题目
Qestion: 试写一个算法假设不带权有向图G采用邻接表存储,分别设计实现求解以下问题的算法。
- 求出图G中每个顶点的入度。
- 求出图G中每个顶点的出度。
- 求出图G中出度最大的一个顶点,输出该顶点编号。
- 计算图G中出度为0的顶点数。
- 判断图G中是否存在边<i,j>
数据结构与定义
#include <stdio.h>
#include <iostream>
using namespace std;
#define MaxSize 20 // 最大顶点的个数
struct Node
{
int weight;
int index;
struct Node *next;
};
struct HNode
{
char nodeData;
struct Node *next;
};
struct Graph
{
int vertexNum;
int arcNum;
bool isDireted;
HNode verList[MaxSize];
};
该题所用的图结构
该图的邻接表
求出图G中每个顶点的入度
void HNodeIndegree(Graph G)
{
int IndegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
IndegreeCnt[tmp->index]++;
tmp = tmp->next;
}
}
cout << "all node's indegree" << endl;
for (int j = 0; j < G.vertexNum; j++)
{
cout << G.verList[j].nodeData << ':' << IndegreeCnt[j] << endl;
}
}
求出图G中每个顶点的出度
void HNodeOutdegree(Graph G)
{
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
cout << "all node's outdegree" << endl;
for (int j = 0; j < G.vertexNum; j++)
{
cout << G.verList[j].nodeData << ':' << OutdegreeCnt[j] << endl;
}
}
求出图G中出度最大的一个顶点,输出该顶点编号
void MaxOutDegreeNode(Graph G)
{
int index = -1; // 出度最大的数组下标
int res = 0; // 出度
// 与HNodeOutdegree同
// same code
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
// same code
for (int j = 0; j < G.vertexNum; j++)
{
if (OutdegreeCnt[j] > res)
{
res = OutdegreeCnt[j];
index = j;
}
}
cout << "the max out degree is" << ':' << G.verList[index].nodeData << endl;
}
计算图G中出度为0的顶点数
void ZeroOutdegree(Graph G)
{
int cnt = 0;
// same code
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
// same code
for (int j = 0; j < G.vertexNum; j++)
{
if (OutdegreeCnt[j] == 0)
{
cnt++;
}
}
cout << "the number of zero outdegree is" << ' ' << cnt;
}
判断图G中是否存在边<i,j>
bool IsArcExist(char a, char b, Graph G)
{
int AIndex, BIndex; // 找到弧头和弧尾的数组下标
for (int i = 0; i < G.vertexNum; i++)
{
if (G.verList[i].nodeData == a)
{
AIndex = i;
continue;
}
if (G.verList[i].nodeData == b)
{
BIndex = i;
continue;
}
}
Node *tmp = G.verList[AIndex].next;
while (tmp != nullptr)
{
if (tmp->index == BIndex)
{
return true;
}
tmp = tmp->next;
}
return false;
}
完整代码
#include <stdio.h>
#include <iostream>
using namespace std;
#define MaxSize 20 // 最大顶点的个数
struct Node
{
int weight;
int index;
struct Node *next;
};
struct HNode
{
char nodeData;
struct Node *next;
};
struct Graph
{
int vertexNum;
int arcNum;
bool isDireted;
HNode verList[MaxSize];
};
int Locate(char c, Graph G)
{
int index = -1;
for (int i = 0; i < G.vertexNum; i++)
{
if (G.verList[i].nodeData == c)
{
index = i;
}
}
return index;
}
void InsertVex(Graph &G, char v)
{
G.verList[G.vertexNum].nodeData = v;
G.verList[G.vertexNum].next = nullptr;
G.vertexNum++;
}
void InsertArc(Graph &G, char tail, char head)
{
int TailIndex, HeadIndex;
TailIndex = Locate(tail, G);
HeadIndex = Locate(head, G);
if (HeadIndex == -1 || TailIndex == -1) // 输入的弧头或者弧尾不存在
{
return;
}
// 无论G为有向图还是无向图
Node *newNode = new Node;
newNode->next = G.verList[TailIndex].next; // 头插法插入到邻接表中
newNode->index = HeadIndex;
G.verList[TailIndex].next = newNode;
if (!G.isDireted) // G为无向图
{
Node *newNode = new Node;
newNode->next = G.verList[HeadIndex].next; // 头插法插入到邻接表中
newNode->index = TailIndex;
G.verList[HeadIndex].next = newNode;
}
}
void DeleteVex(Graph &G, char v)
{
int index = Locate(v, G); // 该顶点的下标
// 释放与该顶点有关的所有边
Node *p = G.verList[index].next; // 临时指针p指向该顶点邻接表的第一个结点
while (p != nullptr)
{
if (!G.isDireted) // G为无向图
{
Node *q = G.verList[p->index].next; // 临时指针q指向待删除结点所在邻接表中的第一个结点
while (q->next->index != index) // 一直找，直到找到q的next结点的index值为删除顶点的index
{
q = q->next;
}
Node *needDel = q->next; // 创建一个临时指针，指向待删除的结点
q->next = needDel->next; // 保证邻接表不断
free(needDel); // 释放空间
}
G.verList[index].next = p->next;
G.arcNum--;
free(p);
}
// 释放顶点
G.verList[index].nodeData = NULL;
G.verList[index].next = nullptr;
G.vertexNum--;
return;
}
void DeleteArc(Graph &G, char tail, char head)
{
int TailIndex = Locate(tail, G);
int HeadIndex = Locate(head, G);
Node *p = G.verList[TailIndex].next; // 临时指针p指向弧尾顶点邻接表的第一个结点
while (p->next->index != HeadIndex)
{
p = p->next;
}
Node *needDel = p->next;
p->next = needDel->next;
free(needDel);
G.arcNum--;
if (!G.isDireted) // G为无向图
{
Node *q = G.verList[HeadIndex].next;
while (q->next->index != TailIndex)
{
q = q->next;
}
needDel = q->next;
q->next = needDel->next;
free(needDel);
}
}
void CreateGraph(Graph &G)
{
cin >> G.vertexNum >> G.arcNum; // 输入顶点数和边数
cin >> G.isDireted; // 输入是否为有向图
if (G.vertexNum > MaxSize)
{
return;
}
// 初始化顶点列表
for (int i = 0; i < G.vertexNum; i++)
{
cin >> G.verList[i].nodeData;
G.verList[i].next = nullptr;
}
// 依次输入各边的信息
for (int j = 0; j < G.arcNum; j++)
{
char ArcHead, ArcTail;
cin >> ArcTail >> ArcHead;
InsertArc(G, ArcTail, ArcHead);
}
}
void HNodeIndegree(Graph G)
{
int IndegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
IndegreeCnt[tmp->index]++;
tmp = tmp->next;
}
}
cout << "all node's indegree" << endl;
for (int j = 0; j < G.vertexNum; j++)
{
cout << G.verList[j].nodeData << ':' << IndegreeCnt[j] << endl;
}
}
void HNodeOutdegree(Graph G)
{
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
cout << "all node's outdegree" << endl;
for (int j = 0; j < G.vertexNum; j++)
{
cout << G.verList[j].nodeData << ':' << OutdegreeCnt[j] << endl;
}
}
void MaxOutDegreeNode(Graph G)
{
int index = -1; // 出度最大的数组下标
int res = 0; // 出度
// 与HNodeOutdegree同
// same code
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
// same code
for (int j = 0; j < G.vertexNum; j++)
{
if (OutdegreeCnt[j] > res)
{
res = OutdegreeCnt[j];
index = j;
}
}
cout << "the max out degree is" << ':' << G.verList[index].nodeData << endl;
}
void ZeroOutdegree(Graph G)
{
int cnt = 0;
// same code
int OutdegreeCnt[G.vertexNum] = {
0};
for (int i = 0; i < G.vertexNum; i++)
{
Node *tmp = G.verList[i].next;
while (tmp != nullptr)
{
OutdegreeCnt[i]++;
tmp = tmp->next;
}
}
// same code
for (int j = 0; j < G.vertexNum; j++)
{
if (OutdegreeCnt[j] == 0)
{
cnt++;
}
}
cout << "the number of zero outdegree is" << ' ' << cnt;
}
bool IsArcExist(char a, char b, Graph G)
{
int AIndex, BIndex; // 找到弧头和弧尾的数组下标
for (int i = 0; i < G.vertexNum; i++)
{
if (G.verList[i].nodeData == a)
{
AIndex = i;
continue;
}
if (G.verList[i].nodeData == b)
{
BIndex = i;
continue;
}
}
Node *tmp = G.verList[AIndex].next;
while (tmp != nullptr)
{
if (tmp->index == BIndex)
{
return true;
}
tmp = tmp->next;
}
return false;
}
int main()
{
Graph G;
CreateGraph(G);
// HNodeIndegree(G);
// HNodeOutdegree(G);
// MaxOutDegreeNode(G);
// ZeroOutdegree(G);
// char head, tail;
// cin >> head >> tail;
// bool isit = IsArcExist(head, tail, G);
// cout << isit << endl;
return 0;
}
结束语
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