Date Structure: Graph --- Represent graph structure with adjacency list
2024-04-29 11:53:02
Date Structure: Graph
Represent graph structure with adjacency list
Basical Structure
/* ---- 邻接表实现图 ---- */
#pragma once
#include "Head.h"
#include "Stack.h"
#include <iostream>#define MAX_VERTEX_NUM 20// 最大顶点个数
#define VertexType char //点类型typedef enum
{DG,DN,UDG,UDN
} GraphKind;// 四种图类型typedef struct ArcNode//边结构体
{int adjvex; // 该弧所指向的顶点的位置struct ArcNode* nextarc;//指向下一条弧的指针int weight; //权重
} ArcNode;typedef struct VNode//顶点结构体
{VertexType data; // 顶点信息ArcNode* firstarc;//指向第一条依附该顶点的弧的指针
} VNode, AdjList[MAX_VERTEX_NUM];typedef struct//图结构体
{AdjList vertices; // 顶点向量int vexnum, arcnum;// 图的当前顶点数和弧数GraphKind Kind; // 图的种类标志
} ALGraph;Create
/*---- 几种不同类型的图的构建 ----*/
void CreateALGraph(ALGraph& ALG);void CreateDG(ALGraph& ALG);//构造有向图 Gvoid CreateDN(ALGraph& ALG);//构造有向网 G(即有权的图)void CreateUDG(ALGraph& ALG);//构造无向图 Gvoid CreateUDN(ALGraph& ALG);//构造无向网 G(即有权的图)void CreateALGraph(ALGraph& ALG)
{printf("请输入构造图的类型: \n");std::string temp;std::cin >> temp;if (temp == "DG")ALG.Kind = DG;else if (temp == "DN")ALG.Kind = DN;else if (temp == "UDG")ALG.Kind = UDG;else if (temp == "UDN")ALG.Kind = UDN;switch (ALG.Kind){case DG:CreateDG(ALG);return;//构造有向图 ALGcase DN:CreateDN(ALG);return;//构造有向网 ALG(即有权的图)case UDG:CreateUDG(ALG);return;//构造无向图 ALGcase UDN:CreateUDN(ALG);return;//构造无向网 ALG(即有权的图)}
}//构造有向网 G(即有权的图)
void CreateDN(ALGraph& ALG)
{InitALGraph(ALG);int from, to, value;ArcNode* q;std::cout << "请输入顶点数和边数: \n";std::cin >> ALG.vexnum >> ALG.arcnum;std::cout << "读入顶点信息，建立顶点表: \n";for (int i = 0; i < ALG.vexnum; i++)//读入顶点信息，建立顶点表std::cin >> ALG.vertices[i].data;std::cout << "输入边(Vi,Vj)上的下标i, 下标j, 权w: \n";for (int i = 0; i < ALG.arcnum; i++){std::cin >> from >> to >> value;ArcNode* p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = to;p->weight = value;p->nextarc = NULL;if (ALG.vertices[from].firstarc){for (q = ALG.vertices[from].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[from].firstarc = p;}
}//构造有向图 G
void CreateDG(ALGraph& ALG)
{InitALGraph(ALG);int from, to;ArcNode* q;std::cout << "请输入顶点数和边数: \n";std::cin >> ALG.vexnum >> ALG.arcnum;std::cout << "读入顶点信息，建立顶点表: \n";for (int i = 0; i < ALG.vexnum; i++)//读入顶点信息，建立顶点表std::cin >> ALG.vertices[i].data;std::cout << "输入边(Vi,Vj)上的下标i, 下标j\n";for (int i = 0; i < ALG.arcnum; i++){std::cin >> from >> to;ArcNode* p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = to;p->weight = 1;//单纯的有向图权重为1, 表示这两个顶点是连接着的.p->nextarc = NULL;if (ALG.vertices[from].firstarc){for (q = ALG.vertices[from].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[from].firstarc = p;}
}//构造无向图 G, 通过测试
void CreateUDG(ALGraph& ALG)
{InitALGraph(ALG);int from, to;ArcNode* q;std::cout << "请输入顶点数和边数: \n";std::cin >> ALG.vexnum >> ALG.arcnum;std::cout << "读入顶点信息，建立顶点表: \n";for (int i = 0; i < ALG.vexnum; i++)//读入顶点信息，建立顶点表std::cin >> ALG.vertices[i].data;std::cout << "输入边(Vi,Vj)上的下标i, 下标j\n";for (int i = 0; i < ALG.arcnum; i++){std::cin >> from >> to;ArcNode* p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = to;p->weight = 1;//单纯的有向图权重为1, 表示这两个顶点是连接着的.p->nextarc = nullptr;if (ALG.vertices[from].firstarc){for (q = ALG.vertices[from].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[from].firstarc = p;p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = from;p->weight = 1;p->nextarc = nullptr;if (ALG.vertices[to].firstarc){for (q = ALG.vertices[to].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[to].firstarc = p;}
}//构造无向网 G(即有权的图)
void CreateUDN(ALGraph& ALG)
{InitALGraph(ALG);int from, to, value;ArcNode* q;std::cout << "请输入顶点数和边数: \n";std::cin >> ALG.vexnum >> ALG.arcnum;std::cout << "读入顶点信息，建立顶点表: \n";for (int i = 0; i < ALG.vexnum; i++)//读入顶点信息，建立顶点表std::cin >> ALG.vertices[i].data;std::cout << "输入边(Vi,Vj)上的下标i, 下标j, 权w: \n";for (int i = 0; i < ALG.arcnum; i++){std::cin >> from >> to >> value;ArcNode* p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = to;p->weight = value;p->nextarc = NULL;if (ALG.vertices[from].firstarc){for (q = ALG.vertices[from].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[from].firstarc = p;p = (ArcNode*)malloc(sizeof(ArcNode));p->adjvex = from;p->weight = value;p->nextarc = NULL;if (ALG.vertices[to].firstarc){for (q = ALG.vertices[to].firstarc; q->nextarc; q = q->nextarc);q->nextarc = p;}elseALG.vertices[to].firstarc = p;}
}Predecessor-free vertex-first algorithm
/* ---- [无前趋的顶点优先算法] ---- */
void FindInDegree(ALGraph ALG, int indegree[]);void FindOutDegree(ALGraph ALG, int outdegree[]);int TopologicalSort(ALGraph ALG);//计算各个节点的入度
void FindInDegree(ALGraph ALG, int indegree[])
{ArcNode* q;for (int i = 0; i < ALG.vexnum; i++)for (q = ALG.vertices[i].firstarc; q; q = q->nextarc)indegree[q->adjvex]++;
}//计算各个顶点的出度
void FindOutDegree(ALGraph ALG, int outdegree[])
{ArcNode* q;for (int i = 0; i < ALG.vexnum; i++)for (q = ALG.vertices[i].firstarc; q; q = q->nextarc)outdegree[i]++;
}//无前趋的顶点优先算法
int TopologicalSort(ALGraph ALG)
{int indegree[MAX_VERTEX_NUM] = {0};FindInDegree(ALG, indegree);//求各顶点入度
#if TEST//检查计算各个顶点的入度是否正确printf("检查入度是否正确: \n") for (int i = 0; i < ALG.vexnum; i++)std::cout<< ALG.vertices[i].data << " " << indegree[i] << std::endl;printf("\n");
#endifSqStack<int> S{};InitStack(S);for (int i = 0; i < ALG.vexnum; i++)if (!indegree[i])Push(S, i);//如果某个顶点的入度为0, 将其入栈int temp;int count = 0;while (!StackEmpty(S)){Pop(S, temp);
#if TESTprintf("顶点编号: %d 顶点值: %c\n", temp, ALG.vertices[temp].data);
#endif++count;for (ArcNode* p = ALG.vertices[temp].firstarc; p; p = p->nextarc){temp = p->adjvex; //修改入度if (!(--indegree[temp]))//入度为0, 则入栈Push(S, temp);}}if (count < ALG.vexnum)return -1;elsereturn 1;
}AOE Graph
/* ---- AOE图 ---- */
int TopologicalOrder(ALGraph ALG, SqStack<int>& T, int eventEarly[]);int CriticalPath(ALGraph ALG);//并用栈T返回G的一个拓扑序列
int TopologicalOrder(ALGraph ALG, SqStack<int>& T, int eventEarly[])
{int indegree[MAX_VERTEX_NUM] = {0};FindInDegree(ALG, indegree);//求各顶点入度//初始化for (int i = 0; i < ALG.vexnum; i++)eventEarly[i] = 0;SqStack<int> S{};InitStack(S);for (int i = 0; i < ALG.vexnum; i++)if (!indegree[i])Push(S, i);//如果某个顶点的入度为0, 将其入栈int temp;int count = 0;int k;while (!StackEmpty(S)){Pop(S, k);Push(T, k);//将节点入栈//下面有一行代码用于输出序列//printf("顶点编号: %d 顶点字符: %c\n", k, ALG.vertices[k].data);++count;for (ArcNode* p = ALG.vertices[k].firstarc; p; p = p->nextarc){temp = p->adjvex; //修改入度if (!(--indegree[temp]))//入度为0, 则入栈Push(S, temp);eventEarly[temp] = MAX(eventEarly[k] + p->weight, eventEarly[temp]);}}#if TEST//检验所求的eventEarly数组的值是否正确printf("检验所求的eventEarly数组的值是否正确: \n");for (int i = 0; i < ALG.vexnum; i++)std::cout << ALG.vertices[i].data << ' ' << eventEarly[i] << std::endl;
#endifif (count < ALG.vexnum)return -1;elsereturn 1;
}//找关键路径.
int CriticalPath(ALGraph ALG)
{/** @brief* 求事件vj(即节点 j )的最早发生时间eventEarly[j] \n* eventEarly(0) = 0 \n* eventEarly(j) = max{ eventEarly(i) + dut<i,j> }, i是j的前驱 \n* eventEarly的初始值全部为0 \n* */int eventEarly[MAX_VERTEX_NUM] = {0};/** @brief* 求事件vj(即节点 j)的最早发生时间eventLast[j] \n* eventLast[n-1] = eventEarly[n-1] \n* eventLast(j) = min{ eventLast(k) - dut<j, k> }, k是j的后继 \n* eventLast的初始值全部为对应的eventEarly \n* */int eventLast[MAX_VERTEX_NUM] = {0};for (int i = 0; i < MAX_VERTEX_NUM; i++)eventEarly[i] = 0;SqStack<int> T{};TopologicalOrder(ALG, T, eventEarly);//寻找出度为0的节点, 其即为AOE的汇点, 并将其eventLast赋值为 对应的eventEarlyint outdegree[MAX_VERTEX_NUM];for (int i = 0; i < ALG.vexnum; i++)outdegree[i] = 0;FindOutDegree(ALG, outdegree);int end;for (int i = 0; i < ALG.vexnum; i++)if (outdegree[i] == 0){end = i;break;}for (int i = 0; i < MAX_VERTEX_NUM; i++)eventLast[i] = INF;eventLast[end] = eventEarly[end];//计算eventLast[]int j;int k;ArcNode* p;Pop(T, j);//将end弹出来while (!StackEmpty(T)){Pop(T, j);for (p = ALG.vertices[j].firstarc; p; p = p->nextarc){k = p->adjvex;eventLast[j] = MIN(eventLast[j], eventLast[k] - p->weight);}}#if TEST//检验所求的eventLast数组和eventEarly数组是否正确printf("\n");printf("检查: eventLast 和 eventEarly\n");for (int i = 0; i < ALG.vexnum; i++)printf("%c eventEarly: %d, eventLsat: %d\n", ALG.vertices[i].data, eventEarly[i], eventEarly[i]);
#endif/**@brief* (边)的edgeEarly, edgeLast \n* j -> k, 则这条边 \n* edgeEarly = eventEarly[j] \n* edgeLast = eventLsat[k] - dut<j, k> \n* */int dut;int edgeEarly, edgeLast;char tag;for (j = 0; j < ALG.vexnum; j++){for (p = ALG.vertices[j].firstarc; p; p = p->nextarc){k = p->adjvex, dut = p->weight;edgeEarly = eventEarly[j];edgeLast = eventLast[k] - dut;tag = (edgeEarly == edgeLast) ? '*' : ' ';printf("%c -> %c: weight: %d edgeEarly: %d, edgeLast: %d %c\n", ALG.vertices[j].data, ALG.vertices[k].data, dut, edgeEarly, edgeLast, tag);//std::cout << j << "->" << k << ' ' << dut << ' ' << edgeEarly << ' ' << edgeLast << ' ' << tag << std::endl;}}return 1;
}
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