C++ Program For Insertion Sort In A Singly Linked List

We have discussed Insertion Sort for arrays. In this article we are going to discuss Insertion Sort for linked list. 
Below is a simple insertion sort algorithm for a linked list. 

1) Create an empty sorted (or result) list.
2) Traverse the given list, do following for every node.
......a) Insert current node in sorted way in sorted or result list.
3) Change head of given linked list to head of sorted (or result) list.

The main step is (2.a) which has been covered in the post Sorted Insert for Singly Linked List
Below is the implementation of the above algorithm:

C++

// C++ program to sort link list
// using insertion sort
#include <bits/stdc++.h>
using namespace std;

struct Node
{
    int val;
    struct Node* next;
    Node(int x)
    {
        val = x;
        next = NULL;
    }
};

class LinkedlistIS
{
    public:
    Node* head;
    Node* sorted;

    void push(int val)
    {
        // Allocate node
        Node* newnode = new Node(val);

        // Link the old list of the
        // new node
        newnode->next = head;
        // Move the head to point to the
        // new node
        head = newnode;
    }

    // Function to sort a singly linked list
    // using insertion sort
    void insertionSort(Node* headref)
    {
        // Initialize sorted linked list
        sorted = NULL;
        Node* current = headref;

        // Traverse the given linked list
        // and insert every node to sorted
        while (current != NULL)
        {
            // Store next for next iteration
            Node* next = current->next;

            // Insert current in sorted
            // linked list
            sortedInsert(current);

            // Update current
            current = next;
        }

        // Update head_ref to point to
        // sorted linked list
        head = sorted;
    }

    /* Function to insert a new_node in a list.
       Note that this function expects a pointer
       to head_ref as this can modify the head of
       the input linked list (similar to push()) */
    void sortedInsert(Node* newnode)
    {
        // Special case for the head end
        if (sorted == NULL ||
            sorted->val >= newnode->val)
        {
            newnode->next = sorted;
            sorted = newnode;
        }
        else
        {
            Node* current = sorted;

            /* Locate the node before the
               point of insertion */
            while (current->next != NULL &&
                   current->next->val < newnode->val)
            {
                current = current->next;
            }
            newnode->next = current->next;
            current->next = newnode;
        }
    }

    // Function to print linked list
    void printlist(Node* head)
    {
        while (head != NULL)
        {
            cout << head->val << " ";
            head = head->next;
        }
    }
};

// Driver code
int main()
{
    LinkedlistIS list;
    list.head = NULL;
    list.push(5);
    list.push(20);
    list.push(4);
    list.push(3);
    list.push(30);
    cout << "Linked List before sorting" <<
             endl;
    list.printlist(list.head);
    cout << endl;
    list.insertionSort(list.head);
    cout << "Linked List After sorting" <<
             endl;
    list.printlist(list.head);
}
// This code is contributed by nirajgusain5

Output

Linked List before sorting
30 3 4 20 5 
Linked List After sorting
3 4 5 20 30 

Time Complexity: O(n²), in the worst case, we might have to traverse all nodes of the sorted list for inserting a node, and there are “n” such nodes.
Auxiliary Space: O(1), no extra space is required depending on the size of the input, thus it is constant.

Please refer complete article on Insertion Sort for Singly Linked List for more details!

Another Approach:

The idea behind this approach is to make use of dummy pointer variable that will store the elements of singly linked list in sorted order.               Below is the insertion sort algorithm for singly linked list.

1) Create a new dummy node with a value equals to INT_MIN.
2) Traverse the given list, do following for every node:
     a) Create two node pointers curr and prev, curr pointer pointing to dummy node variable and prev to nullptr.
     b) Traverse the dummy node list and move pointer curr to its next node and prev to curr uptil the value of
        node to which curr pointer is pointing is less than that of the head node value.
     c) Create a next pointer which will point to the next of head element.
     d) Make prev pointer's next pointing to head node and head node next pointing to curr pointer.
     e) Now move head node pointer to its next node.

C++

#include<bits/stdc++.h>
using namespace std;

// Definition for singly-linked list.

struct ListNode {
    int val;
    ListNode *next;
    ListNode() : val(0), next(nullptr) {}
    ListNode(int x) : val(x), next(nullptr) {}
    ListNode(int x, ListNode *next) : val(x), next(next) {}
};

//inserton sort for singly linked list

ListNode* insertionSortList(ListNode* head) {
    if(!head||!head->next)return head;
    ListNode* dummy=new ListNode(INT_MIN);
    while(head)
    {
        ListNode* curr=dummy,*prev=nullptr;
        while(curr&&curr->val<=head->val)
        {
            prev=curr;
            curr=curr->next;
        }
        ListNode* next=head->next;
        prev->next=head;
        head->next=curr;
        head=next;
     }
     return dummy->next;
}

//Print function

void printlist(ListNode* head){

  while (head != NULL)
  {
      cout << head->val << " ";
      head = head->next;
  }
  cout<<endl;
}


// Driver code
int main()
{
    ListNode *first=new ListNode(30);
    ListNode *second=new ListNode(3);
    ListNode *third=new ListNode(4);
    ListNode *fourth=new ListNode(20);
    ListNode *fifth=new ListNode(5);
    first->next=second;
    second->next=third;
    third->next=fourth;
    fourth->next=fifth;
    //Linked list look like this: 30->3->4->20->5

    cout << "Linked List before sorting" <<
             endl;
    printlist(first);
    cout << endl;
    ListNode* sorted=insertionSortList(first);
    cout << "Linked List After sorting" <<
             endl;
    printlist(sorted);
}

Output

Linked List before sorting
30 3 4 20 5 

Linked List After sorting
3 4 5 20 30 

Time Complexity: O(n2), in the worst case, we might have to traverse all nodes of the sorted list to insert a node, and there are “n” such nodes.
Auxiliary Space: O(1), as the dummy node that we have created takes constant space.