图3 六度空间

题目：https://pintia.cn/problem-sets/1268384564738605056/problems/1281571555116650497

“六度空间”理论又称作“六度分隔（Six Degrees of Separation）”理论。这个理论可以通俗地阐述为：“你和任何一个陌生人之间所间隔的人不会超过六个，也就是说，最多通过五个人你就能够认识任何一个陌生人。”如图1所示。

图1 六度空间示意图

“六度空间”理论虽然得到广泛的认同，并且正在得到越来越多的应用。但是数十年来，试图验证这个理论始终是许多社会学家努力追求的目标。然而由于历史的原因，这样的研究具有太大的局限性和困难。随着当代人的联络主要依赖于电话、短信、微信以及因特网上即时通信等工具，能够体现社交网络关系的一手数据已经逐渐使得“六度空间”理论的验证成为可能。

假如给你一个社交网络图，请你对每个节点计算符合“六度空间”理论的结点占结点总数的百分比。

输入格式:

输入第1行给出两个正整数，分别表示社交网络图的结点数

输出格式:

对每个结点输出与该结点距离不超过6的结点数占结点总数的百分比，精确到小数点后2位。每个结节点输出一行，格式为“结点编号:（空格）百分比%”。

输入样例:

输出样例:

1: 70.00%
2: 80.00%
3: 90.00%
4: 100.00%
5: 100.00%
6: 100.00%
7: 100.00%
8: 90.00%
9: 80.00%
10: 70.00%

题解：https://blog.csdn.net/weixin_30708329/article/details/96271078
代码：

#include <iostream>
#include <queue>
#include <iomanip>
using namespace std;

typedef struct listNode
{
    int data;
    listNode *next;
}*plist, nlist;

typedef struct
{
    plist *listArray;
    int graphSize;
    bool *visited;
    float *sixDegreePercent;
}*pGraph, nGraph;

pGraph CreateGraph(int size);
void ConnectGraphVertex(pGraph pG, int vStart, int vEnd);
void InsertListNode(plist pL, int vertex);
int BFS(pGraph pG, int vertex);
void DestoryGraph(pGraph pG);

pGraph CreateGraph(int size)
{
    pGraph pG = new nGraph;
    pG->graphSize = size;
    pG->listArray = new plist[size];
    pG->visited = new bool[size];
    pG->sixDegreePercent = new float[size];
    for (int i = 0; i < size; i++)
    {
        pG->listArray[i] = new nlist;
        pG->listArray[i]->data = i;
        pG->listArray[i]->next = NULL;
        pG->visited[i] = false;
        pG->sixDegreePercent[i] = 0;
    }
    return pG;
}

void DestoryGraph(pGraph pG)
{
    plist tempListHead;
    plist tempListNode;
    for (int i = 0; i < pG->graphSize; i++)
    {
        tempListHead = pG->listArray[i];
        while ( tempListHead != NULL )
        {
            tempListNode = tempListHead;
            tempListHead = tempListHead->next;
            delete tempListNode;
        }
    }
    delete[]pG->listArray;
    delete[]pG->visited;
    delete[]pG->sixDegreePercent;
    delete pG;
}

void InsertListNode(plist pL, int vertex)
{
    plist temp = new nlist;
    temp->data = vertex;
    temp->next = pL->next;
    pL->next = temp;
    return;
}

void ConnectGraphVertex(pGraph pG, int vStart, int vEnd)
{
    if ( pG == NULL || vStart < 0 || vEnd < 0 || vStart == vEnd )
    {
        return;
    }
    //将vEnd插入vStart链表
    InsertListNode(pG->listArray[vStart], vEnd);
    //将vStart插入vEnd链表
    InsertListNode(pG->listArray[vEnd], vStart);
    return;
}

int BFS(pGraph pG, int vertex)
{
    queue<int> que;
    int source;
    plist listIter;
    int lastest;
    int tail = vertex;
    int level = 0;
    int sum = 1;    //将初始结点也算在内
    int maxLayer = 6;
    if ( pG->visited[vertex] == false )
    {
        que.push(vertex);
        pG->visited[vertex] = true;
    }
    while ( que.empty() != true && level < maxLayer )
    {
        source = que.front();
        que.pop();
        //遍历与vertex相连的点
        listIter = pG->listArray[source]->next;
        while ( listIter != NULL )
        {
            if ( pG->visited[listIter->data] == false )
            {
                pG->visited[listIter->data] = true;
                sum++;
                que.push(listIter->data);
                lastest = listIter->data;
            }
            listIter = listIter->next;
        }
        if ( tail == source )    //判断是否已经遍历完该层所有结点
        {
            level++;
            tail = lastest;
        }
    }
    //完成遍历后，要清空visited的状态
    for ( int i = 0; i < pG->graphSize; i++)
    {
        pG->visited[i] = false;
    }
    return sum;
}

int main()
{
    int N, E;
    cin >> N >> E;
    pGraph pG;
    pG = CreateGraph(N + 1);
    int i;
    int    edgeStart, edgeEnd;
    for (i = 0; i < E; i++)
    {
        cin >> edgeStart >> edgeEnd;
        edgeStart;
        edgeEnd;
        ConnectGraphVertex(pG, edgeStart, edgeEnd);
    }
    float percentage;
    int count;
    for (i = 1; i <= N; i++)
    {
        count = BFS(pG, i);
        percentage = (float)count / N * 100;
        cout << fixed << setprecision(2);
        cout << i << ": " << percentage << '%' << endl;
    }
    DestoryGraph(pG);
    return 0;
}