Merge Sort on a Singly Linked List

Introduction

The linked list is one of the most important concepts and data structures to learn while preparing for interviews. Having a good grasp of Linked Lists can be a huge plus point in a coding interview.

Problem Statement

According to the problem statement, we are given a singly linked list, and we need to sort this singly linked list using merge sort.

Merge Sort

Merge sort is a divide and conquer algorithm.

  • It is a recursive algorithm.
  • In merge sort, we have to divide the container (container can be an array, list etc.) into two halves, then we will call merge sort recursively on the two halves.
  • These two merge sort call return sorted container, and we then merge these sorted container in such a way that the whole container remains sorted.
  • Have a look at the below image to see in a nutshell how merge sort works.

Now, we have a brief understanding of the merge sort algorithm. Let’s learn how to apply merge sort on a singly linked list.

In the case of a linked list, we will recursively divide the list into two sub-lists at each step till list size is reduced to one and while backtracking from the recursive call, we have two sorted lists, which will be merged together into a single list by merge operation in linear time.

Now we will look at the approach and algorithm, to know how to apply merge sort on a singly linked list.

Approach and Algorithm (Merge Sort)

1) If the head of the linked list is NULL or (head→ next == NULL), it shows that our linked list is of size 1 or 0 and a linked list of size zero or one is already sorted. So, Don’t do anything, just return head.
2) If the linked list is of size > 1 then first find the middle of the linked list.

  • For finding middle node, use slow and fast pointer method.
  • In this method, we take two pointers slow and fast and initialize them with head.
  • Then we move the slow pointer by one node and fast pointer by 2 nodes until fast pointer reaches the tail of the list.
  • And when the fast pointer reaches the tail, the slow pointer will be at the middle of the linked list.
  • The only reason why slow pointer will be at the middle of the list, when fast reaches tail is because the slow pointer is moving with half the speed of fast pointer and when the fast pointer has traversed the complete list till then the slow pointer will have only traversed half the list, so that’s why slow pointer will be at the middle of the list.
    3) Now, store slow → next in a pointer named afterMiddle and assign slow → next = NULL.
    4) Recursively call mergeSort() on both left and right sub-linked list and store the new head of the left and right linked list in pointer variable part1 and part2.
    5) When the recursive call on the left and right sub-list returns, merge the two linked lists returned by recursive calls (remember that the recursive call will return the sorted lists).
    6) Return the final head of the merged linkedlist.

Merging two sorted linked list Algorithm:

When the two recursive call will return the two sorted list, then we will merge those sorted list into a single list using these below steps.
1) Initialize two pointer variables named curr1 and curr2 with left sorted sub-list and right sorted sub-list.
2) Initialize two pointer variable named si and ei with NULL; these two pointer variables are the head and tail of the final sorted linked list.
3) If the data of curr1 is less than the data of curr2, then, store curr1 in next of ei & move curr1 to the next of curr1.
4) Else, if the data of curr2 is less than the data of curr1, then store curr2 in next of ei & move curr2 to the next of curr2.
5) Repeat steps 3 and 4 until either of the curr1 or curr2 is not equal to NULL.
6) Now add any remaining nodes of the first or the second linked list to the merged linked list.
7) Return head of merged sorted linked list containing all the nodes of the two sorted sub-lists.

Dry Run









Code Implementation

#include
using namespace std;

/* structure of node */
class Node{
public:
    int data;
    Node* next;
    Node(int data){
        this->data = data;
        this->next = NULL;
    }
};


/* print linked list */
void printList(Node* node){
    while (node != NULL) {
        cout<data<<" ";
        node = node->next;
    }
    printf("\n");
}

/* find and return middle node of the linked list*/
Node* middle(Node* head, Node* tail) {
        Node* slow = head;
        Node* fast = head;
        
        while(fast!=tail && fast->next!=tail){
            slow = slow->next;
            fast = fast->next->next;
        }
        Node* afterMiddle = slow->next;
        slow->next = NULL;
        return afterMiddle;
}
/* merge sort*/
Node* mergeSort(Node* head){
    if(head == NULL || head->next == NULL){
        return head;
    }

    Node* tail = head;

    while(tail->next){
        tail = tail->next;
    }


    Node* afterMiddle = middle(head, tail);
    Node* part1 = mergeSort(head);
    Node* part2 = mergeSort(afterMiddle);

    Node *curr1 = part1, *curr2 = part2;


    Node *si = NULL, *ei = NULL;

    while(curr1 && curr2){
        if(curr1->data <= curr2->data){
            if(si == NULL){
                si = curr1;
                ei = curr1;
            }else{
                ei->next = curr1;
                ei = curr1;
            }
            curr1 = curr1->next;
        }else{
            if(si == NULL){
                si = curr2;
                ei = curr2;
            }else{
                ei->next = curr2;
                ei = curr2;
            }
            curr2 = curr2->next;
        }
    }


    while(curr1){
        ei->next = curr1;
        ei = curr1;
        curr1 = curr1->next;
    }

    while(curr2){
        ei->next = curr2;
        ei = curr2;
        curr2 = curr2->next;
    }


    return si;
}



int main(){
    Node n1 = Node(8);
    Node n2 = Node(9);
    Node n3 = Node(5);
    Node n4 = Node(3);
    Node n5 = Node(2);
    Node n6 = Node(7);
    n1.next = &n2;
    n2.next = &n3;
    n3.next = &n4;
    n4.next = &n5;
    n5.next = &n6;

    Node* head = &n1;
    cout << "Linked List before sorting \n";
    printList(head);
 
    head = mergeSort(head);
 
    cout << "Linked List after sorting \n";
    printList(head);
}

Output

Linked List before sorting
8 9 5 3 2 7
Linked List after sorting
2 3 5 7 8 9

Time Complexity: O(n*log n)

So, In this blog, we have learned How to merge sort on a Singly Linked List. This is an important question when it comes to coding interviews. If you want to practice more questions on linked lists feel free to solve them at Prepbytes (Linked Lists).

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