Say, we have some items, 开发者_运维百科and each defines some partial sorting rules, like this:

I'm A and I want to be before B

I'm C and I want to be after A but before D

So we have items A,B,C,D with these rules:

• A>B
• C<A, C>D
• nothing else! So, B and D have no 'preferences' in ordering and are considered equal.

As you see, transitive relation rules are not working here. However, if A>B it still means that B<A. So, there can be multiple possible results of sorting:

1. A B C D
2. A C D B
3. A C B D
4. A B C D

How can I implement a sorting algorithm that handles such a situation?

The reason: there're multiple loadable modules, and some of them 'depend' on others in a way. Each module can declare simple rules, relative to other modules:

Load me before module A

Load me after module B

Load me before module A but after module B

now I need to implement this ordering somehow.. :)

Answer: code by Paddy McCarthy (MIT)

## {{{ http://code.activestate.com/recipes/577413/ (r1)
try:
    from functools import reduce
except:
    pass

data = {
    'des_system_lib':   set('std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee'.split()),
    'dw01':             set('ieee dw01 dware gtech'.split()),
    'dw02':             set('ieee dw02 dware'.split()),
    'dw03':             set('std synopsys dware dw03 dw02 dw01 ieee gtech'.split()),
    'dw04':             set('dw04 ieee dw01 dware gtech'.split()),
    'dw05':             set('dw05 ieee dware'.split()),
    'dw06':             set('dw06 ieee dware'.split()),
    'dw07':             set('ieee dware'.split()),
    'dware':            set('ieee dware'.split()),
    'gtech':            set('ieee gtech'.split()),
    'ramlib':           set('std ieee'.split()),
    'std_cell_lib':     set('ieee std_cell_lib'.split()),
    'synopsys':         set(),
    }

def toposort2(data):
    for k, v in data.items():
        v.discard(k) # Ignore self dependencies
    extra_items_in_deps = reduce(set.union, data.values()) - set(data.keys())
    data.update({item:set() for item in extra_items_in_deps})
    while True:
        ordered = set(item for item,dep in data.items() if not dep)
        if not ordered:
            break
        yield ' '.join(sorted(ordered))
        data = {item: (dep - ordered) for item,dep in data.items()
                if item not in ordered}
    assert not data, "A cyclic dependency exists amongst %r" % data

print ('\n'.join( toposort2(data) ))
## end of http://code.activestate.com/recipes/577413/ }}}

You'll want to construct a dependency graph (which is just a flavor of directed graph), and then follow a topologically sorted ordering. It's been a while since I took a combinatorics class, so the Wikipedia article will probably be more helpful than I am for a topological sort algorithm. I'm hoping giving you the proper terminology is helpful. :)

As far as constructing the graph, you'll basically just need to have each module with a list of that module's dependencies.

You'll just need to rephrase your rules a bit... "I'm C and I want to be after A but before D" would be expressed as "C depends on A" as well as "D depends on C", such that everything is flowing in a standard direction.

Following will return a dictionary with number as values to the variabes:

list them in the descending order to get the required output

def sorter(var_str: str, the_list: list):
    '''
    1st Argument must be a STRING
        variables, seperated by commas(','),
        WITHOUT ANY SPACES
    Eg: if a, b, c, d are the variables:
            sorter('a,b,c,d', [...])    --> Allowed
            sorter('a, b, c, d', [...]) --> Not Allowed
            sorter('a b c d', [...])    --> Not Allowed

    2nd Argument must be LIST of STRINGS
        having the conditions which can only include
            variables mentioned in the 1st Argument
            seperated with > or = or <,
        WITHOUT ANY SPACES
    Eg: if the conditions are (a > b = c > e), (c > d):
            sorter('...', ['a>b=c>e', 'c>d']        --> Allowed
            sorter('...', ['a > b = c > e', 'c > d']--> Not Allowed
            sorter('...', ['a > b=c > e', 'c > d']  --> Not Allowed
    '''

    level, main_cond_list= {var: 0 for var in var_str.split(',')}, []

    for condition in the_list:
        # Separating conditions & vars
        cond_var = condition.replace('>', ' ').replace('=', ' ').replace('<', ' ').split()
        cond_oper, counter = [], 0
        for i in cond_var[:-1]:
            counter += len(i)
            cond_oper.append(condition[counter])
            counter += + 1

        # SPLITTING THE CORE-CONDITIONS INTO SMALLER ONES
        for id in range(len(cond_oper)):

            # for > operator
            if cond_oper[id] == '>':
                for sub in range(id, -1, -1):
                    if cond_oper[sub] in ['=', '>']:
                        main_cond_list.append(f"{cond_var[sub]} > {cond_var[id + 1]}")
                        continue
                    break

            # for < operator
            if cond_oper[id] == '<':
                for sub in range(id, -1, -1):
                    if cond_oper[sub] in ['=', '<']:
                        main_cond_list.append(f"{cond_var[id + 1]} > {cond_var[sub]}")
                        continue
                    break

            # for = operator
            if cond_oper[id] == '=':
                for sub in range(id, -1, -1):
                    if cond_oper[sub] in ['=']:
                        main_cond_list.append(f"{cond_var[sub]} = {cond_var[id + 1]}")
                        continue
                    break

#             ABOVE 24 lines can be written as below _ commented lines too
#             for signs, strng in [['>', '{cond_var[sub]} > {cond_var[id + 1]}'],
#                                  ['<', '{cond_var[id + 1]} > {cond_var[sub]}'],
#                                  ['=', '{cond_var[sub]} = {cond_var[id + 1]}']]:
#                 exec(f'''
# if cond_oper[id] == '{signs}':
#     for sub in range(id, -1, -1):
#         if cond_oper[sub] in ['=', '{signs}']:
#             main_cond_list.append(f"{strng}")
#             continue
#         break''')

    for i in set(main_cond_list):
        print(i)

    for main_condition in set(main_cond_list):
        var1, cond, var2 = main_condition.split()
        if cond == '>' and var1 < var2:
            level[var1] = level[var2]+1
        if cond == '=':
            level[var1] = level[var2]
        # ABOVE 5 lines can be written as below commented lines also
        # for i in ['', '+1']:
        #     exec(f'''level[{main_cond_list[0]}] {main_cond_list[1]} level[{main_cond_list[0]}[2]{i}''')

    return level