# Merge sorted lists

**merge sorted lists Second, it calls inline-sort/k with a base-case continuation that converts syntax lists to values expressions. Mail Merge: 1: 09-29-2013 08:11 PM: How to create a Main category mirrored in Sub category data entry type of solution? Geza59: Excel: 0: 10-19-2012 05:44 AM: Need advice on category sorted e-mail merge: GeoB: Mail Merge: 3: 09-08-2011 11:03 PM: Where is the category or distribution list or group as I add new e-mail address? Jamal NUMAN Merge Sort can be used to sort an unsorted list or to merge two sorted lists. In this video, I'm also explaining how to merge two sorted a Aug 24, 2012 · This macro does two things. For example, consider lists {1, 3, 5}and {2, 6, 7, 10}. The two unsorted lists are sorted by continually calling the merge-sort algorithm; we eventually get a list of size 1 which is already sorted. Create a new sorted linked list and extend it with the new nodes. Given K sorted linked lists of size N each, merge them and print the sorted output. Oct 03, 2020 · When we analyze the problem, it's quite easy to observe that we can solve this problem by using the merge operation of Merge Sort. Mar 27, 2019 · The merge sort technique is based on divide and conquer technique. ArrayList or LinkedList in Java. Medium #25 Reverse Nodes in k-Group. Jan 18, 2018 · The Above example shows how a merge sort works. *headRef = SortedMerge (a, b); Merge lists two at a time. Merge sort keeps on dividing the list into equal halves until it can no more be divided. Now we need to divide the List into two equal parts. 2340159867 E. Merge two lists and then sort it in Python List_1 = [1,2,3,4,5] List_2 = [6,7,8,9,10] Above we have two list mentioned as List_1(which contains numbers 1-5) and the second list is List_2(which contains numbers 6-10) and now using ‘ + ‘ operator we will combine the two and assign it into the third list which will be named as List_3 /* sort both sublists*/ sublist1 = mergeSortLists (sublist1); sublist2 = mergeSortLists (sublist2); /* merge the two lists to get the sorted result */ return listMerge (sublist1, sublist2); } With this code outlined, the work remaining involves dividing a list into two pieces of approximately equal size. Step 1 − if it is only one element in the list it is already sorted, return. Examples: Input: k = 3, n = 4 list1 = 1->3->5->7->NULL list2 = 2->4->6->8->NULL list3 = 0->9->10->11->NULL Output: 0->1->2->3->4->5->6->7->8->9->10->11 Merged lists in a sorted order where every element is greater than the previous element. All we have to do is divide our array into 2 parts or sub-arrays and those sub-arrays will be divided into other two equal parts. compareto(second. Add the smaller one to the merged list. Now take one element from each of the K list and create HeapNode object and insert into min-Heap. return the head pointer of the merged linked list. Close queues, linked lists, very clueless about trees and I also know my way around a couple searching/sorting algorithms, but I really need In mergesort solution, each original list has been touched O(logk) times, where k is the number of lists. 2 Solutions. /* C++ Program to Merge Two Sorted Linked Lists */ Enter the First List in ascending order :: How many nodes :: 5 Enter 5 Elements :: Enter [ 1 ] Element :: 1 Enter [ 2 ] Element :: 2 Enter [ 3 ] Element :: 3 Enter [ 4 ] Element :: 4 Enter [ 5 ] Element :: 5 The list is created! The algorithm to merge two lists and sort it : Create two empty lists. - LeetCode-Merge Two The algorithm for this question is quite simple since the two linked lists are already sorted. You have two sorted lists of objects that you wish to merge into one sorted list. Oct 31, 2018 · 2) Merge two sorted lists Example: Input: list1: {20, 10, 40, 30, 50} list2: {90, 60, 50, 70, 80} Output: List1 elements are 20 10 40 30 50 list2 elements are 90 60 50 70 80 //sorting the lists List1 (sorted) elements are 10 20 30 40 50 List2 (sorted) elements are 50 60 70 80 90 Merged list elements are 10 20 30 40 50 50 60 70 80 90 Merge Two Sorted Lists is a coding interview question asked by Amazon (and sometimes Microsoft). Basically, in Java 7, we were using Collections. resultHead = resultTail = NULL; Apr 06, 2018 · Merge Two Sorted Linked Lists in Javascript. The conversion should be done in-place without using any other data structure. h> #include <stdlib. Having reached the bottom of the splitting tree, it then works its way back up, merging the two sorted splits into each other, until a single sorted list is left. Though in C#, we already have a LinkedList class under System. Dec 24, 2018 · Merge operation of merge sort can be performed using the naive method which has also been discussed earlier. 简单的实现，也没什么可说的。. DO READ the post and comments firstly. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Problem 3: Part 1 Write a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Now compare data values of head nodes of both the linked lists (x and y): Sep 11, 2019 · Merge two sorted linked lists and return it as a new list. Merge two sorted list. Assume the below declaration for the Node class. Return the result list. Write an algorithm to merge two sorted linked lists and return it as a new sorted list. com/leetcode-21-merge-two-sorted-lists-java/ LeetCode Tutorial by GoodTe Nov 09, 2012 · 2. This gives us N lists and each of them only contain one element. n-1] into an array C [0. Divide: Breaking the list into n sublists. So I'm creating a merge function for linked list which Feb 26, 2020 · Conceptually, a merge sort works as follows : Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted). Merge Two Sorted Lists (Java) http://www. To create an empty list, you First, take the total number for the first list from the user. (HeapNode-Every Node will store the data and the list no from which it belongs). Jun 01, 1999 · Each merge pass halves the number of lists so you make a total of log2 (R) passes. 5. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort . Easy #22 Generate Parentheses. We use cookies to ensure you have the best browsing experience on our website. Example:->9->3->4->2->5->1 Sorted List: ->1->2->3->4->5->9 Approach: Reference : Merge Sort in array. Complete the mergeLists function in the editor below. If the value of two nodes are the same in the two lists, the nodes in the current list are placed before those of other. is encountered. Now, iterate over both the lists (l1 and l2), and for every iteration. Merge both the lists using the '+' operator and then sort the list. Once the two halves are sorted, the Merge two sorted linked lists and return it as a new list. This is very simple to implement without any libraries. The key comparisons that are needed in the worst case using an efficient algorithm are ____. Apr 12, 2019 · MergeSort (headRef) 1) If the head is NULL or there is only one element in the Linked List then return. Then we will start Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, The key to solve the problem is defining a fake head. next Given two linked-lists, each in sorted order, implement merge according to the below signature. Merge sort is based on divide and conquer technique. Like all recursive algorithms, merge sort needs a base case. That said, each node has been touched O(log k ) times. Introduce write-index k to store position of the first free cell in the resulting array. 12 Feb 2019 The problem is about merging two sorted linked lists. Merge sort in action The merge Step of Merge Sort. For example, if an array is to be sorted using mergesort, then the array is divided around its middle element into two sub-arrays. Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order. While comparing two halves for merging, the first element of both lists is taken into consideration. save the address of the top node of the second linked list to the reference (next) of the last node of the first linked list; C++ program to merge two linked list To do this merge, B elements from each sorted list are loaded into internal memory, and the minimum is repeatedly outputted. This will take O(nkLognk) time. Here we will learn how to sort a list of Objects in Java. We will divide the array in this manner until we get single element in each part because single element is already sorted. Oct 30, 2020 · Merge two sorted linked lists. Then, the overall complexity in this case is O(KN). Jan 17, 2016 · This can be solved by comparing each node of first list with second one and inserting nodes from second to first where ever there is a need. size() == 0) return null; Queue<ListNode> q = new LinkedList<ListNode>(); for(ListNode n : lists){ q. Example: Input: [1->4->5, 1->3->4, 2->6] Output: 1->1->2->3->4->4->5->6 Algorithm: 1 Although Write a function that takes two lists, each of which is sorted in increasing order, and merges the two together into one list which is in increasing order and return Sep 17, 2018 · We are given 2 sorted linked lists and we had to merge them into one such that the final list is also a sorted one. filter_none. Find the length of the link list, say it is L. OUTPUT result : 12->9->8->7->5->3->2. In this challenge, you will implement the merge subroutine of merge sort. Example: Input: 1->2->4, 1->3->4 Output: 1->1->2->3->4->4 I have two lists of objects. Function Description. Sep 13, 2019 · Considering time of the merge sort for a length n list while it is in a running state is T(n), then the recurrence T(n)= 2T(n/2)+n follows from the algorithm definition which asks to put the algorithm to half the size of the two lists of the initial list and then the n steps made to merge the two output lists are added. Also, this approach do not take advantage of the fact that each list is already sorted. Insert the next element from the array into the heap, and delete the minimum element from the heap. You will have to implement merge in two different ways: 1. 6,870 Algorithm to merge two arrays A [0. Let's say we have two sorted arrays foo and bar of length fooLength and barLength, respectively. Merge two sorted linked lists from their end Write a function that takes two lists, each of which is sorted in increasing order, and merges the two together into one list which is in decreasing order and return it. During this, we compare the values of both nodes and put the smaller value in the dummy node which will be appended in the output list. 4230156798 С. goodtecher. C++ Algorithm - Merge two sorted linked lists - Linked List - Write a Sorted Merge() function that takes two lists, each of which is sorted in increasing Write a SortedMerge() function that takes two lists, each of which is sorted in increasing order, and merges the two together into one list which is in increasing order. Implementation for Merge Two Sorted Lists Leetcode Divide the unsorted list into n number of single-item sub lists (n is the total number of elements in the unsorted list). For example, for sorting 900 megabytes of data using only 100 megabytes of RAM: Read 100 MB of the data in main memory and sort by some conventional method, like quicksort. In the previous post, we have discussed the merge sort algorithm on a singly linked list. Example: #21 Merge Two Sorted Lists. org/merge-two-sorted-linked-lists/ Practice Problem Online Judge: http://practice. 21 Jun 2020 Today I am going to show how to solve the Leetcode Merge Two Sorted Lists algorithm problem. Let head be the first node of the linked list to be sorted and headRef be the pointer to head. Algorithm for merge sort. As it Merge sort, we apply the same logic , Divide and Conquer. Given two sorted integer arrays A and B, merge B into A as one sorted array. next return head. Merge Two Sorted Linked Lists Interview prepration- Our coding bootcamp focusing on online coding challenges and competitive programming, delivered to. val ≤ 100; Both l1 and l2 are sorted in non-decreasing order Pseudocode for top-down merge sort algorithm which recursively divides the input list into smaller sublists until the sublists are trivially sorted, and then merges the sublists while returning up the call chain. Sort a List of Nov 15, 2020 · Sorting HOW TO¶ Author. Oct 19, 2020 · Merge the two lists, and then sort the result. Merge two sorted linked lists and return it as a new list. Merging k sorted lists. Sep 05, 2020 · We have discussed implementation of above method in Merge two sorted arrays with O (1) extra space Method 2 (O (n1 + n2) Time and O (n1 + n2) Extra Space) The idea is to use Merge function of Merge sort. Write the sorted data to disk. Jul 15, 2018 · Merge k sorted linked lists and return it as one sorted list. Display the elements in the sorted list. Aug 11, 2014 · Merge k sorted linked lists and return it as one sorted list. INPUT list1: 2->5->8->12 list2: 3->7->9. The size of lists may different. Just like a normal merge sort algorithm works by breaking a array into two parts, then breaking the two parts further into smaller data set until a data set has only a single data element and we know that a single data element is by default sorted, then we Merge sort is based on the divide-and-conquer paradigm. Let’s understand that better by a code. There is also a sorted() built-in function that builds a new sorted list from an iterable. We can use Collections. sort() method that modifies the list in-place. Merge k Sorted Lists - What will change - Solution to problem 23 Merge k Sorted Lists will be added. 0. Merge the two lists such that the result is already sorted. # Create a temporary first node head = result = Node() # Merge elements into a new list while curr_a or curr_b: if curr_a and (not curr_b or curr_a. Two sorted lists can then be used by a ‘parent’ process that will merge them. Merge Two Sorted Lists coding solution. Example : You have to return the head of the first node after 2020년 8월 21일 Merge two sorted linked lists and return it as a new sorted list. 2020년 1월 1일 예제: Merge Two Sorted Lists >문제 Merge two sorted linked lists and return it as a new list. In this case, merge() would use node for its input parameters and return value. Easy. 1: ListNode *mergeTwoLists (ListNode *l1, ListNode *l2) { 2: if (l1 == NULL) return l2; 3: if (l2 == NULL) return l1; 4: ListNode *head = new ListNode (-1); 5: ListNode *p = head; 6: while (l1 != NULL && l2!=NULL) 7: { 8: if (l1->val < l2->val) 9: { 10: p->next = l1; 11: l1= l1->next; 12: } 13: else 14: { 15 Aug 02, 2013 · It's quite common to merge two lists, or combine them into a bigger list and there are multiple ways to do it. For an example, suppose A = [1,2,4,7] and B = [1,3,4,5,6,8], then merged list C will be [1,1,2,3,4,4,5,6,7,8] Approach for Merge Two Sorted Linked Lists. We have to merge these lists into one list. #include <bits/stdc++. Input: First line of input contains number of testcases T. All the elements in the list must implement Comparable interface, otherwise IllegalArgumentException is thrown. Here’s simple Menu Driven Program to Merge two sorted single linked lists in C Programming Language. Interview question for Software Engineer. The l1 is empty. You may assume that nums1 has enough space (size that is equal to m + n) to hold additional elements from nums2. The worst case time complexity of this approach will be O(nlog(n)) where N is total number of nodes present in all lists. Next, we can declare another array merged of Write an algorithm to merge two sorted linked lists and return it as a new sorted list. Two parts are sorted by the algorithm. 2 days ago · C++ linked list merge two sorted lists odd behavior. ) (4) Using your answers from (2) and (3), write down the number of comparisons needed to merge all of the 2m-j sized lists into the collection 2-j+1 sized lists. Solution: Merge sort is an efficient technique for sorting linked lists using recursion. public void MergeSortedList(Node first, Node second){ //we would be adding node from second list to first list //If second node data id more than first one then exchange it if(first. We will populate these lists by taking the inputs from the user. ['This', 'is', 'a', 'sample', 'program', 10, 2, 45, 3, 5, 7, 8, 10] list1 and list2 will remain same. In linked lists cells are often scattered throughout memory, there is no locality bonus to accessing adjacent linked list cells, which is one of the most important advantage for huge performance of quick sort. At first I thought this problem was quite easy. We have to merge them and form only one sorted list C. Consider two sorted linked lists as an example. Merge sort is a fast comparison based sorting algorithm which can be utilized in sorting a Linked List as well. Hi, I've got to create a method that merges two sorted linkedlists. The sorted parts are merged by a special merging procedure for sorted lists. Specifically, you must create a function or program or verb or similar which takes two lists, each sorted in increasing order, and combines them into one list sorted in increasing order. The main idea behind merge sort is that, the short list takes less time to be sorted. Accepted. Now, iterate over both the int mergedArray[]=merging(ar1, ar2); //merging both arrays. Example 1: Input: K = 4 value = {{1,2,3},{4 5},{5 6},{7,8}} Output: 1 2 3 4 5 Jun 14, 2020 · You have to complete the SinglyLinkedListNode MergeLists (SinglyLinkedListNode headA, SinglyLinkedListNode headB) method which takes two arguments – the heads of the two sorted linked lists to merge. Traverse all the linked lists and collect the values of the nodes into an array. Hard #24 Swap Nodes in Pairs. Apr 07, 2020 · Merge two sorted linked lists as Shown in the example: Input. Now, point the pointer of last node to the head of LIST2, so as to form the single list. What is Linked List ? Linked list is a linear data structure that contains sequence of elements such that each element links to its next element in the sequence. Each list is already sorted by a property of the object that is of the datetime type. Input Format Input is managed for you Output Format Output is managed for you Constraints Comparisons for merging four arrays Suppose there are 4 sorted lists of 8 elements each. m-1] and B [0. by Kavit · April 6, 2018. geeks make the second linked list and insert data in it. Note that R, the number of sorted sublists, is always less than N, so the total time is never more than O (N log N). Using this, a Scheme implementation of Merge Sort may look like the following: Sep 22, 2020 · Conquer: In this step, we sort and merge the divided arrays from bottom to top and get the sorted array. Note: The number of elements initialized in nums1 and nums2 are m and n respectively. remove(); ListNode l2 = q. Let us assume that we have an array of integers and from the middle index we split it and again split it, till every sub-array is sorted and then merge them in one by one and keep sorting them when the sub-arrays merge into a big sub-array. merge two sorted lists. play_arrow link brightness_4. 1 // Number of Test Case 3 // Length of first Linked List 1 2 3 2 // Length of second Linked List 3 4 Jul 27, 2017 · So we need to merge element from N array to 1 array having all element in sorted order. Hello everyone! If you want to ask a question about the solution. Merging two lists using list. Example refers to refers to . An example of this is given as follows. Merge sort is often preferred for sorting a linked list. Java Code Review: Merge sorted lists into a single sorted list [closed] Ask Question Asked 10 years, 10 months ago. These two sub-arrays are further divided into smaller units until we have only 1 element per unit. Finally, when one of 26 May 2020 Merge k Sorted Lists in Python · make one heap · for each linked list l in lists − if is in not 0, then insert I into a heap · res := null and res_next := null. p] and B [1. Conquer part at each level will merge 2 sorted arrays which takes O(n) at each level. h> struct node { int number; struct node *next; }; /* add a node to the linked list */ struct node *addnode (int number, struct node *next); /* preform merge sort on the linked list */ struct node *mergesort (struct node *head); /* merge the lists. /* C Program to implement Merge Sort using Linked List */ #include <stdio. Given two sorted integer arrays nums1 and nums2, merge nums2 into nums1 as one sorted array. Merge sort takes advantage of the ease of merging already sorted lists into a new sorted list. Jun 14, 2020 · Add the first node from all the lists into the priority queue. The two unsorted lists are then sorted and merged to get a sorted list. I was inspired by a Google engineer on Youtube demonstrating the solution of the same I have recently summarized several list merging approaches here: answer to Which is the best algorithm to merge k ordered lists? Among them, leapfrogging How to Merge k sorted lists (in Python 3)¶. Oct 31, 2019 · Problem statement. Mar 25, 2017 · We can achieve this by hand drawing the sorted and unsorted lists, but lets look at how we can do this programmatically, and for free, using Merge Sort. Given 2 sorted singly linked list. We break down an array into two sub arrays. Sorting the array 2. We create a new linked list and loop through both lists appending the 10 Feb 2020 Problem Description: Merge k sorted linked lists and return it as one sorted list. Algorithm. Microsoft Word; Microsoft Excel; 4 Comments. And, if the original list was mostly sorted, R will be very small and the algorithm will complete quickly. But takes time O(m^2*n) which is small enough if m is not large. Java Program Jan 14, 2020 · In computer science, merge sort (also commonly spelled mergesort) is an O (n log n) comparison-based sorting algorithm. remove(); } public ListNode merge(ListNode l1, ListNode l2) { if (l1 == null) return l2; if (l2 == null) return l1; ListNode head = null; if (l1. h> using namespace std; struct Node { int data; Merge two sorted linked lists and return it as a new sortedlist. Analyze and describe its complexity. sortedInsert () accepts a list head and a node as an argument and iterates through the list until it finds an element greater than the node. i. The solution is accepted by the judge anyway, so I think it's a bug in the description. data) curr_a = curr_a. Blog and explore more. Then compare the first elements from each list. the benefits of working in-place no longer apply, since merge sort’s linked list algorithm doesn’t need any extra auxiliary storage space,merge operation of merge sort can be implemented without extra space for linked lists. Example: Input:1->2->4, 1->3->4Output:1->1->2->3->4->4. Inplace merge two sorted arrays: Given two sorted arrays X[] & Y[] of size m and n each,merge elements of X[] with array Y[] by maintaining the sorted order i. Merge ksorted linked lists and return it as one sorted list. ToString(). Collections. But it requires two Jan 01, 2020 · The complexity of merging two linked lists is O(M+N) where M and N are the length of two sorted linked lists respectively. Combine the sub-arrays to form a single final sorted array maintaining the ordering of the array. Merge sort is more efficient than quicksort for some types of lists if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common. The most important part of the merge sort algorithm is, you guessed it, merge step. If you give me 8 minute This is one of Amazon's most commonly asked interview questions according to LeetCode (2019)! Merge Two Sorted Lists coding solution. Now we return the next of the dummy node. At the bottom, we've got a bunch of "sorted" one-item array s that we want to combine into one Merging sorted array s. Jun 18, 2020 · from heapq import merge # initializing lists test_list1 = [1, 5, 6, 9, 11] test_list2 = [3, 4, 7, 8, 10] # printing original lists print ("The original list 1 is : " + str (test_list1)) print ("The original list 2 is : " + str (test_list2)) # using heapq. Better Approach: O(nkLogk) Create an result[] of size n*k. First, figure out which node should be head of result list. You are required to complete the body of mergeKSortedLists function. Apr 11, 2014 · tl;dr: Please put your code into a <pre>YOUR CODE</pre> section. It takes the list to be sorted and divide it in half to create two unsorted lists. data) curr_b = curr_b. Algorithm to merge two sorted linked list : Let LLOne and LLTwo be the head pointer of two sorted linked list and resultHead and resultTail are the head and tail pointer of merged linked list. A simple solution would be to create an auxiliary array containing all elements of all lists (order doesn't matter). To insert, we will use a helper function sortedInsert () which will return the head of the sorted list after insertion. We need to merge them and return a single sorted linked list. TIP: C users, please malloc the result into a new array and return the result. advertisement. where we always merge list which are the smallest two in the remaining list. Merge Sort In Java. (5) Add up all of the numbers you found in (4) and rewrite your answer in terms of n. Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their May 07, 2016 · Sort them (using recursion of merge sort). Sort the sublists recursively and then merge the sorted lists together to form the answer. GoodTecher LeetCode Tutorial 21. Do not output anything in your code. Note that the call #,(inline-sort/k …) happens at expansion time, and that the continuation (λ (vs) …) it passes is an expansion-time value. Compare One by One. Maintaining a Priority Queue. You are given a list of lists, where each list is sorted. MergeSort is a divide-and-conquer algorithm that splits an array into two halves (sub arrays) and recursively sorts each sub array before merging them back into one giant, sorted array. 2340156789 47. Given the heads of two sorted linked lists, change their links to get a single, sorted linked list. Then use merge sort algorithm for linked list to sort the list in ascending order. If Sorted is unbound at call-time, for each consecutive pair of elements in Sorted, the relation E1 @< E2 will Jul 14, 2014 · Merge k sorted linked lists and return it as one sorted list. when doing recursive, a new headA and headB will be passed in, so it will add the entire list Sep 12, 2020 · Sort a linked list using Merge Sort. The MERGE algorithm follows the procedure of combining two sorted lists into one sorted list. Jan 08, 2020 · Suppose we have two sorted lists A and B. function merge_sort (list m) is // Base case. Ask Question Asked 5 years, 7 months ago. The input is handled by the code in the editor and the format is as follows: Merge k Sorted Linked Lists. The question comes from this nice blog on programming. O(n*n) 46. I will solve it without giving much details, and test it quickly. · Take adjacent pairs of two singleton lists and merge them to form a list of 2 26 Apr 2020 In the classic Leetcode algorithm titled “21: Merge Two Sorted Lists” we are to take two sorted linked lists and merge them into one sorted Merge two sorted linked lists and return it as a new list. It is also very effective for worst cases because this algorithm has lower time complexity for worst case also. By default i = j = k = 0. Try First, Check Solution later Merging k sorted arraysis easy to implement efficiently, because all you have to do is merge and apply mergesort for arrays, acquiring a fairly quick O(n-k log k) asymptotic runtime. Problem : Given list l1 = 1->2->3. A simple solution is to merge the both sorted lists and then reverse the merged list. Constraints: The number of nodes in both lists is in the range [0, 50]. Convert Sorted List to Binary Search Tree Binary Tree Vertical Order Traversal Binary Tree Zigzag Level Order Traversal Convert Sorted List to Binary Search Tree Binary Tree Vertical Order Traversal Binary Tree Zigzag Level Order Traversal Merging Sorted lists using Heap Data Structure. com Try Our Full Platform: https://backtobackswe. The new list should be made by splicing together 30 Oct 2020 SortedMerge() should return the new list. Wondering if you have any thought and feedback for 3 solutions below: Merge k sorted linked lists and return it as one sorted list. start from the top node and find the last node of the first linked list by searching the NULL in the reference (next) of nodes. The idea is to recursively merge the two input linked list such that the sorted order in the merged linked list is maintained. Let’s first define how we split a list into two parts: mergesort'splitinhalf :: [a] -> ([a], [a]) mergesort'splitinhalf xs = (take n xs, drop n xs) where n = (length xs) `div` 2 Aug 31, 2019 · Sort the result[] using Merge Sort. Diving the array will take O(log n) time and will create log n level of sub arrays. head) "merge" function returns an iterator itself whose values are printed as: The problem with that is that "pop" from the left is an expensive operation for a regular Python list. next = Node(curr_b. We Using a SOURCE CODE : : C. All the given lists are sorted, which means that the head of each list would be the smallest 3. Initialize a new LinkedList that represents the merged list (result). Python lists have a built-in list. Repeat. When all elements of one of the linked lists are added in the result linked list then we simply merge the other linked list with the result linked list. First, it names the values to be sorted, so they don’t get re-evaluated every time they’re compared. Here is Tagged with javascript. Pseudo Code. If sorting in ascending order, the smaller element among two becomes a new element of the sorted list. py - list1 = input list2 = input sort_list = sorted(list1 list2 print'Merge of two sorted list sort_list /* Merge two sorted lists A and B as one linked list Node is defined as struct Node { int data; struct Node *next; } */ #include <iomanip> Node* MergeLists(Node *headA, Node* headB) { // check if either linked list is empty, then return the other one. Let’s look at a quick example to sort a list of strings. merge k sorted lists He asked followed up questions about memory allocation, difference Merge Two Sorted Lists Leetcode - Merge both linked list in such a way that the new merged linked list is in increasing order. Define the base case: if any of the linked lists is empty, simply return the other. Example : 1 -> 10 -> 20 4 -> 11 -> 13 3 -> 8 -> 9 will result in 1 -> 3 -> 4 -> 8 C++. Merge two sorted linked lists and return it as a new sorted list. Then use a efficient sorting algorithm to sort the array in ascending order & print elements. Consider the following conditions: 1. That newly sorted list can be used by another parent process and merged with a second child sorted list. Here, the base case is an input array Splitting the Input. One element is always sorted, thus we have N sorted lists. I would need to make a dictionary because the SortedList only supports one-by-one adds. Oflogn) C. fill X[] with first m smallest elements and fill Y[] with remaining elements. Daniel80202 asked on 2011-12-03. Then, merge sort combines the smaller sorted lists keeping the new list sorted too. O(nlogn) E. Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. Merge sort is no different. The new list should be made by splicing together the nodes of the first two lists. Sep 26, 2018 · In Merge Sort, an item let us consider a list or an array, is broken down into several sub-items until each subitem consists of a single element and merging those subitems in a manner that the result consists of the sorted items. If we take a closer look at the diagram, we can see that the array is recursively divided into two halves until the size becomes 1. You have two lists that are already sorted, you have to merge them and return a new list without any new extra nodes. 6. Just for the record. The algorithm can be implemented as below: Merge sort works by divide the unsorted list into N sublists, where N is the number of elements in the list. Generate a new list mergedList 1. So the total running time is O( n log k ), where n is the total number of nodes. The new list should be constructed by joining the nodes of the input lists. Extract the node and add it to our result list. For example: Initial current list: {1, 1, 2, 4}, Initial other list: {3,4,5,8,9,10} Merge K Sorted Lists. Generic namespace, it is always good to build it from ground up since it helps in understanding fundamentals. Using this method, we can combine multiple lists into a single list. Jan 08, 2020 · Suppose we have two sorted arrays A and B. Merging two Lists in Python: We can simply merge two lists using + operator like below. Program/Source Code. For more information you can take a look at this excellent explanation from Khan Academy. This will be the This function merges the nodes of other into the current list such that the current list stays sorted. I’ve chosen the second option, sine it doesn’t require us to spend extra time sorting already-sorted lists. Active 1 year, 9 months ago. Merge Sort: function merge_sort(list m) // if list size is 0 (empty) or 1, consider it sorted and return it // (using less than or equal prevents infinite recursion for a zero length m) if length(m) <= 1 return m // else list size is > 1, so split the list into two sublists // 1. In merge two sorted linked lists we have given head pointer of two linked lists, merge them such that a single linked list is obtained which has nodes with values in sorted order. data): result. next result = result. You should NOT read any input from stdin/console. When either of the list gets exhausted, the other list is appended to the end of merged list. It’s actually one of the earliest problems we teach here at Outco during Oct 04, 2019 · Merge two sorted linked lists and return it as a new list. Merging first two pairs require O(2N), then the list becomes length 2N, the merge 2N and N requires O(3N) etc. Viewed 14 times 1. Every recursive algorithm is dependent on a base case and the ability to combine the results from base cases. Merge M sorted lists. 1. 4964296Add to ListShare. My take on the pseudo-code: lists[k][?] // input lists c = 0 // index in result result[n] // output heap[k] // stores index and applicable list and uses list value for comparison // if i is the index and k is the list // it has functions - insert(i, k) and deleteMin The only way that I can think of merging two SortedList instances would be to union them, then convert to a lookup, then grab the first element of the lookup collection to make a dictionary. Each of the n nodes will first sort N/n of the original input data values, using a fast sequential sort mechianism, such as quicksort. Example: Input: [ 1->4->5, 1->3->4, 2->6 ] Output: 2020년 3월 4일 Merge two sorted linked lists and return it as a new list. The implementation is in C, using natural merge sort. The slow random-access performance of a linked list makes some other algorithms (such as quicksort) perform poorly, and others (such as heapsort) completely impossible. So worst case time taken by merge sort is O(n log n). addAll() method. System. Contribute to eMahtab/merge-k-sorted-lists development by creating an account on GitHub. For each testcase, first line of input conatains length of both linked lists N and M respectively. To solve this, we will use the heap data structure. Active today. Analyze and describe its complexity. Apr 17, 2020 · Merges two sorted ranges [first1, last1) and [first2, last2) into one sorted range beginning at d_first. e. Merge B into A in sorted order. sort() that was accepting a List and, eventually, a Comparator – in Java 8 we have the new List. The new list should also be sorted. The returned list should be sorted as well. Using Min Heap Also learn to join arraylists without duplicates in the combined list. Now in our current problem’s case to merge multiple sorted lists of strings, we already have the lists sorted. For example if the first 30 Jun 2020 Given two sorted lists, merge them so as to produce a combined sorted list ( without using extra space). Divide & Conquer algorithm has 3 steps: 1. Merge k Sorted Lists. Release. Oct 01, 2019 · Sorted merge in one array Last Updated: 10-01-2019 Given two sorted arrays, A and B, where A has a large enough buffer at the end to hold B. OPEN. Implementation of Merge Sort in JavaScript. Example 1 Merge Two Sorted Lists II. Find Complete Code at GeeksforGeeks Article: http://www. MergeSort (a); MergeSort (b); 4) Merge the sorted a and b (using SortedMerge () discussed here) and update the head pointer using headRef. This code sample explains how a merge sort algorithm works and how it is implemented in C#. 5293840167 B. Dec 04, 2019 · It repeats until no element is present in the unsorted part. data. deque double-ended queue would solve it - popleft() is O(1). We divide the while data set into smaller parts and merge them into a larger piece in sorted order. Add the next node (if present) from the extracted node list. Two sorted arrays can be merged so that a single resultant sorted array is obtained. Create Min-Heap of type HeapNode. All we will need is three variables, p, q, and em, and an empty list newlist. Fixed version: from collections import deque def merge_sorted_lists(left, right): """ Merge sort merging function. I would like to combine the two lists into one sorted list. Examples: Input : head1: 5->7->9 2020년 5월 9일 문제 Merge two sorted linked lists and return it as a new list. Type of Issue - Please add/delete options that are not relevant. The total item count for both lists can be different. Aug 22, 2019 · The merge sort algorithm on doubly linked list works in a similar way, which is by splitting the list into two halves, and then sorting each sublist recursively and finally merging both the sorted list together to get single sorted list. In this article, we will take a look at two simple way to join two lists in Java , you can further extend that idea to join any number of List or it's implementation e. The sort/2 predicate can sort a cyclic list, returning a non-cyclic version with the same elements. Merge Two Sorted Lists solution: LeetCode 21 Code and written explanation: https://terriblewhiteboard. # Merge two lists finalList = list1 + list2 It will return a new concatenated lists i. next else: result. h> using namespace std; class Node { public: int data; Node* Jun 30, 2020 · Merge two sorted lists (in-place) filter_none. com/merge-two-sorted-lists-leetcode-21/ Link to problem (b) Let’s Examine A New Merge Sort Algorithm, Where Parameter A In (A,n) Is A List Of Numbers To Be Sorted And N Is The Total Length Of List A. It starts by comparing every two elements (i. Merge K Sorted Lists: Merge k sorted linked lists and return it as one sorted list. Analysis. Merge Sort Algorithm The High-Level Idea. Example: Input: [ 1->4->5, 1->3->4, 2->6 ] Output: 1->1->2->3->4->4->5->6 Solution 1: Min heap. next = Node(curr_a. q] two arrays sorted in increasing order. Adding New Code Improving Code Given the heads of two sorted linked lists, change their links to get a single, sorted linked list. Then it sort each sublist recursively and finally merge the two sorted lists together to form the answer. addAll() method simplest way to append all of the elements in the given collection to the end of another list. To create an empty list, you can use an empty square bracket. Example: Input:[ 1->4->5, 1->3->4, 2->6]Output:1->1->2->3->4->4->5->6. Combining Given K sorted linked lists of different sizes. The task is to merge them in such a way that the resulting list is in decreasing order. Implement and use the helper function _merge , which merges two sorted arrays. The algorithm is straight forward. Brute Force Method: A naive way to solve the problem would be to put all the elements in one single array and then sort the array. Use merge sort like merge routine to merge as the lists are sorted. Exit. In this blog, I will provide a simple implementation of MergeSort using C# with comments on every significant line of code for beginners to quickly grasp the list::merge Merge sorted lists (public member function ) list::reverse Reverse the order of elements (public member function ) list::unique Remove duplicate values now sort a 1 a 2 a n merge two sorted lists Merge Sort Tn 2Tn2 MT n How to from CSCI 1170 at NYU Shanghai The Merge Sort strategy is for sorting data elements of a linked list would be: Split the list into equal part sublists. For example, given following linked lists : 5 -> 8 -> 20 4 -> 11 -> 15 The merged list should be : 4 -> 5 -> 8 -> 11 -> 15 -> 20 Aug 14, 2020 · Objective: Given two sorted linked lists, objective is to merge both the lists in sorted order. Repeatedly merge sublists to produce newly sorted sublists until there is only 1 sublist remaining. Approach-1 for Merge K Sorted Linked Lists Brute Force Traverse all the linked lists and put all the values in an Array/ArrayList/Vector(Whatever storage you find convenient) Sort the data; Create a new linked list from the sorted data; Voila!our merged and sorted linked list is ready. Create an array arr3 [] of size n1 + n2. First, take the total number for the first list from the user. We check for the smaller of two element on the current index and increment the index of the list whose no. size() != 1){ ListNode l1 = q. The following diagram shows the complete merge sort process for an example array {10, 6, 8, 5, 7, 3, 4}. sort(), which accepts a Comparator. Given M sorted lists of variable length, print them in sorted order efficiently. Is the best way just t Merging two sorted linked list using merge function by passing the head of the two linked list itr = merge(ll1. 1. The slow random-access performance of a linked list makes some other algorithms such as Quick Sort perform poorly, and others such as Heap Sort completely impossible. The function is expected to merge k sorted lists to create one sorted list. Compare head nodes of two give lists, whichever is smaller, that should be the head of result list. Mergesort is a divide and conquer algorithm. The sort() method sorts the list ascending by default. Procedure MergeSort (A,n): If N=1 Then Return A Else Divide A Into Three Equal This problem has been solved! Aug 31, 2019 · Objective: Given a Linked List, Sort it using merge sort. Write a function to merge given two sorted linked lists. Sort and iterate over this array to get the proper value of nodes. Repeatedly merge the sub-arrays to produce a new sorted array until there is only 1 array remaining. A program that demonstrates this is given as follows. O(n) D. list1 = [10, 20, 30] list2 = [40, 50, 60] merged_list = list1 + list2 print("Merged List: ", merged_list) list1 += list2 print("Merged List using +=: ", list1) The above solution internally creates a new list (merged_list) with a shallow copy of list1 and is concatenated with a shallow copy of list2. Like all divide and conquer algorithms, merge sort algorithm splits the list into two sublists. Unlike some (efficient) implementations of quicksort, merge sort is a stable sort. Merging two sorted linked list is intuitive: every time choosing the node with a smaller value from two lists and move forward that chosen list, until we reach the end of a list. The new list is . Method 1. Merge Sort is preferred for sorting a linked list. I am having trouble with the code I wrote, and can't seem to Merge k sorted linked lists and return it as one sorted list. Algorithm or recursive method to merge two sorted linked lists in java Create merge method, taking head1 and head2 as method parameter merge (Node head1, Node head2) Create variable mergedList, which will point to head of merge linked list Nov 27, 2018 · A common problem most programmers are probably familiar with is to merge two sorted arrays into a single sorted array. Once the array is sorted we can create a new linked list from the elements and return the result. Andrew Dalke and Raymond Hettinger. head,ll2. Example: Merge k sorted linked lists and return it as one sorted list. Repeatedly merge sublists into sorted sublists until there is only one sorted list. Denote by A [1. Now, finally, we get sorted Consider the following two steps to merge sorted linked lists. The solution doesn't really do that, it reuses and even modifies the nodes in the input lists. Merging of two lists done as follows: The first element of both lists is compared. Split the list into two halves. Free 5-Day Mini-Course: https://backtobackswe. m+n-1] is as following: Introduce read-indices i, j to traverse arrays A and B, accordingly. mergeLists has the following parameters: Merge Sort. 3 Oct 2020 Let's say we have two sorted arrays foo and bar of length fooLength and barLength, respectively. Linked List. Input: Two sorted linked list List a, List b. Understand the problem: The question asks for merging k sorted linked list and return it as one sorted list. The Merge Sort Algorithm works as follows: Divide the unsorted array into n sub-arrays, each array containing a single element. You are given two sorted lists having head as head1 and head2, write a program to merge them into one big sorted list. Thus, instead of having to merge n k elements, we start with only k elements (lists) that we have to merge. Merge Sort · Divide the unsorted list into N sublists, each containing 1 element. Approach: Without Recursion: Create a new node say result; Navigate through both the linked lists at the same time Merge_sorted_list. At the beginning of the algorithm, p will point to the first element of the list1 whereas q will point to the first element of the list2. Initialize a new LinkedList that represents the merged list ( result ). 4213058967 D. sort() method to sort a list in the natural ascending order. 2019년 11월 24일 Problem 문제 링크 난이도 Easy 문제입니다. Call recursive function mergeSort() two sort the individual lists. As for sorting, you can refer here for more about sorting algorithms. add(merge(l1, l2)); } return q. h> using namespace std; struct Node { int data; struct Node* next; }; Node* newNode (int key) { struct Node* temp = edit. If the list consists of more than one item, we split the list into two halves and recursively invoke a merge sort on both halves. 3. Given a linked list, sort it using merge sort algorithm. Hard. Sort an unsorted list The idea is to split the unsorted list into smaller groups until there is only one element in a group. extend() public class Solution { public ListNode mergeKLists(ArrayList<ListNode> lists) { if(lists. FrontBackSplit (head, &a, &b); /* a and b are two halves */ 3) Sort the two halves a and b. Then l2 is the result. The new list should be made by splicing together the nodes of the first two lists, and should also be sorted. Please read our cookie policy for more information about how we use cookies. data <= curr_b. Now, sort the list using some sorting algorithm like bubble, merge or quick. g. com/problems/merge-two-sorted-lists/. val) { head = l1; l1 = l1. Java Sort List. Solution 2: insert the first k elements into a binary heap. 2) Else divide the linked list into two halves. By definition, if it is only one element in the list, it is sorted. . rithm for merging k sorted lists, namely, recur-sively merge the first lists, do likewise for the last lists, then merge the two results. geeksforgeeks. Linked list can be sorted using merge-sort very efficiently. And list l2 = 10->20->30. com/pricing 📹 Intuitive Video Explanations 🏃 Run Code As You L Feb 10, 2020 · Merge K Sorted Lists 1. We can just pick the smallest one from all heads of lists and then connect it to the final list. This is why the variable inside the log Jun 20, 2020 · These lists are sorted. How do you merge and sort two lists at once? We can take advantage of the fact that both lists are already sorted and implement I want to merge two sorted lists of Integers but this is not the general mergesort case because the same number may appear in both lists. The merge sort algorithm on doubly linked list works in similar way by splitting the list into two halves, sorting each sublist recursively, and finally merge the both sorted lists together to get single sorted list. Find These are the two lists we want to merge. Active 5 years, 7 months ago. So if the lists are [1,4,5], [1,3,4], [2,6], then the final list will be [1,1,2,3,4,4,5,6]. (However, each number can only appear once in a particular Given pointers to the heads of two sorted linked lists, merge them into a single, sorted linked list. This will be the sorted list. Analysis: The idea is relative simple, add one list into the other. print("\ nDisplay merged array: " ) 7 Aug 2018 Share this Given two sorted Linked Lists, we need to merge them into the third list in sorted order. com/pricing 📹 Intuitive Video Explanations 🏃 Run Code As You L Merge Sort repeatedly splits the input in two, until an empty list or single-element list is reached. 1 day ago · Merge Two Sorted Lists; Problem Statement. Input 으로 두 ListNode 를 받으면 합쳐서 오름차순으로 정리된 ListNode 를 return 하면 됩니다. val < l2. remove(); q. A sequence is said to be sorted with respect to a comparator comp if for any iterator it pointing to the sequence and any non-negative integer n such that it + n is a valid iterator pointing to an element of the sequence, comp (* (it + n), * it) evaluates to false. Merge the two sorted list in a merge step to produce 1 sorted list. I wrote the following code to merge two sorted lists. Brute Force Solution. merge should create a new list which is made of the merge the two lists in a single sorted list and return a pointer to the head of the new list. 129 Contributed by Richard O'Keefe. This is Jun 23, 2020 · The steps required to merge two sorted linked list is as follows: Traverse the LIST1 to its last node. 2020년 1월 13일 Merge two sorted linked lists and return it as a new list. You can also make a function to decide the sorting criteria(s). Note that List may contain non-ground terms. , 1 with 2, then 3 with 4) and swapping them if the first should come after the second. next Dec 07, 2018 · Merge two sorted arrays in Java. While the priority queue is not empty. When j = 2, we merge twice, etc. We can use + operator to merge two lists i. Problem Statement Given two sorted linked lists, merge them so that the resulting linked list is also sorted. We get a tight bound for the expense, in comparisons made between list elements, of this merge. Given two linked lists of size N and M, which are sorted in non-decreasing order. The purpose of the heap is to give you the minimum, so I'm not sure what the purpose of this for-loop is - for j := 2 to k. - 문제 연결 리스트를 이용 하여 주어진 정렬된 두 리스트를 병합시켜 새 리스트를 만들어 Merge two sorted linked lists and return it as a new list. Initilaize resultHead and resultTail to NULL. Array 1 = 1 3 7 9 10 Array 2 = 2 5 8 Merged array = 1 2 3 5 7 8 9 10. Then, group two elements in the sorted order and gradually build the size of the group. ToString()) > 0) { node t = first; first = second; second = first; }head = first;//Assign head to first Given two linked lists sorted in reverse order, write a function to merge them in such a way that the result list should be in reverse order Example. Conquer means sort the two sub-arrays recursively using the merge sort. Either head pointer may be null meaning that the corresponding list is empty. out. Is there a way I can improve it? Possible ideas (not sure how to implement them): Remove code duplication (setting the returning list node and moving to the next) Avoid the use of the infinite loop; Avoid the use of panic! This is the data structure: The algorithm to merge two lists and sort it : Create two empty lists. It is an extension of merging the two sorted linked list but more complicated. For an example, suppose A = [1,2,4,7] and B = [1,3,4,5,6,8], then merged list C will be [1,1,2,3,4,4,5,6,7,8] May 26, 2020 · Suppose we have some lists, these are sorted. If we merge these lists into a single sorted list of 32 elements. The Time To Merge Two Sorted Lists Of Size N Is B. Next, we can declare another array merged of size fooLength + barLength. The merge() function would be similar to the one shown in the top-down merge lists example, it merges two already sorted lists, and handles empty lists. add(n); } while(q. mid will be L/2. AlgoDaily - Merge Sorted Linked Lists - Description You may see this problem at Microsoft, Adobe, and Netflix. In other words, merge two sorted linked lists from their end. 2. Lets briefly review Merge Sort: Merge Two Sorted Lists Merge two sorted linked lists and return it as a new list. Example: Input: 1->2->4 1->3->4 Output: 1->1->2->3->4->4 Merge Two Sorted Linked lists solution in Java. The merged linked list should look like this: The idea behind this solution is to use the sorted property and iterate over both the lists using two pointers. If you had some troubles in debugging your solution, please try to ask for help on StackOverflow, instead of here. Dec 26, 2018 · Problem statement: Write a C++ program to sort two single linked lists using merge sort technique. List1: 10->15->17->20 List2: 5->9->13->19 Result: 5->9->10->13->15->17->19->20 Merge sorted lists Merges x into the list by transferring all of its elements at their respective ordered positions into the container (both containers shall already be ordered). Definition and Usage. Algorithm 2:-This is an improvement over 1. Time complexity: O(nklogk) Space complexity: O(k) Merging two lists using + operator. Viewed 310 times 1 $\begingroup$ Merging sorted lists help. We show the algorithm is cheapest among all similar divide-and-conquer approaches to k-way merging. Ask Question Asked today. Medium #23 Merge k Sorted Lists. Conquer: Recursively splits the list. The question also asked for analyzing and describing the Nov 11, 2016 · Now, merge each blocks of k elements with the block to its left. Merge sort is based on Divide and conquer method. Merge sorted lists Merges x into the forward_list by transferring all of its elements at their respective ordered positions into the container (both containers shall already be ordered). Note: You have to modify the array A to contain the merge of A and B. This problem is quite similar to Merge Sort in Arrays. The task is to merge them in such a way that after merging they will be a single sorted linked list. Java 8 Object Oriented Programming Programming. Complexity However, instead breaking the list down into each single element (which by definition is sorted), the pairwise merging solution treats each sorted list as its own element. Merge arraylists – List. May 12, 2012 · How to use mail merge to create a list sorted by category in Word. 2020년 2월 1일 https://leetcode. h> using namespace std; class Node { public: int data; Node* next; }; void MoveNode (Node** destRef, Node** edit. Switching to the collections. Answer to Exercise 3: Merge two sorted lists In this exercise, you will write a function called mergeLists that takes two sorted l 4 Oct 2019 Merge Two Sorted Linked lists solution in Java. Suppose You Choose The First Element As A Pivot In The List (5293840167,using The Partition Algorithm In The Book, What Is The New List After The Partition? A. Problem Note: The two linked lists can be of different sizes; The new list must be created by splicing together the nodes of the first two lists. Merge sort is a divide and conquer algorithm. */ struct node *merge (struct node *head_one, struct node *head_two); int main (void) { struct node *head; struct node *current; LeetCode – Merge Sorted Array (Java) Given two sorted integer arrays A and B, merge B into A as one sorted array. Suppose you have k sorted lists with a total of N elements. The method signature is, Node* MergeLists(Node* list1, Node* list2); struct Node{ int data; Node *next; } The following is the solution I came up with, The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists. Example: List a : ->2->6->18 Listb: ->1->3->17->19 Merged List: ->1->2->3->6->17->18->19. Merge Two Sorted Lists: Merge two sorted linked lists and return it as a new list. This is a very famous interview problem that demonstrates the concept of recursion. merge () # to combine two sorted lists res = list (merge (test_list1, test_list2)) # printing result print ("The combined sorted list is : " + str (res)) What is Merge sort in C? Conceptually, merge sort algorithm that recursively splits the unsorted list into n sublists until there is only one element remaining, then merges those sublists to produce a sorted list. We have to merge them and form only one sorted array C. The idea is to insert all the node values from all the k lists into an array. Oct 01, 2013 · COMPARE AND CONTRAST. -100 ≤ Node. The standard algorithm would be to repeatedly compare the heads of the two lists, pop the smaller, and append it to the result. merge sorted lists
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