2017 ACM-ICPC 亚洲区（南宁赛区）网络赛 Minimum Distance in a Star Graph

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 $n$, an $n-dimensional$star graph, also referred to as S_{n}S​n​​, is an undirected graph consisting of $n!$ nodes (or vertices) and $((n-1)\ast n!)/2$ edges. Each node is uniquely assigned a label x_{1} x_{2} ... x_{n}x​1​​ x​2​​ ... x​n​​which is any permutation of the n digits $1,2,3,...,n$. For instance, an S_{4}S​4​​ has the following 24 nodes $1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321$. For each node with label x_{1} x_{2} x_{3} x_{4} ... x_{n}x​1​​ x​2​​x​3​​ x​4​​ ... x​n​​, it has $n-1$ edges connecting to nodes x_{2} x_{1} x_{3} x_{4} ... x_{n}x​2​​ x​1​​ x​3​​ x​4​​ ... x​n​​, x_{3} x_{2} x_{1} x_{4} ... x_{n}x​3​​ x​2​​ x​1​​ x​4​​ ... x​n​​, x_{4} x_{2} x_{3} x_{1} ... x_{n}x​4​​ x​2​​ x​3​​ x​1​​ ... x​n​​, ..., and x_{n} x_{2} x_{3} x_{4} ... x_{1}x​n​​ x​2​​ x​3​​ x​4​​ ... x​1​​. That is, the $n-1$ adjacent nodes are obtained by swapping the first symbol and the $d-th$ symbol of x_{1} x_{2} x_{3} x_{4} ... x_{n}x​1​​ x​2​​ x​3​​ x​4​​ ... x​n​​, for $d=2,...,n$. For instance, in S_{4}S​4​​, node $1234$has $3$ edges connecting to nodes $2134$, $3214$, and $4231$. The following figure shows how S_{4}S​4​​looks (note that the symbols $a$, $b$, $c$, and $d$ 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:

• $n$: the dimension of the star graph. We assume that $n$ ranges from $4$ to $9$.
• Two nodes x_{1}x​1​​ x_{2}x​2​​ x_{3}x​3​​ ... x_{n}x​n​​ and y_{1}y​1​​ y_{2}y​2​​ y_{3} ... y_{n}y​3​​ ... y​n​​ in S_{n}S​n​​.

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

Input Format

$n$ (dimension of the star graph)

A list of $5$ pairs of nodes.

Output Format

A list of $5$ 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

2017 ACM-ICPC 亚洲区（南宁赛区）网络赛

题意：给你1-N的N个数，构建N维（几维其实不重要），然后构图的规则是相邻的顶点只能是由第一个字符跟2-n的字符进行交换得来的，问你给出的五个询问中两个节点的最短距离分别是多少？

思路：宽度优先搜索加剪枝，对搜过的节点进行弹出

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string.h>
#include<string>
#include<set>
#include<queue>
using namespace std;
string numa;
string numb;
int n;
struct node{
	string str;
	int times;
};
int bfs() {
	queue<node> q;
	set<string> ss;
	node now,next;
	now.str = numa;
	now.times = 0;
	q.push(now);
    ss.insert(now.str);
	while (!q.empty()) {
		now = q.front();
		q.pop();
		if (now.str == numb)
			return now.times;
		for (int i = 1; i < n; ++i) {
			next.str = now.str;
			next.times=now.times+1;
			next.str[i] = now.str[0];
			next.str[0] = now.str[i];
            if (ss.count(next.str) == 0)
            {
                ss.insert(next.str);
                q.push(next);
            }else
                continue;

        }
	}
}
int main()
{
	scanf("%d", &n);
    int t = 5;
    while (t--) {
        cin >> numa >> numb;
        cout << bfs() << endl;
    }
	return 0;
}