How to sort a list of full names by how common the ancestors are? - algorithm

Question

If every letter in the following represents a name. What is the best way to sort them by how common the ancestors are?
A B C D
E F G H
I J K L
M N C D
O P C D
Q R C D
S T G H
U V G H
W J K L
X J K L
The result should be:
I J K L # Three names is more important that two names
W J K L
X J K L
A B C D # C D is repeated more than G H
M N C D
O P C D
Q R C D
E F G H
S T G H
U V G H
EDIT:
Names might have spaces in them (Double names).
Consider the following example where each letter represents a single word:
A B C D M
E F G H M
I J K L M
M N C D M
O P C D
Q R C D
S T G H
U V G H
W J K L
X J K L
The output should be:
A B C D M
M N C D M
I J K L M
E F G H M
W J K L
X J K L
O P C D
Q R C D
S T G H
U V G H

Answer 1

First count the number of occurrences for each chain. Then rank each name according to that count. Try this:
from collections import defaultdict
words = """A B C D
E F G H
I J K L
M N C D
O P C D
Q R C D
S T G H
U V G H
W J K L
X J K L"""
words = words.split('\n')
# Count ancestors
counters = defaultdict(lambda: defaultdict(lambda: 0))
for word in words:
parts = word.split()
while parts:
counters[len(parts)][tuple(parts)] += 1
parts.pop(0)
# Calculate tuple of ranks, used for sorting
ranks = {}
for word in words:
rank = []
parts = word.split()
while parts:
rank.append(counters[len(parts)][tuple(parts)])
parts.pop(0)
ranks[word] = tuple(rank)
# Sort by ancestor count, longest chain comes first
words.sort(key=lambda word: ranks[word], reverse=True)
print(words)

Answer 2

Here's how you could do it in Java - essentially the same method as #fafl's solution:
static List<Name> sortNames(String[] input)
{
List<Name> names = new ArrayList<>();
for (String name : input)
names.add(new Name(name));
Map<String, Integer> partCount = new HashMap<>();
for (Name name : names)
for (String part : name.parts)
partCount.merge(part, 1, Integer::sum);
for (Name name : names)
for (String part : name.parts)
name.counts.add(partCount.get(part));
Collections.sort(names, new Comparator<Name>()
{
public int compare(Name n1, Name n2)
{
for (int c, i = 0; i < n1.parts.size(); i++)
if ((c = Integer.compare(n2.counts.get(i), n1.counts.get(i))) != 0)
return c;
return 0;
}
});
return names;
}
static class Name
{
List<String> parts = new ArrayList<>();
List<Integer> counts = new ArrayList<>();
Name(String name)
{
List<String> s = Arrays.asList(name.split("\\s+"));
for (int i = 0; i < s.size(); i++)
parts.add(String.join(" ", s.subList(i, s.size())));
}
}
Test:
public static void main(String[] args)
{
String[] input = {
"A B C D",
"W J K L",
"E F G H",
"I J K L",
"M N C D",
"O P C D",
"Q R C D",
"S T G H",
"U V G H",
"X J K L" };
for (Name name : sortNames(input))
System.out.println(name.parts.get(0));
}
Output:
I J K L
W J K L
X J K L
A B C D
M N C D
O P C D
Q R C D
E F G H
S T G H
U V G H