Non-Recursive Merge Sort

Just in case anyone's still lurking in this thread ... I've adapted Rama Hoetzlein's non-recursive merge sort algorithm above to sort double linked lists. This new sort is in-place, stable and avoids time costly list dividing code that's in other linked list merge sorting implementations.

// MergeSort.cpp
// Angus Johnson 2017
// License: Public Domain

#include "io.h"
#include "time.h"
#include "stdlib.h"

struct Node {
    int data;
    Node *next;
    Node *prev;
    Node *jump;
};

inline void Move2Before1(Node *n1, Node *n2)
{
    Node *prev, *next;
    //extricate n2 from linked-list ...
    prev = n2->prev;
    next = n2->next;
    prev->next = next; //nb: prev is always assigned
    if (next) next->prev = prev;
    //insert n2 back into list ...  
    prev = n1->prev;
    if (prev) prev->next = n2;
    n1->prev = n2;
    n2->prev = prev;
    n2->next = n1;
}

void MergeSort(Node *&nodes)
{
    Node *first, *second, *base, *tmp, *prev_base;

    if (!nodes || !nodes->next) return;
    int mul = 1;
    for (;;) {
        first = nodes;
        prev_base = NULL;
        //sort each successive mul group of nodes ...
        while (first) {
            if (mul == 1) {
                second = first->next;
                if (!second) { 
                  first->jump = NULL;
                  break;
                }
                first->jump = second->next;
            }
            else
            {
                second = first->jump;
                if (!second) break;
                first->jump = second->jump;
            }
            base = first;
            int cnt1 = mul, cnt2 = mul;
            //the following 'if' condition marginally improves performance 
            //in an unsorted list but very significantly improves
            //performance when the list is mostly sorted ...
            if (second->data < second->prev->data) 
                while (cnt1 && cnt2) {
                    if (second->data < first->data) {
                        if (first == base) {
                            if (prev_base) prev_base->jump = second;
                            base = second;
                            base->jump = first->jump;
                            if (first == nodes) nodes = second;
                        }
                        tmp = second->next;
                        Move2Before1(first, second);
                        second = tmp;
                        if (!second) { first = NULL; break; }
                        --cnt2;
                    }
                    else
                    {
                        first = first->next;
                        --cnt1;
                    }
                } //while (cnt1 && cnt2)
            first = base->jump;
            prev_base = base;
        } //while (first)
        if (!nodes->jump) break;
        else mul <<= 1;
    } //for (;;)
}

void InsertNewNode(Node *&head, int data)
{
    Node *tmp = new Node;
    tmp->data = data;
    tmp->next = NULL;
    tmp->prev = NULL;
    tmp->jump = NULL;
    if (head) {
        tmp->next = head;
        head->prev = tmp;
        head = tmp;
    }
    else head = tmp;
}

void ClearNodes(Node *head)
{
    if (!head) return;
    while (head) {
        Node *tmp = head;
        head = head->next;
        delete tmp;
    }
}

int main()
{  
    srand(time(NULL));
    Node *nodes = NULL, *n;
    const int len = 1000000; //1 million nodes 
    for (int i = 0; i < len; i++)
        InsertNewNode(nodes, rand() >> 4);

    clock_t t = clock();
    MergeSort(nodes);    //~1/2 sec for 1 mill. nodes on Pentium i7. 
    t = clock() - t;
    printf("Sort time: %d msec\n\n", t * 1000 / CLOCKS_PER_SEC);

    n = nodes;
    while (n)
    {
        if (n->prev && n->data < n->prev->data) { 
            printf("oops! sorting's broken\n"); 
            break;
        }
        n = n->next;
    }
    ClearNodes(nodes);
    printf("All done!\n\n");
    getchar();
    return 0;
}

Edited 2017-10-27: Fixed a bug affecting odd numbered lists

Any interest in this anymore? Probably not. Oh well. Here goes nothing.

The insight of merge-sort is that you can merge two (or several) small sorted runs of records into one larger sorted run, and you can do so with simple stream-like operations "read first/next record" and "append record" -- which means you don't need a big data set in RAM at once: you can get by with just two records, each taken from a distinct run. If you can just keep track of where in your file the sorted runs start and end, you can simply merge pairs of adjacent runs (into a temp file) repeatedly until the file is sorted: this takes a logarithmic number of passes over the file.

A single record is trivially sorted: each time you merge two adjacent runs, the size of each run doubles. So that's one way to keep track. The other is to work on a priority queue of runs. Take the two smallest runs from the queue, merge them, and enqueue the result -- until there is only one remaining run. This is appropriate if you expect your data to naturally start with sorted runs.

In practice with enormous data sets you'll want to exploit the memory hierarchy. Suppose you have gigabytes of RAM and terabytes of data. Why not merge a thousand runs at once? Indeed you can do this, and a priority-queue of runs can help. That will significantly decrease the number of passes you have to make over a file to get it sorted. Some details are left as an exercise for the reader.