2017ICPC南宁赛区网络赛 Minimum Distance in a Star Graph （bfs）

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 nnn, an n−dimensionaln-dimensionaln−dimensional star graph, also referred to as SnS_{n}Sn, is an undirected graph consisting of n!n!n! nodes (or vertices) and ((n−1) ∗ n!)/2((n-1)\ *\ n!)/2((n−1) ∗ n!)/2 edges. Each node is uniquely assigned a label x1 x2 ... xnx_{1}\ x_{2}\ ...\ x_{n}x1 x2 ... xn which is any permutation of the n digits 1,2,3,...,n{1, 2, 3, ..., n}1,2,3,...,n. For instance, an S4S_{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}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 x1 x2x3 x4 ... xnx_{1}\ x_{2} x_{3}\ x_{4}\ ...\ x_{n}x1 x2x3 x4 ... xn, it has n−1n-1n−1 edges connecting to nodes x2 x1 x3 x4 ... xnx_{2}\ x_{1}\ x_{3}\ x_{4}\ ...\ x_{n}x2 x1 x3 x4 ... xn, x3 x2 x1 x4 ... xnx_{3}\ x_{2}\ x_{1}\ x_{4}\ ...\ x_{n}x3 x2 x1 x4 ... xn, x4 x2 x3 x1 ... xnx_{4}\ x_{2}\ x_{3}\ x_{1}\ ...\ x_{n}x4 x2 x3 x1 ... xn, ..., and xn x2 x3 x4 ... x1x_{n}\ x_{2}\ x_{3}\ x_{4}\ ...\ x_{1}xn x2 x3 x4 ... x1. That is, the n−1n-1n−1 adjacent nodes are obtained by swapping the first symbol and the d−thd-thd−th symbol of x1 x2 x3 x4 ... xnx_{1}\ x_{2}\ x_{3}\ x_{4}\ ...\ x_{n}x1 x2 x3 x4 ... xn, for d=2,...,nd = 2, ..., nd=2,...,n. For instance, in S4S_{4}S4, node 123412341234 has 333 edges connecting to nodes 213421342134, 321432143214, and 423142314231. The following figure shows how S4S_{4}S4 looks (note that the symbols aaa, bbb, ccc, and ddd 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:

nnn: the dimension of the star graph. We assume that nnn ranges from 444 to 999.
Two nodes x1x_{1}x1 x2x_{2}x2 x3x_{3}x3 ... xnx_{n}xn and y1y_{1}y1 y2y_{2}y2 y3 ... yny_{3}\ ...\ y_{n}y3 ... yn in SnS_{n}Sn.

You have to calculate the distance between these two nodes (which is an integer).

Input Format

nnn (dimension of the star graph)

A list of 555 pairs of nodes.

Output Format

A list of 555 values, each representing the distance of a pair of nodes.

样例输入

样例输出

1

2

2

1

3

题目读完以后就是看看一个n位数能不能够通过题目中要求的变化变化到另一个n位数，求变化的最小次数。
用bfs搜索即可。
题目中要求的变化是指，将第一位数与之后的n-1位数分别交换得到的新数。

 #include<iostream>

 #include<cstdio>

 #include<algorithm>

 #include<cstring>

 #include<queue>

 #include<map>

 using namespace std;

 int n,t;

 char ch1[],ch2[];

 map<string,bool> mp;

 struct node

 {

     string s;

     int step;

 };

 int bfs()

 {

     queue<node> Q;

     mp.clear();

     node st;

     st.s=ch1;

     st.step=;

     Q.push(st);

     while(!Q.empty())

     {

         node u=Q.front();

         if (u.s==ch2) return u.step;

         Q.pop();

         for(int i=; i<n; i++)

         {

             swap(u.s[],u.s[i]);

             if (mp[u.s]==)

             {

                 swap(u.s[],u.s[i]);

                 continue;

             }

             mp[u.s]=;

             node ed;

             ed.s=u.s;

             ed.step=u.step+;

             Q.push(ed);

             swap(u.s[],u.s[i]);

         }

     }

 }

 int main()

 {

     scanf("%d",&n);

     for(int t=;t<=;t++)

     {

         scanf("%s %s",&ch1,&ch2);

         printf("%d\n",bfs());

     }

     return ;

 }