C++ Program to Implement Merge Sort Algorithm on Linked List

The merge sort technique is based on divide and conquer technique. We divide the while data set into smaller parts and merge them into a larger piece in sorted order. It is also very effective for worst cases because this algorithm has lower time complexity for worst case also.

Linked list can be sorted using merge-sort very efficiently. For the linked list the merging task is very simple. We can simply update the links to merge them. In this section we will see how to sort the linked list using this approach.

The complexity of Merge Sort Technique

• Time Complexity − O(n log n) for all cases

• Space Complexity − O(n)

Input − The unsorted list: 14 20 78 98 20 45
Output − Array after Sorting: 14 20 20 45 78 98

Algorithm

mergeList(ll1, ll2)

Input − It takes two linked lists ll1 and ll2

Output − The merged list

Begin
   if ll1 is empty, then
      return ll2
   if ll2 is empty, then
      return ll1
   if data(ll1) <= data(ll2), then
      new_head = ll1;
      next(new_head) = mergeList(next(ll1), ll2)
   else
      new_head = ll2;
      next(new_head) = mergeList(ll1, next(ll2))
   return new_head
End

split_list(start, ll1, ll2)

Input − The start pointer of a linked list, two output arguments ll1 and ll2

Output − Two linked list generated from the linked list

Begin
   slow := start
   fast := next(start)
   while fast is not null, do
      fast := next(fast)
      if fast is not null, then
         slow := next(slow)
         fast := next(fast)
   end while
   ll1 := start
   ll2 := next(slow)
   next(slow) := null
End

mergeSort(start)

Input − The linked list

Output − Sorted linked list

Begin
   head = start
   if head is null or next(head) is null, then
      return
   split_list(head, ll1, ll2)
   mergeSort(ll1)
   mergeSort(ll2)
   start := mergeList(ll1, ll2)
End

Source Code (C++)

#include<bits/stdc++.h>
using namespace std;
class node { //define node to store data and next address
   public:
   int data;
   node *next;
};
void display(class node* start) {
   node* p = start; // current node set to head
   while(p != NULL) { //traverse until current node isn't NULL
      cout << p -> data << " ";
      p = p -> next; // go to next node
   }
}
node* getNode(int d) {
   node* temp = new node;
   temp -> data = d;
   temp -> next = NULL;
   return temp;
}
node* mergeList(node* ll1, node* ll2) { //function for merging two sorted list
   node* newhead = NULL;
   if(ll1 == NULL)
      return ll2;
   if(ll2 == NULL)
      return ll1;
   //recursively merge the lists
   if(ll1 -> data <= ll2 -> data) {
      newhead = ll1;
      newhead -> next = mergeList(ll1->next,ll2);
   } else {
      newhead = ll2;
      newhead -> next = mergeList(ll1,ll2->next);
   }
   return newhead;
}
void splitList(node* start, node** ll1,node** ll2) {
   //similar to flyod's tortoise algorithm
   node* slow = start;
   node* fast = start -> next;
   while(fast!= NULL) {
      fast = fast -> next;
      if(fast!= NULL) {
         slow = slow -> next;
         fast = fast -> next;
      }
   }
   *ll1 = start;
   *ll2 = slow -> next;
   //spliting
   slow -> next = NULL;
}
void mergeSort(node** start) {
   node* head = *start;
   node* ll1,*ll2;
   //base case
   if(head == NULL || head->next == NULL) {
      return;
   }
   splitList(head,&ll1,&ll2); //split the list in two halves
   //sort left and right sublists
   mergeSort(&ll1);
   mergeSort(&ll2);
   //merge two sorted list
   *start = mergeList(ll1,ll2);
   return;
}
int main() {
   cout << "Creating the linked list: " << endl;
   cout << "Enter 0 to stop building the list, else enter any integer" << endl;
   int k,count = 1,x;
   node* curr,*temp;
   cin >> k;
   node* head = getNode(k);   //buliding list, first node
   cin >> k;
   temp = head;
   while(k) {
      curr = getNode(k);
      temp -> next = curr;//appending each node
      temp = temp -> next;
      cin >> k;
   }
   cout<<"Before sorting: " << endl;
   display(head); // displaying the list
   cout<<"\nAfter sorting: " << endl;
   mergeSort(&head);
   display(head);
   return 0;
}

Output

Creating the linked list:
Enter 0 to stop building the list, else enter any integer
89
54
15
64
74
98
10
24
26
0
Before sorting:
89 54 15 64 74 98 10 24 26
After sorting:
10 15 24 26 54 64 74 89 98