Sort numbers stored on different machines

Last Updated : 23 Jul, 2025

Given n machines in the form of the Linked list. Each machine contains some numbers in sorted form. But the amount of numbers, each machine has is not fixed. Output the numbers from all the machine in sorted non-decreasing form.

Examples:

Input: Machine M1 : [30, 40, 50]
Machine M2 : [35, 45]
Machine M3 : [10, 60, 70, 80, 100]
Output: [10, 30, 35, 40, 45, 50, 60, 70, 80, 100]
Explanation: Sorted Number from all Machine is [10, 30, 35, 40, 45, 50, 60, 70, 80, 100]
Input: Machine M1 : [1, 5 , 10]
Machine M2 : [35, 45]
Machine M3 : [30, 90, 130]
Output: [1, 5, 10, 30, 35, 45, 90, 130]
Explanation: Sorted Number from all Machine is [1, 5, 10, 30, 35, 45, 90, 130]

[Approach 1] - Using a Priority Queue - Good for Varying-Sized Arrays or Lists

The mergeLists function merges sorted linked lists using a min heap, repeatedly extracting the smallest element and inserting the next node. The externalSort function converts the linked lists into a vector, calls mergeLists to get the final sorted list, and prints it. Changing the comparison in CompareNode allows sorting in descending order.

C++

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

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

struct CompareNode {
    bool operator()(const ListNode* a, const ListNode* b) {
        return a->data > b->data;
    }
};

void push(ListNode*& head, int data) {
    ListNode* newNode = new ListNode(data);
    newNode->next = head;
    head = newNode;
}

void PrintList(ListNode* head) {
    while (head) {
        cout << head->data;
        if (head->next) cout << " ";
        head = head->next;
    }
    cout << endl;
}

ListNode* mergelist(vector<ListNode*>& list) {
    priority_queue<ListNode*, vector<ListNode*>, CompareNode> minHeap;
    
    for (auto li : list)
        if (li) minHeap.push(li);

    ListNode dummy(0), *tail = &dummy;
    
    while (!minHeap.empty()) {
        ListNode* node = minHeap.top();
        minHeap.pop();
        tail->next = node;
        tail = tail->next;

        if (node->next) minHeap.push(node->next);
    }

    return dummy.next;
}

ListNode*  externalSort(vector<ListNode*>& list) {
    ListNode* sortedList = mergelist(list);
     return sortedList;
}

int main() {
    int N = 3;
    vector<ListNode*> list(N, nullptr);

    push(list[0], 50);
    push(list[0], 40);
    push(list[0], 30);

    push(list[1], 45);
    push(list[1], 35);

    push(list[2], 100);
    push(list[2], 80);
    push(list[2], 70);
    push(list[2], 60);
    push(list[2], 10);

    ListNode* ans = externalSort(list);
    PrintList(ans);
    return 0;
}

Java

import java.util.*;

class ListNode {
    int data;
    ListNode next;

    ListNode(int data)
    {
        this.data = data;
        this.next = null;
    }
}

class CompareNode implements Comparator<ListNode> {
    @Override public int compare(ListNode a, ListNode b)
    {
        return Integer.compare(a.data, b.data);
    }
}

public class GfG {

    static ListNode createNode(int data)
    {
        return new ListNode(data);
    }

    static void push(ListNode[] head, int data, int index)
    {
        if (head[index] == null) {
            head[index] = createNode(data);
        }
        else {
            ListNode newNode = createNode(data);
            newNode.next = head[index];
            head[index] = newNode;
        }
    }

    static void PrintList(ListNode head)
    {
        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
    }

    static ListNode mergeLists(List<ListNode> lists)
    {
        ListNode dummy = createNode(0);
        ListNode tail = dummy;

        PriorityQueue<ListNode> minHeap
            = new PriorityQueue<>(new CompareNode());

        for (ListNode list : lists) {
            if (list != null) {
                minHeap.offer(list);
            }
        }

        while (!minHeap.isEmpty()) {
            ListNode node = minHeap.poll();

            tail.next = node;
            tail = tail.next;

            if (node.next != null) {
                minHeap.offer(node.next);
            }
        }

        return dummy.next;
    }

    static ListNode externalSort(ListNode[] list)
    {
        List<ListNode> lists = new ArrayList<>();
        for (ListNode node : list) {
            lists.add(node);
        }
        return mergeLists(lists);
    }

    public static void main(String[] args)
    {
        int n = 3;

        ListNode[] list = new ListNode[n];

        list[0] = null;
        push(list, 50, 0);
        push(list, 40, 0);
        push(list, 30, 0);

        list[1] = null;
        push(list, 45, 1);
        push(list, 35, 1);

        list[2] = null;
        push(list, 100, 2);
        push(list, 80, 2);
        push(list, 70, 2);
        push(list, 60, 2);
        push(list, 10, 2);

        ListNode ans = externalSort(list);
        PrintList(ans);
    }
}

Python

import heapq

class ListNode:
    def __init__(self, data):
        self.data = data
        self.next = None

def push(head, data):
    # Function to insert a new node at the beginning of a linked list
    new_node = ListNode(data)
    new_node.next = head
    head = new_node
    return head

def PrintList(head):
    # Function to print the linked list
    while head:
        print(head.data, end=" ")
        head = head.next
    print()

def merge_lists(lists):
    # Function to merge K sorted linked lists into a single sorted linked list
    dummy = ListNode(0)
    tail = dummy

    # Use a min heap to keep track of the smallest nodes from each list
    min_heap = []

    for lst in lists:
        if lst:
            # Push the first node of each list into the min heap
            heapq.heappush(min_heap, (lst.data, lst))

    while min_heap:
        # Pop the smallest node from the min heap
        data, node = heapq.heappop(min_heap)

        # Append the smallest node to the sorted linked list
        tail.next = node
        tail = tail.next

        # If the popped node has a next node, push it into the min heap
        if node.next:
            heapq.heappush(min_heap, (node.next.data, node.next))

    return dummy.next

def externalSort(list):
    # Function to perform external sorting on an list of linked lists
    sorted_list = merge_lists(list)
    return sorted_list

if __name__ == "__main__":
    N = 3  # Number of machines

    list = [None] * N

    # Create the linked lists for each machine
    list[0] = None
    list[0] = push(list[0], 50)
    list[0] = push(list[0], 40)
    list[0] = push(list[0], 30)

    list[1] = None
    list[1] = push(list[1], 45)
    list[1] = push(list[1], 35)

    list[2] = None
    list[2] = push(list[2], 100)
    list[2] = push(list[2], 80)
    list[2] = push(list[2], 70)
    list[2] = push(list[2], 60)
    list[2] = push(list[2], 10)

    # Sort all elements
    ans = externalSort(list)
    PrintList(ans)

using System;
using System.Collections.Generic;

public class ListNode {
    public int data;
    public ListNode next;
}

public class MinHeap {
    private List<Tuple<ListNode, int> > heap;

    public MinHeap()
    {
        heap = new List<Tuple<ListNode, int> >();
    }

    public void Enqueue(ListNode node, int value)
    {
        heap.Add(new Tuple<ListNode, int>(node, value));
        HeapifyUp();
    }

    public ListNode Dequeue()
    {
        if (heap.Count == 0)
            throw new InvalidOperationException(
                "Heap is empty.");

        var root = heap[0].Item1;
        heap[0] = heap[heap.Count - 1];
        heap.RemoveAt(heap.Count - 1);
        HeapifyDown();
        return root;
    }

    public int Count => heap.Count;

    private void HeapifyUp()
    {
        int index = heap.Count - 1;
        while (index > 0) {
            int parentIndex = (index - 1) / 2;
            if (heap[index].Item2
                >= heap[parentIndex].Item2)
                break;

            var temp = heap[index];
            heap[index] = heap[parentIndex];
            heap[parentIndex] = temp;

            index = parentIndex;
        }
    }

    private void HeapifyDown()
    {
        int index = 0;
        while (index * 2 + 1 < heap.Count) {
            int leftChildIndex = index * 2 + 1;
            int rightChildIndex = leftChildIndex + 1;
            int smallestChildIndex = leftChildIndex;

            if (rightChildIndex < heap.Count
                && heap[rightChildIndex].Item2
                       < heap[leftChildIndex].Item2) {
                smallestChildIndex = rightChildIndex;
            }

            if (heap[index].Item2
                <= heap[smallestChildIndex].Item2)
                break;

            var temp = heap[index];
            heap[index] = heap[smallestChildIndex];
            heap[smallestChildIndex] = temp;

            index = smallestChildIndex;
        }
    }
}

public class GfG {
    public static ListNode CreateNode(int data)
    {
        return new ListNode{ data = data, next = null };
    }

    public static void Push(ref ListNode head, int data)
    {
        ListNode newNode = CreateNode(data);
        newNode.next = head;
        head = newNode;
    }

    public static void PrintList(ListNode head)
    {
        while (head != null) {
            Console.Write(head.data + " ");
            head = head.next;
        }
        Console.WriteLine();
    }

    public static ListNode MergeLists(List<ListNode> lists)
    {
        ListNode dummy = CreateNode(0);
        ListNode tail = dummy;

        MinHeap minHeap = new MinHeap();

        foreach(ListNode list in lists)
        {
            if (list != null)
                minHeap.Enqueue(list, list.data);
        }

        while (minHeap.Count > 0) {
            ListNode node = minHeap.Dequeue();
            tail.next = node;
            tail = tail.next;

            if (node.next != null)
                minHeap.Enqueue(node.next, node.next.data);
        }

        return dummy.next;
    }

    public static ListNode ExternalSort(ListNode[] list,
                                        int N)
    {
        List<ListNode> lists = new List<ListNode>(list);
        return MergeLists(lists);
    }

    public static void Main(string[] args)
    {
        int N = 3;

        ListNode[] list = new ListNode[N];

        list[0] = null;
        Push(ref list[0], 50);
        Push(ref list[0], 40);
        Push(ref list[0], 30);

        list[1] = null;
        Push(ref list[1], 45);
        Push(ref list[1], 35);

        list[2] = null;
        Push(ref list[2], 100);
        Push(ref list[2], 80);
        Push(ref list[2], 70);
        Push(ref list[2], 60);
        Push(ref list[2], 10);

        ListNode ans = ExternalSort(list, N);
        PrintList(ans);
    }
}

JavaScript

class ListNode {
    constructor(data) {
        this.data = data;
        this.next = null;
    }
}

class PriorityQueue {
    constructor(comparator) {
        this.comparator = comparator || ((a, b) => a - b);
        this.data = [];
    }

    get count() {
        return this.data.length;
    }

    enqueue(item) {
        this.data.push(item);
        this.data.sort(this.comparator);
    }

    dequeue() {
        if (this.count === 0) {
            throw new Error("Priority queue is empty.");
        }
        return this.data.shift();
    }
}

function createNode(data) {
    return new ListNode(data);
}

function push(head, data) {
    if (!head) {
        return createNode(data);
    } else {
        const newNode = createNode(data);
        newNode.next = head;
        return newNode;
    }
}

function printList(head) {
    let current = head;
    let result = [];
    while (current) {
        result.push(current.data);
        current = current.next;
    }
    console.log(result.join(' '));
}

function mergeLists(lists) {
    const dummy = createNode(0);
    let tail = dummy;
    const minHeap = new PriorityQueue((a, b) => a.data - b.data);

    lists.forEach(list => {
        if (list !== null) {
            minHeap.enqueue(list);
        }
    });

    while (minHeap.count > 0) {
        const node = minHeap.dequeue();
        tail.next = node;
        tail = tail.next;

        if (node.next !== null) {
            minHeap.enqueue(node.next);
        }
    }

    return dummy.next;
}

function externalSort(list, n) {
    return mergeLists(list);
}

function main() {
    const n = 3;
    const list = new Array(n);

    list[0] = null;
    list[0] = push(list[0], 50);
    list[0] = push(list[0], 40);
    list[0] = push(list[0], 30);

    list[1] = null;
    list[1] = push(list[1], 45);
    list[1] = push(list[1], 35);

    list[2] = null;
    list[2] = push(list[2], 100);
    list[2] = push(list[2], 80);
    list[2] = push(list[2], 70);
    list[2] = push(list[2], 60);
    list[2] = push(list[2], 10);

    const ans = externalSort(list, n);
    printList(ans);
}

main();

Output

10 30 35 40 45 50 60 70 80 100

Time Complexity: O(K log₂n), where n is the numbers of array.
Auxiliary Space: O(K), where K is number of total elements in all array.

[Approach 2] - Using Merge of Merge Sort - Good for Equal-Sized

This problem is closely related to Merging K Sorted Arrays & Merge K sorted linked lists. In all cases, the goal is to efficiently merge multiple sorted sequences into a single sorted output. Here, instead of traditional arrays or linked lists, the numbers are distributed across different machines, making it a distributed computing variation of the same concept.

Analysis of Algorithms

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Practice Tags :

Sort numbers stored on different machines

[Approach 1] - Using a Priority Queue - Good for Varying-Sized Arrays or Lists

[Approach 2] - Using Merge of Merge Sort - Good for Equal-Sized

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