I was recently brushing up on some fundamentals and found merge sorting a linked list to be a pretty good challenge. If you have a good implementation then show it off here.
Merge Sort a Linked List
Asked Answered
https://mcmap.net/q/197228/-non-recursive-merge-sort –
Melantha
Cross-posting a recursive implementation in the solution here - #71444324 –
Arreola
Wonder why it should be big challenge as it is stated here, here is a straightforward implementation in Java with out any "clever tricks".
//The main function
public static Node merge_sort(Node head)
{
if(head == null || head.next == null)
return head;
Node middle = getMiddle(head); //get the middle of the list
Node left_head = head;
Node right_head = middle.next;
middle.next = null; //split the list into two halfs
return merge(merge_sort(left_head), merge_sort(right_head)); //recurse on that
}
//Merge subroutine to merge two sorted lists
public static Node merge(Node a, Node b)
{
Node dummyHead = new Node();
for(Node current = dummyHead; a != null && b != null; current = current.next;)
{
if(a.data <= b.data)
{
current.next = a;
a = a.next;
}
else
{
current.next = b;
b = b.next;
}
}
dummyHead.next = (a == null) ? b : a;
return dummyHead.next;
}
//Finding the middle element of the list for splitting
public static Node getMiddle(Node head)
{
if(head == null)
return head;
Node slow = head, fast = head;
while(fast.next != null && fast.next.next != null)
{
slow = slow.next;
fast = fast.next.next;
}
return slow;
}
non-web.archive explanation in stead of stale link removed in revision 4. –
Honeyhoneybee
A simpler/clearer implementation might be the recursive implementation, from which the NLog(N) execution time is more clear.
typedef struct _aList {
struct _aList* next;
struct _aList* prev; // Optional.
// some data
} aList;
aList* merge_sort_list_recursive(aList *list,int (*compare)(aList *one,aList *two))
{
// Trivial case.
if (!list || !list->next)
return list;
aList *right = list,
*temp = list,
*last = list,
*result = 0,
*next = 0,
*tail = 0;
// Find halfway through the list (by running two pointers, one at twice the speed of the other).
while (temp && temp->next)
{
last = right;
right = right->next;
temp = temp->next->next;
}
// Break the list in two. (prev pointers are broken here, but we fix later)
last->next = 0;
// Recurse on the two smaller lists:
list = merge_sort_list_recursive(list, compare);
right = merge_sort_list_recursive(right, compare);
// Merge:
while (list || right)
{
// Take from empty lists, or compare:
if (!right) {
next = list;
list = list->next;
} else if (!list) {
next = right;
right = right->next;
} else if (compare(list, right) < 0) {
next = list;
list = list->next;
} else {
next = right;
right = right->next;
}
if (!result) {
result=next;
} else {
tail->next=next;
}
next->prev = tail; // Optional.
tail = next;
}
return result;
}
NB: This has a Log(N) storage requirement for the recursion. Performance should be roughly comparable with the other strategy I posted. There is a potential optimisation here by running the merge loop while (list && right), and simple appending the remaining list (since we don't really care about the end of the lists; knowing that they're merged suffices).
Heavily based on the EXCELLENT code from: http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
Trimmed slightly, and tidied:
typedef struct _aList {
struct _aList* next;
struct _aList* prev; // Optional.
// some data
} aList;
aList *merge_sort_list(aList *list,int (*compare)(aList *one,aList *two))
{
int listSize=1,numMerges,leftSize,rightSize;
aList *tail,*left,*right,*next;
if (!list || !list->next) return list; // Trivial case
do { // For each power of two<=list length
numMerges=0,left=list;tail=list=0; // Start at the start
while (left) { // Do this list_len/listSize times:
numMerges++,right=left,leftSize=0,rightSize=listSize;
// Cut list into two halves (but don't overrun)
while (right && leftSize<listSize) leftSize++,right=right->next;
// Run through the lists appending onto what we have so far.
while (leftSize>0 || (rightSize>0 && right)) {
// Left empty, take right OR Right empty, take left, OR compare.
if (!leftSize) {next=right;right=right->next;rightSize--;}
else if (!rightSize || !right) {next=left;left=left->next;leftSize--;}
else if (compare(left,right)<0) {next=left;left=left->next;leftSize--;}
else {next=right;right=right->next;rightSize--;}
// Update pointers to keep track of where we are:
if (tail) tail->next=next; else list=next;
// Sort prev pointer
next->prev=tail; // Optional.
tail=next;
}
// Right is now AFTER the list we just sorted, so start the next sort there.
left=right;
}
// Terminate the list, double the list-sort size.
tail->next=0,listSize<<=1;
} while (numMerges>1); // If we only did one merge, then we just sorted the whole list.
return list;
}
NB: This is O(NLog(N)) guaranteed, and uses O(1) resources (no recursion, no stack, nothing).
I thought I'd try this code on my own Linked List. For some reason it runs slower than the recursive version over an int list of 10 million items. It took around 6-7 seconds for the recursive version and around 10 for this one? –
Croaky
No surprise. The recursive one uses extra storage to speed things up. –
Phoebephoebus
One interesting way is to maintain a stack, and only merge if the list on the stack has the same number of elements, and otherwise push the list, until you run out of elements in the incoming list, and then merge up the stack.
The simplest is from Gonnet + Baeza Yates Handbook of Algorithms. You call it with the number of sorted elements you want, which recursively gets bisected until it reaches a request for a size one list which you then just peel off the front of the original list. These all get merged up into a full sized sorted list.
[Note that the cool stack-based one in the first post is called the Online Mergesort and it gets the tiniest mention in an exercise in Knuth Vol 3]
Here's an alternative recursive version. This does not need to step along the list to split it: we supply a pointer to a head element (which is not part of the sort) and a length, and the recursive function returns a pointer to the end of the sorted list.
element* mergesort(element *head,long lengtho)
{
long count1=(lengtho/2), count2=(lengtho-count1);
element *next1,*next2,*tail1,*tail2,*tail;
if (lengtho<=1) return head->next; /* Trivial case. */
tail1 = mergesort(head,count1);
tail2 = mergesort(tail1,count2);
tail=head;
next1 = head->next;
next2 = tail1->next;
tail1->next = tail2->next; /* in case this ends up as the tail */
while (1) {
if(cmp(next1,next2)<=0) {
tail->next=next1; tail=next1;
if(--count1==0) { tail->next=next2; return tail2; }
next1=next1->next;
} else {
tail->next=next2; tail=next2;
if(--count2==0) { tail->next=next1; return tail1; }
next2=next2->next;
}
}
}
I came up with essentially the same implementation, except with pointers-to-pointers instead of dummy nodes, thinking clearly my innovative code must be a quantum leap in computer science. Nothing new under the sun I suppose. Any suggestions for a clean way of speeding up the mostly pre-sorted case? –
Blowpipe
I'd been obsessing over optimizing clutter for this algorithm and below is what I've finally arrived at. Lot of other code on Internet and StackOverflow is horribly bad. There are people trying to get middle point of the list, doing recursion, having multiple loops for left over nodes, maintaining counts of ton of things - ALL of which is unnecessary. MergeSort naturally fits to linked list and algorithm can be beautiful and compact but it's not trivial to get to that state.
Below code maintains minimum number of variables and has minimum number of logical steps needed for the algorithm (i.e. without making code unmaintainable/unreadable) as far as I know. However I haven't tried to minimize LOC and kept as much white space as necessary to keep things readable. I've tested this code through fairly rigorous unit tests.
Note that this answer combines few techniques from other answer https://mcmap.net/q/196952/-merge-sort-a-linked-list. While the code is in C#, it should be trivial to convert in to C++, Java, etc.
SingleListNode<T> SortLinkedList<T>(SingleListNode<T> head) where T : IComparable<T>
{
int blockSize = 1, blockCount;
do
{
//Maintain two lists pointing to two blocks, left and right
SingleListNode<T> left = head, right = head, tail = null;
head = null; //Start a new list
blockCount = 0;
//Walk through entire list in blocks of size blockCount
while (left != null)
{
blockCount++;
//Advance right to start of next block, measure size of left list while doing so
int leftSize = 0, rightSize = blockSize;
for (;leftSize < blockSize && right != null; ++leftSize)
right = right.Next;
//Merge two list until their individual ends
bool leftEmpty = leftSize == 0, rightEmpty = rightSize == 0 || right == null;
while (!leftEmpty || !rightEmpty)
{
SingleListNode<T> smaller;
//Using <= instead of < gives us sort stability
if (rightEmpty || (!leftEmpty && left.Value.CompareTo(right.Value) <= 0))
{
smaller = left; left = left.Next; --leftSize;
leftEmpty = leftSize == 0;
}
else
{
smaller = right; right = right.Next; --rightSize;
rightEmpty = rightSize == 0 || right == null;
}
//Update new list
if (tail != null)
tail.Next = smaller;
else
head = smaller;
tail = smaller;
}
//right now points to next block for left
left = right;
}
//terminate new list, take care of case when input list is null
if (tail != null)
tail.Next = null;
//Lg n iterations
blockSize <<= 1;
} while (blockCount > 1);
return head;
}
Points of interest
- There is no special handling for cases like null list of list of 1 etc required. These cases "just works".
- Lot of "standard" algorithms texts have two loops to go over leftover elements to handle the case when one list is shorter than other. Above code eliminates need for it.
- We make sure sort is stable
- The inner while loop which is a hot spot evaluates 3 expressions per iteration on average which I think is minimum one can do.
Update: @ideasman42 has translated above code to C/C++ along with suggestions for fixing comments and bit more improvement. Above code is now up to date with these.
This is absolutely brilliant ! I converted it to Delphi and it works very nice. Thank you, sir ! –
Rhaetian
The comments look like they're not updated to match the code. They refer to variables which don't exist in the code
p q & k which (I think) should be left right & block_size respectively. –
Bilbe Made an improved version of this answer: gist.github.com/ideasman42/5921b0edfc6aa41a9ce0 1) Use a pointer to the tail (remove 2x conditional checks, reduces code-size). 2) Avoid re-assigning empty values the size doesn't change. 3) Corrected comments. –
Bilbe
Thanks @ideaman42. I've added one improvement in above code. For tail_p, there is no direct C# equivalent so it stays same :(. –
Furnish
While this is quite good, the version from Mono's eglib performs slightly faster in my tests (optimized C) ~10-20%, See: https://mcmap.net/q/196952/-merge-sort-a-linked-list –
Bilbe
I decided to test the examples here, and also one more approach, originally written by Jonathan Cunningham in Pop-11. I coded all the approaches in C# and did a comparison with a range of different list sizes. I compared the Mono eglib approach by Raja R Harinath, the C# code by Shital Shah, the Java approach by Jayadev, the recursive and non-recursive versions by David Gamble, the first C code by Ed Wynn (this crashed with my sample dataset, I didn't debug), and Cunningham's version. Full code here: https://gist.github.com/314e572808f29adb0e41.git.
Mono eglib is based on a similar idea to Cunningham's and is of comparable speed, unless the list happens to be sorted already, in which case Cunningham's approach is much much faster (if its partially sorted, the eglib is slightly faster). The eglib code uses a fixed table to hold the merge sort recursion, whereas Cunningham's approach works by using increasing levels of recursion - so it starts out using no recursion, then 1-deep recursion, then 2-deep recursion and so on, according to how many steps are needed to do the sort. I find the Cunningham code a little easier to follow and there is no guessing involved in how big to make the recursion table, so it gets my vote. The other approaches I tried from this page were two or more times slower.
Here is the C# port of the Pop-11 sort:
/// <summary>
/// Sort a linked list in place. Returns the sorted list.
/// Originally by Jonathan Cunningham in Pop-11, May 1981.
/// Ported to C# by Jon Meyer.
/// </summary>
public class ListSorter<T> where T : IComparable<T> {
SingleListNode<T> workNode = new SingleListNode<T>(default(T));
SingleListNode<T> list;
/// <summary>
/// Sorts a linked list. Returns the sorted list.
/// </summary>
public SingleListNode<T> Sort(SingleListNode<T> head) {
if (head == null) throw new NullReferenceException("head");
list = head;
var run = GetRun(); // get first run
// As we progress, we increase the recursion depth.
var n = 1;
while (list != null) {
var run2 = GetSequence(n);
run = Merge(run, run2);
n++;
}
return run;
}
// Get the longest run of ordered elements from list.
// The run is returned, and list is updated to point to the
// first out-of-order element.
SingleListNode<T> GetRun() {
var run = list; // the return result is the original list
var prevNode = list;
var prevItem = list.Value;
list = list.Next; // advance to the next item
while (list != null) {
var comp = prevItem.CompareTo(list.Value);
if (comp > 0) {
// reached end of sequence
prevNode.Next = null;
break;
}
prevItem = list.Value;
prevNode = list;
list = list.Next;
}
return run;
}
// Generates a sequence of Merge and GetRun() operations.
// If n is 1, returns GetRun()
// If n is 2, returns Merge(GetRun(), GetRun())
// If n is 3, returns Merge(Merge(GetRun(), GetRun()),
// Merge(GetRun(), GetRun()))
// and so on.
SingleListNode<T> GetSequence(int n) {
if (n < 2) {
return GetRun();
} else {
n--;
var run1 = GetSequence(n);
if (list == null) return run1;
var run2 = GetSequence(n);
return Merge(run1, run2);
}
}
// Given two ordered lists this returns a list that is the
// result of merging the two lists in-place (modifying the pairs
// in list1 and list2).
SingleListNode<T> Merge(SingleListNode<T> list1, SingleListNode<T> list2) {
// we reuse a single work node to hold the result.
// Simplifies the number of test cases in the code below.
var prevNode = workNode;
while (true) {
if (list1.Value.CompareTo(list2.Value) <= 0) {
// list1 goes first
prevNode.Next = list1;
prevNode = list1;
if ((list1 = list1.Next) == null) {
// reached end of list1 - join list2 to prevNode
prevNode.Next = list2;
break;
}
} else { // same but for list2
prevNode.Next = list2;
prevNode = list2;
if ((list2 = list2.Next) == null) {
prevNode.Next = list1;
break;
}
}
}
// the result is in the back of the workNode
return workNode.Next;
}
}
The mono eglib method is similar to what I posted in my answer and both are essentially the same as HP / Microsoft STL std::list::sort(). In the mono eglib example, the "recursion" table is reversed, rank[i] points to a run of length 2 to the power i, except the last entry rank[MAX_RANKS-1] points to a list of unlimited size, and is added to by merging runs of length 2 to the power (MAX_RANK-2). A MAX_RANK of 26 to 32 is more than enough. –
Engaged
A similar strategy is used in a floating point summation function where an array of partial sums indexed by the exponent of a floating point number is used to hold the partial sums, so that only values with identical exponents are added, until it's time to return the full sum by adding up the values in the array from smallest to largest. I'm not sure which was invented first, the summation function or the linked list merge sort. –
Engaged
Here is my implementation of Knuth's "List merge sort" (Algorithm 5.2.4L from Vol.3 of TAOCP, 2nd ed.). I'll add some comments at the end, but here's a summary:
On random input, it runs a bit faster than Simon Tatham's code (see Dave Gamble's non-recursive answer, with a link) but a bit slower than Dave Gamble's recursive code. It's harder to understand than either. At least in my implementation, it requires each element to have TWO pointers to elements. (An alternative would be one pointer and a boolean flag.) So, it's probably not a useful approach. However, one distinctive point is that it runs very fast if the input has long stretches that are already sorted.
element *knuthsort(element *list)
{ /* This is my attempt at implementing Knuth's Algorithm 5.2.4L "List merge sort"
from Vol.3 of TAOCP, 2nd ed. */
element *p, *pnext, *q, *qnext, head1, head2, *s, *t;
if(!list) return NULL;
L1: /* This is the clever L1 from exercise 12, p.167, solution p.647. */
head1.next=list;
t=&head2;
for(p=list, pnext=p->next; pnext; p=pnext, pnext=p->next) {
if( cmp(p,pnext) > 0 ) { t->next=NULL; t->spare=pnext; t=p; }
}
t->next=NULL; t->spare=NULL; p->spare=NULL;
head2.next=head2.spare;
L2: /* begin a new pass: */
t=&head2;
q=t->next;
if(!q) return head1.next;
s=&head1;
p=s->next;
L3: /* compare: */
if( cmp(p,q) > 0 ) goto L6;
L4: /* add p onto the current end, s: */
if(s->next) s->next=p; else s->spare=p;
s=p;
if(p->next) { p=p->next; goto L3; }
else p=p->spare;
L5: /* complete the sublist by adding q and all its successors: */
s->next=q; s=t;
for(qnext=q->next; qnext; q=qnext, qnext=q->next);
t=q; q=q->spare;
goto L8;
L6: /* add q onto the current end, s: */
if(s->next) s->next=q; else s->spare=q;
s=q;
if(q->next) { q=q->next; goto L3; }
else q=q->spare;
L7: /* complete the sublist by adding p and all its successors: */
s->next=p;
s=t;
for(pnext=p->next; pnext; p=pnext, pnext=p->next);
t=p; p=p->spare;
L8: /* is this end of the pass? */
if(q) goto L3;
if(s->next) s->next=p; else s->spare=p;
t->next=NULL; t->spare=NULL;
goto L2;
}
The overall strategy is that we hold two chains of sublists, extending from the two dummy elements head1 and head2. A sublist is known to be sorted. We make several passes, merging the first sublist from head1 with the first from head2, then the second with the second, and so on. (It is essential that there are equal numbers of sublists, or one extra in head1's chain.) The newly merged sublists are attached alternately to the first and second chain, in place, stably, and without recursion. –
Dropout
A significant quirk of this implementation is that it uses a second pointer, e->spare, with each element. Before the end of a sublist, e->next gives the next element. At the end, e->next is NULL. The start of the next sublist (if any) is given by e->spare. At the end of the sort, the entire list is linked via ->next. Knuth's pseudo-code used array indices instead of pointers, and a negative index announced the end of a sublist (and the absolute value gave the next sublist's start). –
Dropout
Step L1 arranges the input list into sublists. A "vanilla" version starts with all sublists of length 1. The "clever" version here keeps any ordered sequences in the input list. In particular, if the list is sorted on arrival, the sort terminates after (n-1) comparisons. The clever version therefore gives a massive saving on sorted input, and a lesser saving on input that has some bias towards being sorted. On random input, the clever version is usually very slightly faster (by a couple of percent) although it uses more comparisons. –
Dropout
As I said at the start, I'm not expecting anyone to like this as an algorithm (unless you often sort an almost-perfectly-sorted list). I've added this (to a fairly old post) to save you the trouble and disappointment I've just gone through ;-) –
Dropout
There's a non-recursive linked-list mergesort in mono eglib.
The basic idea is that the control-loop for the various merges parallels the bitwise-increment of a binary integer. There are O(n) merges to "insert" n nodes into the merge tree, and the rank of those merges corresponds to the binary digit that gets incremented. Using this analogy, only O(log n) nodes of the merge-tree need to be materialized into a temporary holding array.
This is the best implementation I've found so far, made a portable implementation of it (which can be included directly, with addition of optiona
thunk argument ~ like qsort_r). See gist.github.com/ideasman42/… –
Bilbe Another example of a non-recursive merge sort for linked lists, where the functions are not part of a class. This example code and HP / Microsoft std::list::sort both use the same basic algorithm. A bottom up, non-recursive, merge sort that uses a small (26 to 32) array of pointers to the first nodes of a list, where array[i] is either 0 or points to a list of size 2 to the power i. On my system, Intel 2600K 3.4ghz, it can sort 4 million nodes with 32 bit unsigned integers as data in about 1 second.
typedef struct NODE_{
struct NODE_ * next;
uint32_t data;
}NODE;
NODE * MergeLists(NODE *, NODE *); /* prototype */
/* sort a list using array of pointers to list */
/* aList[i] == NULL or ptr to list with 2^i nodes */
#define NUMLISTS 32 /* number of lists */
NODE * SortList(NODE *pList)
{
NODE * aList[NUMLISTS]; /* array of lists */
NODE * pNode;
NODE * pNext;
int i;
if(pList == NULL) /* check for empty list */
return NULL;
for(i = 0; i < NUMLISTS; i++) /* init array */
aList[i] = NULL;
pNode = pList; /* merge nodes into array */
while(pNode != NULL){
pNext = pNode->next;
pNode->next = NULL;
for(i = 0; (i < NUMLISTS) && (aList[i] != NULL); i++){
pNode = MergeLists(aList[i], pNode);
aList[i] = NULL;
}
if(i == NUMLISTS) /* don't go beyond end of array */
i--;
aList[i] = pNode;
pNode = pNext;
}
pNode = NULL; /* merge array into one list */
for(i = 0; i < NUMLISTS; i++)
pNode = MergeLists(aList[i], pNode);
return pNode;
}
/* merge two already sorted lists */
/* compare uses pSrc2 < pSrc1 to follow the STL rule */
/* of only using < and not <= */
NODE * MergeLists(NODE *pSrc1, NODE *pSrc2)
{
NODE *pDst = NULL; /* destination head ptr */
NODE **ppDst = &pDst; /* ptr to head or prev->next */
if(pSrc1 == NULL)
return pSrc2;
if(pSrc2 == NULL)
return pSrc1;
while(1){
if(pSrc2->data < pSrc1->data){ /* if src2 < src1 */
*ppDst = pSrc2;
pSrc2 = *(ppDst = &(pSrc2->next));
if(pSrc2 == NULL){
*ppDst = pSrc1;
break;
}
} else { /* src1 <= src2 */
*ppDst = pSrc1;
pSrc1 = *(ppDst = &(pSrc1->next));
if(pSrc1 == NULL){
*ppDst = pSrc2;
break;
}
}
}
return pDst;
}
Visual Studio 2015 changed std::list::sort to be based on iterators instead of lists, and also changed to a top down merge sort, which requires the overhead of scanning. I initially assumed that the switch to top down was needed to work with the iterators, but when it was asked about again, I investigated this and determined that the switch to the slower top down method was not needed, and bottom up could be implemented using the same iterator based logic. The answer in this link explains this and provide a stand-alone example as well as a replacement for VS2019's std::list::sort() in the include file "list".
`std::list<>::sort()` - why the sudden switch to top-down strategy?
A tested, working C++ version of single linked list, based on the highest voted answer.
singlelinkedlist.h:
#pragma once
#include <stdexcept>
#include <iostream>
#include <initializer_list>
namespace ythlearn{
template<typename T>
class Linkedlist{
public:
class Node{
public:
Node* next;
T elem;
};
Node head;
int _size;
public:
Linkedlist(){
head.next = nullptr;
_size = 0;
}
Linkedlist(std::initializer_list<T> init_list){
head.next = nullptr;
_size = 0;
for(auto s = init_list.begin(); s!=init_list.end(); s++){
push_left(*s);
}
}
int size(){
return _size;
}
bool isEmpty(){
return size() == 0;
}
bool isSorted(){
Node* n_ptr = head.next;
while(n_ptr->next != nullptr){
if(n_ptr->elem > n_ptr->next->elem)
return false;
n_ptr = n_ptr->next;
}
return true;
}
Linkedlist& push_left(T elem){
Node* n = new Node;
n->elem = elem;
n->next = head.next;
head.next = n;
++_size;
return *this;
}
void print(){
Node* loopPtr = head.next;
while(loopPtr != nullptr){
std::cout << loopPtr->elem << " ";
loopPtr = loopPtr->next;
}
std::cout << std::endl;
}
void call_merge(){
head.next = merge_sort(head.next);
}
Node* merge_sort(Node* n){
if(n == nullptr || n->next == nullptr)
return n;
Node* middle = getMiddle(n);
Node* left_head = n;
Node* right_head = middle->next;
middle->next = nullptr;
return merge(merge_sort(left_head), merge_sort(right_head));
}
Node* getMiddle(Node* n){
if(n == nullptr)
return n;
Node* slow, *fast;
slow = fast = n;
while(fast->next != nullptr && fast->next->next != nullptr){
slow = slow->next;
fast = fast->next->next;
}
return slow;
}
Node* merge(Node* a, Node* b){
Node dummyHead;
Node* current = &dummyHead;
while(a != nullptr && b != nullptr){
if(a->elem < b->elem){
current->next = a;
a = a->next;
}else{
current->next = b;
b = b->next;
}
current = current->next;
}
current->next = (a == nullptr) ? b : a;
return dummyHead.next;
}
Linkedlist(const Linkedlist&) = delete;
Linkedlist& operator=(const Linkedlist&) const = delete;
~Linkedlist(){
Node* node_to_delete;
Node* ptr = head.next;
while(ptr != nullptr){
node_to_delete = ptr;
ptr = ptr->next;
delete node_to_delete;
}
}
};
}
main.cpp:
#include <iostream>
#include <cassert>
#include "singlelinkedlist.h"
using namespace std;
using namespace ythlearn;
int main(){
Linkedlist<int> l = {3,6,-5,222,495,-129,0};
l.print();
l.call_merge();
l.print();
assert(l.isSorted());
return 0;
}
Thanks for the modular code. I have one doubt regarding the condition for getting the middle element of the list . I am using while(slow ! = nullptr && fast->next != nullptr){ slow = slow->next; fast = fast->next->next; } It is not giving me the proper output. it is crashing. could you please explain the condition that you've use ie:
while(fast->next != nullptr && fast->next->next != nullptr){ slow = slow->next; fast = fast->next->next; } Why are we checking for fast->next->next ? Thanks –
Hake Simplest Java Implementation:
Time Complexity: O(nLogn) n = number of nodes. Each iteration through the linked list doubles the size of the sorted smaller linked lists. For example, after the first iteration, the linked list will be sorted into two halves. After the second iteration, the linked list will be sorted into four halves. It will keep sorting up to the size of the linked list. This will take O(logn) doublings of the small linked lists' sizes to reach the original linked list size. The n in nlogn is there because each iteration of the linked list will take time proportional to the number of nodes in the originial linked list.
class Node {
int data;
Node next;
Node(int d) {
data = d;
}
}
class LinkedList {
Node head;
public Node mergesort(Node head) {
if(head == null || head.next == null) return head;
Node middle = middle(head), middle_next = middle.next;
middle.next = null;
Node left = mergesort(head), right = mergesort(middle_next), node = merge(left, right);
return node;
}
public Node merge(Node first, Node second) {
Node node = null;
if (first == null) return second;
else if (second == null) return first;
else if (first.data <= second.data) {
node = first;
node.next = merge(first.next, second);
} else {
node = second;
node.next = merge(first, second.next);
}
return node;
}
public Node middle(Node head) {
if (head == null) return head;
Node second = head, first = head.next;
while(first != null) {
first = first.next;
if (first != null) {
second = second.next;
first = first.next;
}
}
return second;
}
}
Nice explanation of the time complexity. –
Fernanda
This is the entire Piece of code which shows how we can create linklist in java and sort it using Merge sort. I am creating node in MergeNode class and there is another class MergesortLinklist where there is divide and merge logic.
class MergeNode {
Object value;
MergeNode next;
MergeNode(Object val) {
value = val;
next = null;
}
MergeNode() {
value = null;
next = null;
}
public Object getValue() {
return value;
}
public void setValue(Object value) {
this.value = value;
}
public MergeNode getNext() {
return next;
}
public void setNext(MergeNode next) {
this.next = next;
}
@Override
public String toString() {
return "MergeNode [value=" + value + ", next=" + next + "]";
}
}
public class MergesortLinkList {
MergeNode head;
static int totalnode;
public MergeNode getHead() {
return head;
}
public void setHead(MergeNode head) {
this.head = head;
}
MergeNode add(int i) {
// TODO Auto-generated method stub
if (head == null) {
head = new MergeNode(i);
// System.out.println("head value is "+head);
return head;
}
MergeNode temp = head;
while (temp.next != null) {
temp = temp.next;
}
temp.next = new MergeNode(i);
return head;
}
MergeNode mergesort(MergeNode nl1) {
// TODO Auto-generated method stub
if (nl1.next == null) {
return nl1;
}
int counter = 0;
MergeNode temp = nl1;
while (temp != null) {
counter++;
temp = temp.next;
}
System.out.println("total nodes " + counter);
int middle = (counter - 1) / 2;
temp = nl1;
MergeNode left = nl1, right = nl1;
int leftindex = 0, rightindex = 0;
if (middle == leftindex) {
right = left.next;
}
while (leftindex < middle) {
leftindex++;
left = left.next;
right = left.next;
}
left.next = null;
left = nl1;
System.out.println(left.toString());
System.out.println(right.toString());
MergeNode p1 = mergesort(left);
MergeNode p2 = mergesort(right);
MergeNode node = merge(p1, p2);
return node;
}
MergeNode merge(MergeNode p1, MergeNode p2) {
// TODO Auto-generated method stub
MergeNode L = p1;
MergeNode R = p2;
int Lcount = 0, Rcount = 0;
MergeNode tempnode = null;
while (L != null && R != null) {
int val1 = (int) L.value;
int val2 = (int) R.value;
if (val1 > val2) {
if (tempnode == null) {
tempnode = new MergeNode(val2);
R = R.next;
} else {
MergeNode store = tempnode;
while (store.next != null) {
store = store.next;
}
store.next = new MergeNode(val2);
R = R.next;
}
} else {
if (tempnode == null) {
tempnode = new MergeNode(val1);
L = L.next;
} else {
MergeNode store = tempnode;
while (store.next != null) {
store = store.next;
}
store.next = new MergeNode(val1);
L = L.next;
}
}
}
MergeNode handle = tempnode;
while (L != null) {
while (handle.next != null) {
handle = handle.next;
}
handle.next = L;
L = null;
}
// Copy remaining elements of L[] if any
while (R != null) {
while (handle.next != null) {
handle = handle.next;
}
handle.next = R;
R = null;
}
System.out.println("----------------sorted value-----------");
System.out.println(tempnode.toString());
return tempnode;
}
public static void main(String[] args) {
MergesortLinkList objsort = new MergesortLinkList();
MergeNode n1 = objsort.add(9);
MergeNode n2 = objsort.add(7);
MergeNode n3 = objsort.add(6);
MergeNode n4 = objsort.add(87);
MergeNode n5 = objsort.add(16);
MergeNode n6 = objsort.add(81);
MergeNode n7 = objsort.add(21);
MergeNode n8 = objsort.add(16);
MergeNode n9 = objsort.add(99);
MergeNode n10 = objsort.add(31);
MergeNode val = objsort.mergesort(n1);
System.out.println("===============sorted values=====================");
while (val != null) {
System.out.println(" value is " + val.value);
val = val.next;
}
}
}
I don't see any C++ solutions posted here. So, here it goes. Hope it helps someone.
class Solution {
public:
ListNode *merge(ListNode *left, ListNode *right){
ListNode *head = NULL, *temp = NULL;
// Find which one is the head node for the merged list
if(left->val <= right->val){
head = left, temp = left;
left = left->next;
}
else{
head = right, temp = right;
right = right->next;
}
while(left && right){
if(left->val <= right->val){
temp->next = left;
temp = left;
left = left->next;
}
else{
temp->next = right;
temp = right;
right = right->next;
}
}
// If some elements still left in the left or the right list
if(left)
temp->next = left;
if(right)
temp->next = right;
return head;
}
ListNode* sortList(ListNode* head){
if(!head || !head->next)
return head;
// Find the length of the list
int length = 0;
ListNode *temp = head;
while(temp){
length++;
temp = temp->next;
}
// Reset temp
temp = head;
// Store half of it in left and the other half in right
// Create two lists and sort them
ListNode *left = temp, *prev = NULL;
int i = 0, mid = length / 2;
// Left list
while(i < mid){
prev = temp;
temp = temp->next;
i++;
}
// The end of the left list should point to NULL
if(prev)
prev->next = NULL;
// Right list
ListNode *right = temp;
// Sort left list
ListNode *sortedLeft = sortList(left);
// Sort right list
ListNode *sortedRight = sortList(right);
// Merge them
ListNode *sortedList = merge(sortedLeft, sortedRight);
return sortedList;
}
};
Here is the Java Implementation of Merge Sort on Linked List:
- Time Complexity: O(n.logn)
- Space Complexity: O(1) - Merge sort implementation on Linked List avoids the O(n) auxiliary storage cost normally associated with the algorithm
class Solution
{
public ListNode mergeSortList(ListNode head)
{
if(head == null || head.next == null)
return head;
ListNode mid = getMid(head), second_head = mid.next; mid.next = null;
return merge(mergeSortList(head), mergeSortList(second_head));
}
private ListNode merge(ListNode head1, ListNode head2)
{
ListNode result = new ListNode(0), current = result;
while(head1 != null && head2 != null)
{
if(head1.val < head2.val)
{
current.next = head1;
head1 = head1.next;
}
else
{
current.next = head2;
head2 = head2.next;
}
current = current.next;
}
if(head1 != null) current.next = head1;
if(head2 != null) current.next = head2;
return result.next;
}
private ListNode getMid(ListNode head)
{
ListNode slow = head, fast = head.next;
while(fast != null && fast.next != null)
{
slow = slow.next;
fast = fast.next.next;
}
return slow;
}
}
while(fast != null && fast.next != null), doesn't it cause a infinite recursion for a list that only has 2 elements? –
Puccoon @Puccoon the first line of
mergeSortList checks the same condition and breaks the recursion in that case. –
Fanechka Hey I know that this is a bit late an answer but got a fast simple one.
The code is in F# but will goes in any language. Since this is an uncommen language of the ML family, I'll give some point to enhance the readability. F# are nesting done by tabulating. the last line of code in a function (nested part) are the return value. (x, y) is a tuple, x::xs is a list of the head x and tail xs (where xs can be empty), |> take the result of last line an pipe it as argument to the expression right of it (readability enhancing) and last (fun args -> some expression) are a lambda function.
// split the list into a singleton list
let split list = List.map (fun x -> [x]) lst
// takes to list and merge them into a sorted list
let sort lst1 lst2 =
// nested function to hide accumulator
let rec s acc pair =
match pair with
// empty list case, return the sorted list
| [], [] -> List.rev acc
| xs, [] | [], xs ->
// one empty list case,
// append the rest of xs onto acc and return the sorted list
List.fold (fun ys y -> y :: ys) acc xs
|> List.rev
// general case
| x::xs, y::ys ->
match x < y with
| true -> // cons x onto the accumulator
s (x::acc) (xs,y::ys)
| _ ->
// cons y onto the accumulator
s (y::acc) (x::xs,ys)
s [] (lst1, lst2)
let msort lst =
let rec merge acc lst =
match lst with
| [] ->
match acc with
| [] -> [] // empty list case
| _ -> merge [] acc
| x :: [] -> // single list case (x is a list)
match acc with
| [] -> x // since acc are empty there are only x left, hence x are the sorted list.
| _ -> merge [] (x::acc) // still need merging.
| x1 :: x2 :: xs ->
// merge the lists x1 and x2 and add them to the acummulator. recursiv call
merge (sort x1 x2 :: acc) xs
// return part
split list // expand to singleton list list
|> merge [] // merge and sort recursively.
It is important to notice that this is fully tail recursive so no possibility of stack overflow, and by first expanding the list to a singleton list list in one go we, lower the constant factor on the worst cost. Since merge are working on list of list, we can recursively merge and sort the inner list until we get to the fix point where all inner list are sorted into one list and then we return that list, hence collapsing from a list list to a list again.
Here is the solution using Swift Programming Language.
//Main MergeSort Function
func mergeSort(head: Node?) -> Node? {
guard let head = head else { return nil }
guard let _ = head.next else { return head }
let middle = getMiddle(head: head)
let left = head
let right = middle.next
middle.next = nil
return merge(left: mergeSort(head: left), right: mergeSort(head: right))
}
//Merge Function
func merge(left: Node?, right: Node?) -> Node? {
guard let left = left, let right = right else { return nil}
let dummyHead: Node = Node(value: 0)
var current: Node? = dummyHead
var currentLeft: Node? = left
var currentRight: Node? = right
while currentLeft != nil && currentRight != nil {
if currentLeft!.value < currentRight!.value {
current?.next = currentLeft
currentLeft = currentLeft!.next
} else {
current?.next = currentRight
currentRight = currentRight!.next
}
current = current?.next
}
if currentLeft != nil {
current?.next = currentLeft
}
if currentRight != nil {
current?.next = currentRight
}
return dummyHead.next!
}
And here are the Node Class & getMiddle Method
class Node {
//Node Class which takes Integers as value
var value: Int
var next: Node?
init(value: Int) {
self.value = value
}
}
func getMiddle(head: Node) -> Node {
guard let nextNode = head.next else { return head }
var slow: Node = head
var fast: Node? = head
while fast?.next?.next != nil {
slow = slow.next!
fast = fast!.next?.next
}
return slow
}
/**
* Definition for singly-linked list.
* public class ListNode {
* int val;
* ListNode next;
* ListNode() {}
* ListNode(int val) { this.val = val; }
* ListNode(int val, ListNode next) { this.val = val; this.next = next; }
* }
*/
class Solution {
public ListNode mergeKLists(ListNode[] lists) {
if(lists == null || lists.length == 0)
return null;
List<Integer> list = new ArrayList<>();
for(int i = 0; i < lists.length; i++){
ListNode listNode = lists[i];
while(listNode != null){
list.add(listNode.val);
listNode = listNode.next;
}
}
if(list.size() == 0)
return null;
Collections.sort(list);
ListNode result = new ListNode(list.remove(0));
list.forEach(v -> doAdd(v, result));
return result;
}
private void doAdd(int val, ListNode node){
if(node.next == null){
node.next = new ListNode(val);
return;
}
doAdd(val, node.next);
}
}
public int[] msort(int[] a) {
if (a.Length > 1) {
int min = a.Length / 2;
int max = min;
int[] b = new int[min];
int[] c = new int[max]; // dividing main array into two half arrays
for (int i = 0; i < min; i++) {
b[i] = a[i];
}
for (int i = min; i < min + max; i++) {
c[i - min] = a[i];
}
b = msort(b);
c = msort(c);
int x = 0;
int y = 0;
int z = 0;
while (b.Length != y && c.Length != z) {
if (b[y] < c[z]) {
a[x] = b[y];
//r--
x++;
y++;
} else {
a[x] = c[z];
x++;
z++;
}
}
while (b.Length != y) {
a[x] = b[y];
x++;
y++;
}
while (c.Length != z) {
a[x] = c[z];
x++;
z++;
}
}
return a;
}
First of all, your answer is nowhere matching with OP question. Second, not sure, what are your commenting ? –
Accolade
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