C语言拓补排序有向无环图

拓补排序简介
- 实现过程
- 代码实现

拓补排序简介

对一个有向无环图(Directed Acyclic Graph简称DAG)G进行拓扑排序，是将G中所有顶点排成一个线性序列，使得图中任意一对顶点u和v，若边(u,v)∈E(G)，则u在线性序列中出现在v之前

首先需要知道一个概念：入度。

通常指有向图中某点作为图中边的终点的次数之和。

比如：

节点	A	B	C	D	E
入度	0	1	1	1	3

实现过程

对图进行深度优化搜索，将顶点放入数组中，改变与之连接的下个节点的入度。

图片取自：拓扑排序（Topological Sorting）

代码实现

核心代码：

BOOLEAN isInTop(VTYPE *topNum, int length, VTYPE key) {for (int i = 0; i < length; i++) {if (topNum[i] == key) {return TRUE;}}return FALSE;
}int degreePos(AdjGraphPtr adj, VTYPE *topNum , int length) {int pos = -1;for (int i = 0; i < adj->vNum; i++) {if (adj->vertexList[i]->degree == 0) {if (isInTop(topNum, length, adj->vertexList[i]->v) == FALSE) {pos = i;return pos;}}}return pos;
}int getEmptyPos(VTYPE *topNum, int length) {//获得未使用的位置for (int i = 0; i < 5; i++) {if (topNum[i] == 0) {return i;}}return -1;
}int dfs(AdjGraphPtr adj, VTYPE *topNum, int length, int pos) {EdgePtr tmp = adj->vertexList[pos]->firstEdge;while (tmp != NULL) {VTYPE w = tmp->w;int w_pos = getVertexPos(adj, w);adj->vertexList[w_pos]->degree--;if (adj->vertexList[w_pos]->degree == 0)continue;if (isInTop(topNum, length, w) == FALSE) {int emptyPos = getEmptyPos(topNum, length);if(emptyPos != -1)topNum[emptyPos] = w;}dfs(adj, topNum, length, w_pos);tmp = tmp->next;}
}void topSort(AdjGraphPtr adj, int length) {VTYPE topNum[5];for (int i = 0; i < length; i++) {topNum[i] = 0;}for (int i = 0; i < length; i++) {int pos = degreePos(adj, topNum, length);if (pos == -1) {return;}int emptyPos = getEmptyPos(topNum, length);if (emptyPos != -1)topNum[emptyPos] = adj->vertexList[pos]->v;dfs(adj, topNum, length, pos);}
}

完整代码：

#include <stdio.h>
#include <malloc.h>
#include <memory.h>
#include <assert.h>
#define MAXVEX 100
#define MAXNUM 10
#define INFINITE 65525#define VTYPE char
#define QUETYPE EdgePtr
#define SORTTYPE int#define BOOLEAN int
#define TRUE 1
#define FALSE 0typedef struct EdgeNode {VTYPE v;VTYPE w;int weight;struct EdgeNode *next;
} Edge, *EdgePtr;typedef struct VertexNode {VTYPE v;int degree;EdgePtr firstEdge;
} Vertex, *VertexPtr;typedef struct {VertexPtr vertexList[MAXVEX];int vNum;int eNum;
} AdjGraph, *AdjGraphPtr;void freeAdj(AdjGraphPtr a);
EdgePtr createEdgeNode(VTYPE v, VTYPE w, int weight);
int getVertexPos(const AdjGraphPtr m, const VTYPE key);
void insertVertex(AdjGraphPtr adj, const VTYPE key);
void insertEdge(AdjGraphPtr adj, VTYPE a, VTYPE b, int weight);
void addEdge(AdjGraphPtr adj, VTYPE a, VTYPE b, int weight);
AdjGraphPtr createAdjGraph(VTYPE *v, const int v_length, int *e, const int e_length_1, const int e_length_2);
AdjGraphPtr createDirectedGraph(VTYPE *v, const int v_length, int *e, const int e_length_1, const int e_length_2);void print(int *a, int length);BOOLEAN isInTop(VTYPE *topNum, int length, VTYPE key) {for (int i = 0; i < length; i++) {if (topNum[i] == key) {return TRUE;}}return FALSE;
}int degreePos(AdjGraphPtr adj, VTYPE *topNum , int length) {int pos = -1;for (int i = 0; i < adj->vNum; i++) {if (adj->vertexList[i]->degree == 0) {if (isInTop(topNum, length, adj->vertexList[i]->v) == FALSE) {pos = i;return pos;}}}return pos;
}int getEmptyPos(VTYPE *topNum, int length) {//获得未使用的位置for (int i = 0; i < 5; i++) {if (topNum[i] == 0) {return i;}}return -1;
}int dfs(AdjGraphPtr adj, VTYPE *topNum, int length, int pos) {EdgePtr tmp = adj->vertexList[pos]->firstEdge;while (tmp != NULL) {VTYPE w = tmp->w;int w_pos = getVertexPos(adj, w);adj->vertexList[w_pos]->degree--;if (adj->vertexList[w_pos]->degree == 0)continue;if (isInTop(topNum, length, w) == FALSE) {int emptyPos = getEmptyPos(topNum, length);if(emptyPos != -1)topNum[emptyPos] = w;}dfs(adj, topNum, length, w_pos);tmp = tmp->next;}
}void topSort(AdjGraphPtr adj, int length) {VTYPE topNum[5];for (int i = 0; i < length; i++) {topNum[i] = 0;}for (int i = 0; i < length; i++) {int pos = degreePos(adj, topNum, length);if (pos == -1) {return;}int emptyPos = getEmptyPos(topNum, length);if (emptyPos != -1)topNum[emptyPos] = adj->vertexList[pos]->v;dfs(adj, topNum, length, pos);}
}void main() {int e[6][3] = {{ 'A', 'B', 3 },{ 'B', 'D', 1 },{ 'B', 'E', 5 },{ 'B', 'C', 6 },{ 'D', 'E', 7 },{ 'C', 'E', 6 },};const int e_length_1 = 6;const int e_length_2 = 3;VTYPE v[5] = { 'A','B','C','D','E' };const int v_length = 5;AdjGraphPtr adj = createDirectedGraph(v, v_length, e, e_length_1, e_length_2);topSort(adj, v_length);freeAdj(adj);
}void freeAdj(AdjGraphPtr a) {for (int i = 0; i < a->vNum; i++) {if (a->vertexList[i]->firstEdge != NULL) {EdgePtr tmp = a->vertexList[i]->firstEdge;while (tmp->next != NULL) {EdgePtr t = tmp;tmp = tmp->next;free(t);}free(tmp);}free(a->vertexList[i]);}free(a);
}EdgePtr createEdgeNode(VTYPE v, VTYPE w, int weight) {EdgePtr a = (EdgePtr)malloc(sizeof(Edge));memset(a, 0, sizeof(Edge));a->v = v;a->w = w;a->weight = weight;a->next = NULL;return a;
}int getVertexPos(const AdjGraphPtr m, const VTYPE key) {for (int i = 0; i < m->vNum; i++) {if (m->vertexList[i]->v == key)return i;}return -1;
}void insertVertex(AdjGraphPtr adj, const VTYPE key) {for (int i = 0; i < adj->vNum; i++) {if (adj->vertexList[i]->v == key)return;}VertexPtr vNode = (VertexPtr)malloc(sizeof(Vertex));memset(vNode, 0, sizeof(Vertex));vNode->v = key;vNode->firstEdge = NULL;adj->vertexList[adj->vNum] = vNode;adj->vNum++;
}void insertEdge(AdjGraphPtr adj, VTYPE a, VTYPE b, int weight) {int pos_a = getVertexPos(adj, a);EdgePtr avex = createEdgeNode(a, b, weight);if (adj->vertexList[pos_a]->firstEdge == NULL) {adj->vertexList[pos_a]->firstEdge = avex;}else {EdgePtr tmp = adj->vertexList[pos_a]->firstEdge;while (tmp->next != NULL) {tmp = tmp->next;}tmp->next = avex;}int pos_b = getVertexPos(adj, b);adj->vertexList[pos_b]->degree++;
}void addEdge(AdjGraphPtr adj, VTYPE a, VTYPE b, int weight) {insertEdge(adj, a, b, weight);insertEdge(adj, b, a, weight);adj->eNum++;
}AdjGraphPtr createAdjGraph(VTYPE *v, const int v_length, int *e, const int e_length_1, const int e_length_2) {AdjGraphPtr adj = (AdjGraphPtr)malloc(sizeof(AdjGraph));memset(adj, 0, sizeof(AdjGraph));for (int i = 0; i < v_length; i++) {insertVertex(adj, v[i]);}for (int i = 0; i < e_length_1; i++) {VTYPE a = *(e + e_length_2 * i + 0);VTYPE b = *(e + e_length_2 * i + 1);int weight = *(e + e_length_2 * i + 2);addEdge(adj, a, b, weight);}return adj;
}AdjGraphPtr createDirectedGraph(VTYPE *v, const int v_length, int *e, const int e_length_1, const int e_length_2) {AdjGraphPtr adj = (AdjGraphPtr)malloc(sizeof(AdjGraph));memset(adj, 0, sizeof(AdjGraph));for (int i = 0; i < v_length; i++) {insertVertex(adj, v[i]);}for (int i = 0; i < e_length_1; i++) {VTYPE a = *(e + e_length_2 * i + 0);VTYPE b = *(e + e_length_2 * i + 1);int weight = *(e + e_length_2 * i + 2);insertEdge(adj, a, b, weight);}adj->eNum++;return adj;
}void print(int *a, int length) {for (int i = 0; i < length; i++) {printf("%d ", a[i]);}putchar('\n');
}

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C语言拓补排序有向无环图

拓补排序简介

实现过程

代码实现

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