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

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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 $SnS_{n}Sn, is an undirected graph consisting of n!n!n! nodes (or vertices) and ((n−1) ∗ n!)/2((n-1) * n!)/2((n−1) ∗ n!)/2 edges. Each node is uniquely assigned a label x1 x2 ... xnx_{1} x_{2} ... x_{n}x1 x2 ... xn which is any permutation of the n digits 1,2,3,...,n{1, 2, 3, ..., n}1,2,3,...,n. For instance, an S4S_{4}S4 has the following 24 nodes 1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321{1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321}1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321. For each node with label x1 x2x3 x4 ... xnx_{1} x_{2} x_{3} x_{4} ... x_{n}x1 x2x3 x4 ... xn, it has n−1n-1n−1 edges connecting to nodes x2 x1 x3 x4 ... xnx_{2} x_{1} x_{3} x_{4} ... x_{n}x2 x1 x3 x4 ... xn, x3 x2 x1 x4 ... xnx_{3} x_{2} x_{1} x_{4} ... x_{n}x3 x2 x1 x4 ... xn, x4 x2 x3 x1 ... xnx_{4} x_{2} x_{3} x_{1} ... x_{n}x4 x2 x3 x1 ... xn, ..., and xn x2 x3 x4 ... x1x_{n} x_{2} x_{3} x_{4} ... x_{1}xn x2 x3 x4 ... x1. That is, the n−1n-1n−1 adjacent nodes are obtained by swapping the first symbol and the d−thd-thd−th symbol of x1 x2 x3 x4 ... xnx_{1} x_{2} x_{3} x_{4} ... x_{n}x1 x2 x3 x4 ... xn, for d=2,...,nd = 2, ..., nd=2,...,n. For instance, in S4S_{4}S4, node 123412341234 has 333 edges connecting to nodes 213421342134, 321432143214, and 423142314231. The following figure shows how S4S_{4}S4 looks (note that the symbols aaa, bbb, ccc, and ddd are not nodes; we only use them to show the connectivity between nodes; this is for the clarity of the figure).$

In this problem, you are given the following inputs:
- 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

A list of

Output Format

A list of
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。

1 #include<iostream> 2 #include<cstdio> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<map> 7 using namespace std; 8 int n,t; 9 char ch1[15],ch2[15]; 10 map<string,bool> mp; 11 struct node 12 { 13 string s; 14 int step; 15 }; 16 int bfs() 17 { 18 queue<node> Q; 19 mp.clear(); 20 node st; 21 st.s=ch1; 22 st.step=0; 23 Q.push(st); 24 while(!Q.empty()) 25 { 26 node u=Q.front(); 27 if (u.s==ch2) return u.step; 28 Q.pop(); 29 for(int i=1; i<n; i++) 30 { 31 swap(u.s[0],u.s[i]); 32 if (mp[u.s]==1) 33 { 34 swap(u.s[0],u.s[i]); 35 continue; 36 } 37 mp[u.s]=1; 38 node ed; 39 ed.s=u.s; 40 ed.step=u.step+1; 41 Q.push(ed); 42 swap(u.s[0],u.s[i]); 43 } 44 } 45 } 46 int main() 47 { 48 scanf("%d",&n); 49 for(int t=1;t<=5;t++) 50 { 51 scanf("%s %s",&ch1,&ch2); 52 printf("%d ",bfs()); 53 } 54 return 0; 55 }
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原文地址：https://www.cnblogs.com/Annetree/p/7596222.html

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

Input Format

Output Format

样例输入

样例输出