
Sorting Algorithm

This is a sorting algorithm.   It may be applied to a set of data in order to sort it.    
For comparing various sorts, see compare sorts.  
For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort


Given   M   as a list of items and another list   N   of items chosen from   M,   create   M'   as a list with the first occurrences of items from   N   sorted to be in one of the set of indices of their original occurrence in   M   but in the order given by their order in   N.

That is, items in   N   are taken from   M   without replacement, then the corresponding positions in   M'   are filled by successive items from   N.



For example

if   M   is   'the cat sat on the mat'
And   N   is   'mat cat' 
Then the result   M'   is   'the mat sat on the cat'. 
The words not in   N   are left in their original positions.



If there are duplications then only the first instances in   M   up to as many as are mentioned in   N   are potentially re-ordered.



For example

  M = 'A B C A B C A B C' 
  N = 'C A C A' 
Is ordered as:

 M' = 'C B A C B A A B C' 


Show the output, here, for at least the following inputs:

Data M: 'the cat sat on the mat' Order N: 'mat cat'
Data M: 'the cat sat on the mat' Order N: 'cat mat'
Data M: 'A B C A B C A B C'      Order N: 'C A C A'
Data M: 'A B C A B D A B E'      Order N: 'E A D A'
Data M: 'A B'                    Order N: 'B'      
Data M: 'A B'                    Order N: 'B A'    
Data M: 'A B B A'                Order N: 'B A'



Cf

 Sort disjoint sublist


from __future__ import print_function
 
def order_disjoint_list_items(data, items):
    #Modifies data list in-place
    itemindices = []
    for item in set(items):
        itemcount = items.count(item)
        #assert data.count(item) >= itemcount, 'More of %r than in data' % item
        lastindex = [-1]
        for i in range(itemcount):
            lastindex.append(data.index(item, lastindex[-1] + 1))
        itemindices += lastindex[1:]
    itemindices.sort()
    for index, item in zip(itemindices, items):
        data[index] = item
 
if __name__ == '__main__':
    tostring = ' '.join
    for data, items in [ (str.split('the cat sat on the mat'), str.split('mat cat')),
                         (str.split('the cat sat on the mat'), str.split('cat mat')),
                         (list('ABCABCABC'), list('CACA')),
                         (list('ABCABDABE'), list('EADA')),
                         (list('AB'), list('B')),
                         (list('AB'), list('BA')),
                         (list('ABBA'), list('BA')),
                         (list(''), list('')),
                         (list('A'), list('A')),
                         (list('AB'), list('')),
                         (list('ABBA'), list('AB')),
                         (list('ABAB'), list('AB')),
                         (list('ABAB'), list('BABA')),
                         (list('ABCCBA'), list('ACAC')),
                         (list('ABCCBA'), list('CACA')),
                       ]:
        print('Data M: %-24r Order N: %-9r' % (tostring(data), tostring(items)), end=' ')
        order_disjoint_list_items(data, items)
        print("-> M' %r" % tostring(data))