged. Conquer: Then sort the each sub sequences recursively using merge sort. The idea is to start sorting the array elements from the start in groups of 2, 4, 8, 16, and so on (powers of two). Iterative Merge sort Language: Ada Assembly Bash C# C++ (gcc) C++ (clang) C++ (vc++) C (gcc) C (clang) C (vc) Client Side Common Lisp D Elixir Erlang F# Fortran Go Haskell Java Javascript Kotlin Lua MySql Node. Sorting & Searching in C 9. Finally, pass the two halves to merge and see if it works. Concise presentations of java programming practices, tasks, and conventions, amply illustrated with syntax highlighted code examples. Merge sort is a comparison based sorting algorithm. By continuing to use this site you consent to the use of cookies on your device as described in our cookie policy unless you have disabled them. To sort an array using insertion sort technique in Java Programming, you have to ask to the user to enter the array size and array elements in random order, now start sorting the element of the array in ascending order using insertion sort technique. You must write the code to perform the benchmarking of the algorithm you selected. /L1"C/C++" C_LANG Line Comment = // Block Comment On = /* Block Comment Off = */ Escape Char = \ String Chars = "' File Extensions = C CPP CC CXX H HPP AWK. Writing Mergesort in Java is significantly more complex that writing selection sort or insertion sort: The basic procedure (the sort() method) isn't bad. Selection Sort (Basic idea, example, code, brief analysis) 6. , left and right and then sorting each list and then merging the two sorted lists back together as one. Short-coming of the naive recursive (top-down) merge sort algorithm. In this sorting algorithm we use the idea of divide and conquer. If this problem does not have the constant space limitation, we can easily sort using a sorting method from Java SDK. To merge the smaller arrays first you do need to divide your array into smaller arrays too so effectively Merge sort is a two step process. The problem with bubble sort is that it has an average time complexity of O(n^2), meaning that for every n items, it takes n^2. Quicksort will in the best case divide the array into almost two identical parts. Here is the source code and project structure for the MergeSort. Define divide and conquer approach to algorithm design ; Describe and answer questions about example divide and conquer algorithms. I had multiplied 3 matrices in the incorrect order. , call ourselves) The "work toward base case" is where we make the problem simpler (e. Merge sort is one of the most efficient sorting techniques and it's based on the “divide and conquer” paradigm. Merge code in Java. -----import java. sort utility methods for sorting arrays and collections, respectively. Java Practices->Compare and sort Strings Home. See Program 8. A merge sort recursively breaks the values to be sorted in half until there is only one value to be sorted and then it merges the two sorted lists into one sorted list. Java Program Insertion Sort. GitHub Gist: instantly share code, notes, and snippets. Most of the code is already completed, the only thing that I believe I need are two for loops (an inner and an outter) that will make calls to the merge method. Short-coming of the naive recursive (top-down) merge sort algorithm. This sorting algorithm is known as merge sort. (Initially, =). Merging two Sorted Singly Linked List. This worksheet/quiz combo will test what you know about merge sort in Java. Merge Sort is a divide and conquers algorithm in which original data is divided into a smaller set of data to sort the array. a = 2 since we call merge sort twice at every recursion (once on each half). After that, the merge function picks up the sorted sub-arrays and merges them to gradually sort the entire array. It is very efficient sorting algorithm with near optimal number of comparison. Firstly a quick recap on the merge sort. The method uses the merge sort technique and * must be recursive. The next example does not have any corresponding recursive definition. An implementation of odd-even mergesort in Java is given in the following. Do you need make a sort algorithm? because Java has library for this aim. In particular, some of the symbols are not rendered correctly. This asynchronous patch is a security update for wildfly-security-manager package in Red Hat JBoss Enterprise Application Platform 7. It seems as though it is breaking down the lists and sorting them correctly but is not carrying over those sorted lists into the next recursive call. Pesudo Code :. 2007-01-01. Write a Java program to sort an array of given non-negative integers using Stooge Sort Algorithm. asciiz"n" _spaces:. Merge sort is a comparison sort which means that it can sort any input for which a less-than relation is defined. As you can see in the implementation example that is given here it needs an extra temporary array called : mergedSortedArray to store the temp sorted element. Like most recursive sorts, the merge sort has an algorithmic has an complexity of O(n log n). Merge Sort using Java with program code In computer science, merge sort or mergesort is a sorting algorithm for rearranging lists (or any such linear sequential data storage structure) into a specified order. The idea behind merge sort is that it is merging two sorted lists. The recursion is the same, however the outer structure is slightly different. The video and code below will make recursion easy to understand. Divide means breaking a problem into many small sub problems. Merge sort is one of the commonly used sorting algorithms in computer science. /* * You are free to use this code anywhere, copy, modify and redistribute at your * own risk. You start with an unordered sequence. hello everyone, hope you are having a good weekend :) I am working on an algorithm problem, I wrote a psuedo code for iterative merge sort and transferred it to a java code, Iterative merge code is the non-recursive version of mergeSort, every thing is working perfectly but the annoying problem is that when I try my code on an odd-array I just neglects the last element and keep it in place. Includes a Java animation of Insertion sort, but it is hard to read the numbers (too small). Conceptually, a merge sort works as follows: If the list is of length 0 or 1, then it is already sorted. » Combine the results. Merge algorithm. Similar to insertion-sort, merge-sort is an algorithm for sorting numbers in a set but the mechanics are different. datastructures, which forms a coherent library of data structures and algorithms in Java specifically designed for educational purposes in a way that is complementary with the Java Collections Framework. • In some cases, recursive algorithms (such as the ones used for Divide and Conquer algorithms) won’t work. It uses divide-and-conquer policy to sort input elements. I want to be able to build locally, test it out, and then trigger a deploy by doing what I already do, a git commit and / or merge 2. If this problem does not have the constant space limitation, we can easily sort using a sorting method from Java SDK. Java generic mergesort. One can learn how to operate with several arrays and master read/write indices. a) Pick element arr[i] and insert it into sorted sequence arr[0. Merge sort is divide and conquer sorting algorithm. We will study its implementation and its time and space complexity. Merge the two sorted subsequences to produce the sorted answer. Write a recurrence for the running time of this recursive version of insertion sort. Write a recurrence for the running time of this recursive version of insertion sort. Contribute to HSatwick/ProgrammersCorner development by creating an account on GitHub. N Queen Problem can be solved using a recursive backtracking algorithm. Algorithm. When the CPU is available it is assigned to the process that has the smallest next CPU burst. Processes have independent data and code segments. To split a collection, Mergesort will take the middle of the collection and split the collection into its left and its right part. Java: SelectionSort animated demo with code - Duration: Algorithm lecture 8 -- Merge sort algorithm, analysis and problems. Also we have many sorting algorithms. In this tutorial, we will go over Merge Sort Algorithm. A merge sort is a sorting algorithm with complexity of O(nlogn). For example front = the first n/2 elements in anArray back = the remaining elements in anArray Sort frontand back by recursively calling MergeSort with each one. Having gone through and re-read sections of the CIRCULARSTRING code, it is amazing how much easier the code is to read without the confusion of a curve being either a CIRCULARSTRING or LINESTRING as per the SQL-MM spec. hello everyone, hope you are having a good weekend :) I am working on an algorithm problem, I wrote a psuedo code for iterative merge sort and transferred it to a java code, Iterative merge code is the non-recursive version of mergeSort, every thing is working perfectly but the annoying problem is that when I try my code on an odd-array I just neglects the last element and keep it in place. However it derives from tail end recursion removal and is quite tricky. Iterative Destructive Merge 69. Merge Sort is a comparison-based sorting algorithm which works on the divide and conquer paradigm. Tracing Sort and. (array) inside both sort and merge but with prefix for example How recursive function works in merge sort ?. Some code in this lecture is based on code from the book: Java Structures by Duane A. The merge() function is used for merging two halves. It is possible to sort in constant. If a given array A has zero or one element, simply return; it is already. Given the abundance of built-in libraries that perform tasks like sorting and binary search, we often become forgetful of exactly how these tasks are accomplished. Collections class. Merge Sort String Array in Java. Code posting. The case 3 of the Master Method is not very common in real life. Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands. An array of n elements is split around its center producing two smaller arrays. Another fast algorithm, Merge Sort starts sorting from small pieces and repeatedly merges the sorted pieces together until the whole array is. This gives us N lists and each of them only contain one element. Learn: Merge Sort in C++ with Example, Algorithm. Tail Recursive Merge in Java 63. i implemented both recursive and non-recursive versions and non-recursive version is much slower than recursive version. To split a collection, Mergesort will take the middle of the collection and split the collection into its left and its right part. I did review the algorithm, to answer your question, my answer is that we have to go through the merge sort as normal, but piggyback a task to count the inversions. Merge sort visualized, Wikimedia Commons Instead, the most expensive part of any merge sort algorithm is the work of merging, itself — the work of putting back together the small sublists, in. In particular, some of the symbols are not rendered correctly. /***** ***** Non-recursive version of Mergesort using a stack ***** ***** Programmed by Olac Fuentes ***** ***** Last modified September 12, 2011 ***** *****/ import. Merge sort has gained its popularity because of its runtime and simplicity. reference P 21. USGS Publications Warehouse. This worksheet/quiz combo will test what you know about merge sort in Java. But, it is useful to demonstrate a few characteristics of programming techniques in Scala. The merge() function is used for merging two halves. Hello, I am trying to implement a merge sort algorithm that sorts an array of Strings. b = 2 since each of the new subproblem has half the elements in the original list. Non recursive merge sort - Answered by a verified Programmer We use cookies to give you the best possible experience on our website. Divide and Conquer definition. * Your are solely responsibly for any damage that may occur by using this code. The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely. In this sorting algorithm we use the idea of divide and conquer. Some code in this lecture is based on code from the book: Java Structures by Duane A. In this tutorial you will learn about merge sort in Java with program and example. Java sorting The quickSort and mergeSort algorithms are both fast although quickSort is considered the fastest. LeetCode - Sort List: Sort a linked list in O(n log n) time using constant space complexity. e] in non-decreasing order. The merge sort splits the list to be sorted into two equal halves, and places them in separate arrays. The Java code implementing fu:pcla:n. Keep in mind that despite its quadratic complexity it sorts in place without the need of auxiliary space as is the case for merge sort. As these calls are made the problem gets simpler until you reach a condition that leads to the method no longer making calls upon itself. It uses a work array of pointers to lists (or of references in the Java environment). The array of size N is divided into the maximum of logN parts, and the merging of all subarrays into a single array takes O(N) time. Learn the strengths and weaknesses of a variety of data structures, so you can choose the best data structure for your data and applications Code an implementation of each data structure, so you understand how they work under the covers Learn many of the algorithms commonly used to sort data, so. This property helps us to deduce a threaded version of merge sort algorithm where, we can really solve the left and right sub-portion of a range in a parallel fashion by. To split a collection, Mergesort will take the middle of the collection and split the collection into its left and its right part. Memory-mapped files are loaded into memory one. Divide means breaking a problem into many small sub problems. As you can see in the implementation example that is given here it needs an extra temporary array called : mergedSortedArray to store the temp sorted element. These are the steps a human would take to emulate merge sort (top-down). The task is to complete merge() function which is used to implement Merge Sort. Sorting in-place is possible but requires an extremely. Merging linked lists with and without recursion. Submitted by Shubham Singh Rajawat, on June 09, 2017 Merge sort follows the approach of Divide and Conquer. Tasks Complete the Sort class without modifying the public sort methods or the method signatures of the private mergesort methods. This algorithm is a recursive algorithm and works very well for large sets of data. simple recursive merge sort. In this algorithm the heap build is used to rebuild the heap. We break down an array into two sub arrays. /* * You are free to use this code anywhere, copy, modify and redistribute at your * own risk. Combine: Then merge the two sub sequences which are sorted to produce the sorted answer. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves. Rukstales, Kenneth S. A summary of Recursion in Sorting in 's Examples of Recursion. {"categories":[{"categoryid":387,"name":"app-accessibility","summary":"The app-accessibility category contains packages which help with accessibility (for example. In such an algorithm, we divide the data into smaller pieces, recursively conquer each piece, and then combine the results into a final result. Stooge sort is a recursive sorting algorithm with a time complexity of O(nlog 3 / log 1. ! Is biggest element in first half " smallest element in second half?! Helps for nearly ordered lists. For implementation details, one may refer to this code for MKTHNUM problem on Spoj. What Is Recursion? Recursion is a process of a method calling itself. Optimisation - Merge Sort can be optimised to perform better. merge sort java,merge sort pseudocode,merge sort c++,merge sort algorithm in c,merge sort python,mergesort,merge sort complexity,merge sort algorithm,mergesort and quick sort,mergsort c code, merge sort example,merge sort recursive java,merge sort animation,,tutorial,ai1tutorial. This web page gives an introduction to how recurrence relations can be used to help determine the big-Oh running time of recursive functions. PHP array_merge_recursive() function. On each loop iteration, you look at the last element in the key. im having a little trouble getting started with this. This sorting algorithm is known as merge sort. /L1"C/C++ for qDecoder" C_LANG Line Comment = // Block Comment On = /* Block Comment Off = */ Escape Char = \ String Chars = "' File Extensions = C CPP H HPP. Merge sort is one of the most powerful sorting algorithms. Merge Sort using Java with program code In computer science, merge sort or mergesort is a sorting algorithm for rearranging lists (or any such linear sequential data storage structure) into a specified order. An interesting solution, though if the point of the exercise is to sort an array using recursion, I feel it is somewhat defeated by using a for loop. For other Backtracking algorithms, check my posts under tag Backtracking. Merge Sort In Java This is sequel to my other article (available here), where I explained the merge sort algorithm through C program. Honors: Comparators, Searching, Sorting in Java 1. To understand merge sort, we take an. If most work is done outside the recursion, it means that we can re-write the code in a non-recursive way. I am having some trouble understanding the non-recursive mergesort algorithm. Sorting by Merge 69. Merge sort is widely used in various applications as well. In addition, it contains one extra null reference, so that when the number of lists to merge is odd, the last merge is of an existing list with an empty list. Merge Sort in Java Example | Java Merge Sort Program is today’s topic. Quicksort is a fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. This section introduces the students to elementary Java. This algorithm is a recursive algorithm and works very well for large sets of data. Mergesort guarantees to sort an array of N items in time proportional to N log N, no matter what the input. I have seen numerous examples of merge-sorting integers but i can not understand how to this with String. Below is a recursive implementation of the Bubble Sort algorithm, with associated code for reading the input from the command line. Algorithm to merge sorted arrays. -----import java. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Specifically, we want to make sure that you have the right to give away copies of the programs that relate to Texinfo, that you receive source code or else can get it if you want it, that you can change these programs or use pieces of them in new free programs, and that you know you can do these things. I know the void merge function works because it works with my recursive sort, so it has to be with the iterative function. When a page must be replaced ,the oldest page is chosen. Also, we'll try sorting the array 'in place', rather than creating a new array to contain the result. I little bit improved daniel's and gabriel's contribution to behave more like original array_merge function to append numeric keys instead of overwriting them and added usefull option of specifying which elements to merge as you more often than not need to merge only specific part of array tree, and some parts of array just need to let overwrite previous. This section introduces only those aspects of Java that are necessary for understanding the Java code offered in this book. Java is a vast computer language and programming environment, it is not possible to touch upon all Java-related issues. The merge(arr, l, m, r) is key process that assumes that arr[l.