Problem: Family Trees
Background
Expression trees, B and B* trees, red-black trees, quad trees, PQ
trees; trees play a significant role in many domains of computer
science. Sometimes the name of a problem may indicate that trees are
used when they are not, as in the Artificial Intelligence planning
problem traditionally called the Monkey and Bananas problem .
Sometimes trees may be used in a problem whose name gives no
indication that trees are involved, as in the Huffman code .
This problem involves determining how pairs of people who may be part of
a ``family tree'' are related.
The Problem
Given a sequence of child-parent
pairs, where a pair consists of
the child's name followed by the (single) parent's name, and a list of
query pairs also expressed as two names, you are to write a program to
determine whether the query pairs are related. If the names comprising a
query pair are related the program should determine what the
relationship is. Consider academic advisees and advisors as exemplars
of such a single parent genealogy (we assume a single advisor, i.e., no
co-advisors).
In this problem the child-parent pair p q denotes that p
is the child of q . In determining relationships
between names we use the following definitions:
- p is a 0-descendent
of q (respectively 0-ancestor )
if and only if the child-parent pair p q
(respectively q p ) appears
in the input sequence of child-parent pairs.
- p is a
k-descendent of q
(respectively k-ancestor )
if and only if the child-parent pair p r
(respectively q r ) appears
in the input sequence and r is a (k-1)-descendent of
q
(respectively p is a (k-1)-ancestor of r).
For the purposes of this problem the relationship between a person
p and a person q is expressed as exactly one of the
following four relations:
- child --- grand child, great grand child, great great grand child,
etc.
By definition p is
the ``child'' of q if and only if the pair p q
appears in the input sequence of child-parent pairs (i.e., p is a
0-descendent of q); p is the ``grand
child'' of q if and only if p is a 1-descendent of
q;
and
p is the ``great great ... great'' grandchild of q
---------------------
n occurrences
if and only if p is an (n+1)-descendent of q.
- parent --- grand parent, great grand parent, great great grand
parent, etc.
By definition p is the ``parent'' of q
if and only if the pair q p
appears in the input sequence of child-parent pairs (i.e., p is a
0-ancestor of q); p is the ``grand
parent'' of q if and only if p
is a 1-ancestor of q; and
p is the ``great great ... great'' grand parent of q
---------------------
n occurrences
if and only if p is an (n+1)-ancestor of q.
- cousin --- 0-th cousin, 1-st cousin, 2-nd
cousin, etc.;
cousins may be once removed, twice removed, three times
removed, etc.
By definition p and q are ``cousins'' if and only if
they are related (i.e., there is a path from p to q in
the implicit undirected parent-child tree). Let r represent
the least common ancestor of p and q (i.e., no
descendent of r is an ancestor of both p and
q), where p is an m-descendent of r
and q is an n-descendent of r.
Then, by definition, cousins p and q
are ``k-th cousins''
if and only if k = min (n, m), and, also by definition,
p
and q are ``cousins removed j times''
if and only if j = | n - m | .
- sibling --- 0-th
cousins removed 0 times are ``siblings'' (they have the same parent).
The Input
The input consists of parent-child pairs of names, one pair per line.
Each name in a pair consists of lower-case alphabetic characters or
periods (used to separate first and last names, for example). Child
names are separated from parent names by one or more spaces.
Parent-child pairs are terminated by a pair whose first component is the
string ``no.child''.
Such a pair is NOT to be considered as a parent-child
pair, but only as a delimiter to separate the parent-child
pairs from the query pairs. There will be no circular relationships,
i.e., no name p can be both
an ancestor and a descendent of
the same name q.
The parent-child pairs are followed by a sequence of query pairs in the
same format as the parent-child pairs, i.e., each name in a query pair
is a sequence of lower-case alphabetic characters and periods, and names
are separated by one or more spaces. Query pairs are terminated by
end-of-file.
There will be a maximum of 300 different names overall
(parent-child and query pairs). All names will be fewer than 31
characters in length. There will be no more than 100 query pairs.
The Output
For each query-pair p q
of names the output should indicate the relationship
p is-the-relative-of
q by the appropriate string of the form
- child, grand child, great grand child, great great ... great
grand child
- parent, grand parent, great grand parent, great great ... great
grand parent
- sibling
- n cousin removed m
- no relation
If an m-cousin is removed 0 times then only m cousin should be
printed, i.e., removed 0 should NOT be printed. Do not print
st, nd, rd, th after the numbers.
Sample Input
alonzo.church oswald.veblen
stephen.kleene alonzo.church
dana.scott alonzo.church
martin.davis alonzo.church
pat.fischer hartley.rogers
mike.paterson david.park
dennis.ritchie pat.fischer
hartley.rogers alonzo.church
les.valiant mike.paterson
bob.constable stephen.kleene
david.park hartley.rogers
no.child no.parent
stephen.kleene bob.constable
hartley.rogers stephen.kleene
les.valiant alonzo.church
les.valiant dennis.ritchie
dennis.ritchie les.valiant
pat.fischer michael.rabin
Sample Output
parent
sibling
great great grand child
1 cousin removed 1
1 cousin removed 1
no relation