???Minimum Distance in a Star Graph
2017-09-25 22:44
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In this problem, we will define a graph called star graph, and the question is to find the minimum distance between two given nodes in the star graph.
Given an integer nn,
an n-dimensionaln−dimensional star
graph, also referred to as S_{n}Sn,
is an undirected graph consisting of n!n! nodes
(or vertices) and ((n-1)\
*\ n!)/2((n−1) ∗ n!)/2 edges.
Each node is uniquely assigned a label x_{1}\
x_{2}\ ...\ x_{n}x1 x2 ... xnwhich
is any permutation of the n digits {1,
2, 3, ..., n}1,2,3,...,n.
For instance, an S_{4}S4 has
the following 24 nodes {1234,
1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321}1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321.
For each node with label x_{1}\
x_{2} x_{3}\ x_{4}\ ...\ x_{n}x1 x2x3 x4 ... xn,
it has n-1n−1 edges
connecting to nodes x_{2}\
x_{1}\ x_{3}\ x_{4}\ ...\ x_{n}x2 x1 x3 x4 ... xn, x_{3}\
x_{2}\ x_{1}\ x_{4}\ ...\ x_{n}x3 x2 x1 x4 ... xn, x_{4}\
x_{2}\ x_{3}\ x_{1}\ ...\ x_{n}x4 x2 x3 x1 ... xn,
..., and x_{n}\
x_{2}\ x_{3}\ x_{4}\ ...\ x_{1}xn x2 x3 x4 ... x1.
That is, the n-1n−1 adjacent
nodes are obtained by swapping the first symbol and the d-thd−th symbol
of x_{1}\
x_{2}\ x_{3}\ x_{4}\ ...\ x_{n}x1 x2 x3 x4 ... xn,
for d
= 2, ..., nd=2,...,n.
For instance, in S_{4}S4,
node 12341234 has 33 edges
connecting to nodes 21342134, 32143214,
and 42314231.
The following figure shows how S_{4}S4 looks
(note that the symbols aa, bb, cc,
and dd are
not nodes; we only use them to show the connectivity between nodes; this is for the clarity of the figure).
In this problem, you are given the following inputs:
nn:
the dimension of the star graph. We assume that nn ranges
from 44 to 99.
Two nodes x_{1}x1 x_{2}x2 x_{3}x3 ... x_{n}xn and y_{1}y1 y_{2}y2 y_{3}\
...\ y_{n}y3 ... yn in S_{n}Sn.
You have to calculate the distance between these two nodes (which is an integer).
nn (dimension
of the star graph)
A list of 55 pairs
of nodes.
A list of 55 values,
each representing the distance of a pair of nodes.
2017
ACM-ICPC 亚洲区（南宁赛区）网络赛
Given an integer nn,
an n-dimensionaln−dimensional star
graph, also referred to as S_{n}Sn,
is an undirected graph consisting of n!n! nodes
(or vertices) and ((n-1)\
*\ n!)/2((n−1) ∗ n!)/2 edges.
Each node is uniquely assigned a label x_{1}\
x_{2}\ ...\ x_{n}x1 x2 ... xnwhich
is any permutation of the n digits {1,
2, 3, ..., n}1,2,3,...,n.
For instance, an S_{4}S4 has
the following 24 nodes {1234,
1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321}1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321.
For each node with label x_{1}\
x_{2} x_{3}\ x_{4}\ ...\ x_{n}x1 x2x3 x4 ... xn,
it has n-1n−1 edges
connecting to nodes x_{2}\
x_{1}\ x_{3}\ x_{4}\ ...\ x_{n}x2 x1 x3 x4 ... xn, x_{3}\
x_{2}\ x_{1}\ x_{4}\ ...\ x_{n}x3 x2 x1 x4 ... xn, x_{4}\
x_{2}\ x_{3}\ x_{1}\ ...\ x_{n}x4 x2 x3 x1 ... xn,
..., and x_{n}\
x_{2}\ x_{3}\ x_{4}\ ...\ x_{1}xn x2 x3 x4 ... x1.
That is, the n-1n−1 adjacent
nodes are obtained by swapping the first symbol and the d-thd−th symbol
of x_{1}\
x_{2}\ x_{3}\ x_{4}\ ...\ x_{n}x1 x2 x3 x4 ... xn,
for d
= 2, ..., nd=2,...,n.
For instance, in S_{4}S4,
node 12341234 has 33 edges
connecting to nodes 21342134, 32143214,
and 42314231.
The following figure shows how S_{4}S4 looks
(note that the symbols aa, bb, cc,
and dd are
not nodes; we only use them to show the connectivity between nodes; this is for the clarity of the figure).
In this problem, you are given the following inputs:
nn:
the dimension of the star graph. We assume that nn ranges
from 44 to 99.
Two nodes x_{1}x1 x_{2}x2 x_{3}x3 ... x_{n}xn and y_{1}y1 y_{2}y2 y_{3}\
...\ y_{n}y3 ... yn in S_{n}Sn.
You have to calculate the distance between these two nodes (which is an integer).
Input Format
nn (dimensionof the star graph)
A list of 55 pairs
of nodes.
Output Format
A list of 55 values,each representing the distance of a pair of nodes.
样例输入
4 1234 4231 1234 3124 2341 1324 3214 4213 3214 2143
样例输出
1 2 2 1 3
题目来源
2017ACM-ICPC 亚洲区（南宁赛区）网络赛
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