05-1. List Components (PAT) - 图的遍历问题

 

For a given undirected graph with N vertices and E edges, please list all the connected components by both DFS and BFS. Assume that all the vertices are numbered from 0 to N-1. While searching, assume that we always start from the vertex with the smallest index, and visit its adjacent vertices in ascending order of their indices.

Input Specification:

Each input file contains one test case. For each case, the first line gives two integers N (0<N<=10) and E, which are the number of vertices and the number of edges, respectively. Then E lines follow, each described an edge by giving the two ends. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in each line a connected component in the format "{ v1 v2 ... vk }". First print the result obtained by DFS, then by BFS.

Sample Input:

8 6
0 7
0 1
2 0
4 1
2 4
3 5

Sample Output:

{ 0 1 4 2 7 }
{ 3 5 }
{ 6 }
{ 0 1 2 7 4 }
{ 3 5 }
{ 6 }

题意：给出图中各个顶点的连通关系，要求输出DFS与BFS的遍历结果
解题思路：根据输入建立邻接矩阵，再进行图的遍历，注意：图中可能不是所有顶点都连通的，因此需要对图中每个顶点进行遍历

#include <iostream>
#include <string>
#include <memory.h>
using namespace std;

typedef struct Graph{
    int *graphMatrix;
    bool *visited;
    int vertexNumber;
}*pGraph, nGraph;

typedef struct{
    int *queData;
    int queFront;
    int queEnd;
    int MaxSize;
}*pQue, nQue;

pGraph CreateGraph( int vertexNumber );
pGraph InsertEdge( pGraph pG, int edgeStart, int edgeEnd );
void DFS( pGraph pG, int vertex );
pQue CreateQueue( int queSize );
bool IsEmptyQ( pQue pQ );
void AddQ( pQue pQ, int item );
int DeleteQ( pQue pQ );
void BFS( pGraph pG, int vertex, int vertexNum );

int main()
{
    int N, E;
    cin >> N >> E;
    pGraph pG;
    pG = CreateGraph( N );
    int i;
    int    edgeStart, edgeEnd;
    for ( i = 0; i < E; i++ )
    {
        cin >> edgeStart >> edgeEnd;
        InsertEdge( pG, edgeStart, edgeEnd );
    }
    for ( i = 0; i < N; i++ )
    {
        if ( pG->visited[i] == false )
        {
            cout << "{ ";
            DFS( pG, i);
            cout << "}" << endl;
        }
    }
    for ( i = 0; i < N; i++ )    //清空visited状态
    {
        pG->visited[i] = false;
    }
    for ( i = 0; i < N; i++ )
    {
        if ( pG->visited[i] == false )
        {
            cout << "{ ";
            BFS( pG, i, N);
            cout << "}" << endl;
        }
    }
    return 0;
}

pGraph CreateGraph( int vertexNumber )
{
    pGraph pG;
    pG = ( pGraph )malloc( sizeof( nGraph ) );
    pG->vertexNumber = vertexNumber;
    int len = ( vertexNumber * ( vertexNumber + 1 ) / 2 );
    pG->graphMatrix = ( int* )malloc( len * sizeof( int ) );
    memset( pG->graphMatrix, 0, sizeof( int ) * len);
    pG->visited = ( bool* )malloc( vertexNumber * sizeof( bool ) );
    memset( pG->visited, false, sizeof( bool ) * vertexNumber );
    return pG;
}

pGraph InsertEdge( pGraph pG, int edgeStart, int edgeEnd )
{
    if ( edgeStart >= pG->vertexNumber || edgeEnd >= pG->vertexNumber )
    {
        cout << "Error Edge!" << endl;
        return pG;
    }
    int tmp;
    if ( edgeStart < edgeEnd )
    {
        tmp = edgeStart;
        edgeStart = edgeEnd;
        edgeEnd = tmp;
    }
    int item = edgeStart * ( edgeStart + 1 ) / 2 + edgeEnd;
    pG->graphMatrix[item] = 1;
    return pG;
}

void DFS( pGraph pG, int vertex )
{
    if ( pG->visited[vertex] == false )
    {
        cout << vertex << ' ';
    }
    pG->visited[vertex] = true;
    int    rows, cols;
    int materixIndex;
    for ( cols = 0; cols < vertex; cols++ )    //扫描行
    {
        materixIndex = vertex * ( vertex + 1 ) / 2 + cols;
        if ( pG->graphMatrix[materixIndex] == 1 && pG->visited[ cols ] == false )
        {
            DFS( pG, cols );
        }
    }
    for ( rows = vertex; rows < pG->vertexNumber; rows++ )
    {
        materixIndex = rows * ( rows + 1 ) / 2 + vertex;
        if ( pG->graphMatrix[materixIndex] == 1 && pG->visited[ rows ] == false )
        {
            DFS( pG, rows );
        }
    }
}



pQue CreateQueue( int queSize )
{
    pQue pQ;
    pQ = ( pQue )malloc( sizeof( nQue ) );
    pQ->MaxSize = queSize + 1;
    pQ->queData = ( int * )malloc( pQ->MaxSize * sizeof( int ) );
    pQ->queFront = pQ->queEnd = 0;
    return pQ;
}

bool IsEmptyQ( pQue pQ )
{
    if ( pQ->queFront == pQ->queEnd )    //队列为空
    {
        return true;
    }
    else
    {
        return false;
    }
}

void AddQ( pQue pQ, int item )
{
    if ( ( pQ->queEnd + 1 ) % pQ->MaxSize == pQ->queFront  )
    {
        cout << "Queue Is Full!" << endl;
        return;
    }
    pQ->queEnd = ( pQ->queEnd + 1 ) % pQ->MaxSize;
    pQ->queData[ pQ->queEnd ] = item;
}

int DeleteQ( pQue pQ )
{
    if ( pQ->queFront == pQ->queEnd )
    {
        cout << "Queue Is Empty!" << endl;
        return -1;
    }
    else
    {
        pQ->queFront = ( pQ->queFront + 1 ) % pQ->MaxSize;
        return pQ->queData[ pQ->queFront ];
    }
}

void BFS( pGraph pG, int vertex, int vertexNum )
{
    cout << vertex << ' ';
    pG->visited[vertex] = true;
    pQue pQ;
    pQ = CreateQueue( vertexNum );
    AddQ( pQ, vertex);
    int cols, rows;
    int materixIndex;
    while ( IsEmptyQ( pQ ) != true )
    {
        vertex = DeleteQ( pQ );
        for ( cols = 0; cols < vertex; cols++ )    //扫描行
        {
            materixIndex = vertex * ( vertex + 1 ) / 2 + cols;
            if ( pG->graphMatrix[materixIndex] == 1 && pG->visited[ cols ] == false )
            {
                cout << cols << ' ';
                pG->visited[cols] = true;
                AddQ( pQ, cols );
            }
        }
        for ( rows = vertex; rows < pG->vertexNumber; rows++ )
        {
            materixIndex = rows * ( rows + 1 ) / 2 + vertex;
            if ( pG->graphMatrix[materixIndex] == 1 && pG->visited[ rows ] == false )
            {
                cout << rows << ' ';
                pG->visited[rows] = true;
                AddQ( pQ, rows );
            }
        }
    }
}