05-图3. 六度空间 (30)

最新推荐文章于 2022-05-15 21:37:59 发布

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最新推荐文章于 2022-05-15 21:37:59 发布

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本文介绍了一种使用下三角矩阵表示社交网络的方法，并通过宽度优先搜索（BFS）算法来计算社交网络中个体与其六度分隔内的联系人数量。详细介绍了如何创建和操作下三角矩阵图，实现节点之间的连接判断与建立，以及如何通过BFS算法遍历图并计算紧密度。

1 1500ms时间能够慷慨挥霍

2 内存一般也能够挥霍，可是要记得释放用完的内存，否则可能累积到内存超限

3 BFS分层注意细节，下三角矩阵找邻接节点也要注意细节

#include <iostream>
#include <malloc.h>
#include <queue>

using namespace std;

bool* CreateMatrixGraph(const int& N)
{
    int arraySize = N * (N + 1) / 2;
    bool* graph = (bool*) malloc(sizeof(bool) * arraySize);
    for (int i = 0; i < arraySize; i++)
    {
        graph[i] = 0;
    }
    return graph;
}

bool IsMatrixConnected(const int& a, const int& b, bool* graph, const int& N)
{
    if (a == b)
    {
        return false;
    }
    if (a > b)
    {
        return (graph[a * (a + 1) / 2 + b]);
    }
    else
    {
        return (graph[b * (b + 1) / 2 + a]);
    }
}

void MatrixConnect(const int& a, const int& b, bool* graph, const int& N)
{
    if (a >= N || b >= N)
    {
        printf("ERROR : NODE OUT OF RANGE\n");
        //return;
    }
    if (IsMatrixConnected(a, b, graph, N))
    {
        printf("ERROR : %d AND %d ALREADY CONNECTED\n", a, b);
        //return;
    }
    if (a == b)
    {
        printf("ERROR : THE SAME VERTICE\n");
        //return;
    }
    if (a > b)
    {
        graph[a * (a + 1) / 2 + b] = 1;
    }
    else
    {
        graph[b * (b + 1) / 2 + a] = 1;
    }
}

void GetAdjoinVertice(const int& vertice, bool* graph, int* adjoinVertice, int N)
{
    int currentIndex = 0;
    // 横行计算
    const int VERTICALPRIMEINDEX = (vertice*vertice + vertice) / 2;
    for (int j = 0; j <= vertice; j++)  // 共遍历了(vertice+1)个元素
    {
        if (graph[VERTICALPRIMEINDEX + j] == 1)
        {
            adjoinVertice[currentIndex++] = j;
        }
    }
    // 竖向计算初始位置。该位置是横向计算的最后一个位置
    const int COLUMNPRIMEINDEX = (vertice*vertice + vertice) / 2 + vertice;
    for (int j = 0; j < N - vertice - 1; j++)
    {
        if (graph[COLUMNPRIMEINDEX + (j+1) * (vertice+1) + (j*j + j) / 2] == 1)
        {
            adjoinVertice[currentIndex++] = vertice + j + 1;
        }
    }
}

int BFS(bool* graph, int vertice, bool* isVisited, int N)
{
    // 找vertice的朋友
    queue<int> t;
    t.push(vertice);
    isVisited[vertice] = true;
    // 近处的朋友包含自己我也是醉的不行
    int closeFriendship = 1;
    int lastLevelFriend = 0;

    int currentLevel = 0;
    int currentLevelFriend = 0;

    while (!t.empty())
    {
        int currentVertice = t.front();
        t.pop();
        //printf("%d ", currentVertice);

        int* adjoinVertice = (int*) malloc(sizeof(int) * N);
        for (int i = 0; i < N; i++)
        {
            adjoinVertice[i] = -1;
        }
        GetAdjoinVertice(currentVertice, graph, adjoinVertice, N);
        int i = 0;

        // 假设上层朋友数已经为0，即当前层遍历已经结束，将当前层朋友数设为上层朋友数。然后当前层朋友数置0
        if (lastLevelFriend == 0)
        {
            currentLevel++;
            lastLevelFriend = currentLevelFriend;
            currentLevelFriend = 0;
        }
        if (currentLevel > 6)
        {
            return closeFriendship;
        }
        // 遍历当前层的朋友
        while (adjoinVertice[i] != -1)
        {
            if (!isVisited[adjoinVertice[i]])
            {
                t.push(adjoinVertice[i]);
                isVisited[adjoinVertice[i]] = true;

                closeFriendship++;
                currentLevelFriend++;
            }
            i++;
        }
        if (lastLevelFriend > 0)
        {
            lastLevelFriend--;
        }
        free(adjoinVertice);
    }

    return closeFriendship;
}

int main()
{
    int N;
    int M;
    scanf("%d %d", &N, &M);
    N++;
    bool* graph = CreateMatrixGraph(N);
    for (int i = 0; i < M; i++)
    {
        int node1;s
        int node2;
        scanf("%d %d", &node1, &node2);
        MatrixConnect(node1, node2, graph, N);
    }
    bool* isVisited = (bool*) malloc(sizeof(bool) * N);
    // 输出
    for (int m = 1; m <= N - 1; m++)
    {
        for (int i = 0; i < N; i++)
        {
            isVisited[i] = false;
        }
        float closeFriend = BFS(graph, m, isVisited, N);
        float percent = closeFriend / (N - 1) * 100;
        printf("%d: %.2f%%\n", m, percent);
    }

    return 0;
}