拓撲排序是求一個AOV網(頂點代表活動, 各條邊表示活動之間的率先關系的有向圖)中各活動的一個拓撲序列的運算, 可用於測試AOV

網絡的可行性.

整個算法包含三步:

1.計算每一個頂點的入度, 存入InDegree數組中.

2.檢查InDegree數組中頂點的入度, 將入度為零的頂點進棧.

3.不斷從棧中彈出入度為0的頂點並輸出, 並將該頂點為尾的全部鄰接點的入度減1, 若此時某個鄰接點的入度為0, 便領其進棧. 反復步驟

3, 直到棧為空時為止. 此時, 或者所有頂點都已列出, 或者因圖中包括有向回路, 頂點未能所有列出.

實現代碼:

#include "iostream"
#include "cstdio"
#include "cstring"
#include "algorithm"
#include "queue"
#include "stack"
#include "cmath"
#include "utility"
#include "map"
#include "set"
#include "vector"
#include "list"
#include "string"
using namespace std;
typedef long long ll;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
enum ResultCode { Underflow, Overflow, Success, Duplicate, NotPresent, Failure, HasCycle };
template <class T>
struct ENode
{
	ENode() { nxtArc = NULL; }
	ENode(int vertex, T weight, ENode *nxt) {
		adjVex = vertex;
		w = weight;
		nxtArc = nxt;
	}
	int adjVex;
	T w;
	ENode *nxtArc;
	/* data */
};
template <class T>
class Graph
{
public:
	virtual ~Graph() {}
	virtual ResultCode Insert(int u, int v, T &w) = 0;
	virtual ResultCode Remove(int u, int v) = 0;
	virtual bool Exist(int u, int v) const = 0;
	/* data */
};
template <class T>
class LGraph: public Graph<T>
{
public:
	LGraph(int mSize);
	~LGraph();
	ResultCode Insert(int u, int v, T &w);
	ResultCode Remove(int u, int v);
	bool Exist(int u, int v) const;
	int Vertices() const { return n; }
	void Output();
protected:
	ENode<T> **a;
	int n, e;
	/* data */
};
template <class T>
void LGraph<T>::Output()
{
	ENode<T> *q;
	for(int i = 0; i < n; ++i) {
		q = a[i];
		while(q) {
			cout << '(' << i << ' ' << q -> adjVex << ' ' << q -> w << ')';
			q = q -> nxtArc;
		}
		cout << endl;
	}
	cout << endl << endl;
}
template <class T>
LGraph<T>::LGraph(int mSize)
{
	n = mSize;
	e = 0;
	a = new ENode<T>*[n];
	for(int i = 0; i < n; ++i)
		a[i] = NULL;
}
template <class T>
LGraph<T>::~LGraph()
{
	ENode<T> *p, *q;
	for(int i = 0; i < n; ++i) {
		p = a[i];
		q = p;
		while(p) {
			p = p -> nxtArc;
			delete q;
			q = p;
		}
	}
	delete []a;
}
template <class T>
bool LGraph<T>::Exist(int u, int v) const
{
	if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v) return false;
	ENode<T> *p = a[u];
	while(p && p -> adjVex != v) p = p -> nxtArc;
	if(!p) return false;
	return true;
}
template <class T>
ResultCode LGraph<T>::Insert(int u, int v, T &w)
{
	if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v) return Failure;
	if(Exist(u, v)) return Duplicate;
	ENode<T> *p = new ENode<T>(v, w, a[u]);
	a[u] = p;
	e++;
	return Success;
}
template <class T>
ResultCode LGraph<T>::Remove(int u, int v)
{
	if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v) return Failure;
	ENode<T> *p = a[u], *q = NULL;
	while(p && p -> adjVex != v) {
		q = p;
		p = p -> nxtArc;
	}
	if(!p) return NotPresent;
	if(q) q -> nxtArc = p -> nxtArc;
	else a[u] = p -> nxtArc;
	delete p;
	e--;
	return Success;
}
template <class T>
class ExtLgraph: public LGraph<T>
{
public:
	ExtLgraph(int mSize): LGraph<T>(mSize) {}
	void TopoSort(int *order);
private:
	void CallInDegree(int *InDegree);
	/* data */
};
template <class T>
void ExtLgraph<T>::TopoSort(int *order)
{
	int *InDegree = new int[LGraph<T>::n];
	int top = -1; // 置棧頂指針為-1, 代表空棧
	ENode<T> *p;
	CallInDegree(InDegree); // 計算每一個頂點的入度
	for(int i = 0; i < LGraph<T>::n; ++i)
		if(!InDegree[i]) { // 圖中入度為零的頂點進棧
			InDegree[i] = top;
			top = i;
		}
	for(int i = 0; i < LGraph<T>::n; ++i) { // 生成拓撲排序
		if(top == -1) throw HasCycle; // 若堆棧為空, 說明圖中存在有向環
		else {
			int j = top;
			top = InDegree[top]; // 入度為0的頂點出棧
			order[i] = j;
			cout << j << ' ';
			for(p = LGraph<T>::a[j]; p; p = p -> nxtArc) { // 檢查以頂點j為尾的全部鄰接點
				int k = p -> adjVex; // 將j的出鄰接點入度減1
				InDegree[k]--;
				if(!InDegree[k]) { // 頂點k入度為0時進棧
					InDegree[k] = top;
					top = k;
				}
			}
		}
	}
}
template <class T>
void ExtLgraph<T>::CallInDegree(int *InDegree)
{
	for(int i = 0; i < LGraph<T>::n; ++i)
		InDegree[i] = 0; // 初始化InDegree數組
	for(int i = 0; i < LGraph<T>::n; ++i)
		for(ENode<T> *p = LGraph<T>::a[i]; p; p = p -> nxtArc) // 檢查以頂點i為尾的全部鄰接點
			InDegree[p -> adjVex]++; // 將頂點i的鄰接點p -> adjVex的入度加1
}
int main(int argc, char const *argv[])
{
	ExtLgraph<int> lg(9);
	int w = 10; lg.Insert(0, 2, w); lg.Insert(0, 7, w);
	lg.Insert(2, 3, w); lg.Insert(3, 5, w);
	lg.Insert(3, 6, w); lg.Insert(4, 5, w);
	lg.Insert(7, 8, w); lg.Insert(8, 6, w);
	int *order = new int[9];
	lg.TopoSort(order);
	cout << endl;
	delete []order;
	return 0;
}

拓撲排序的實現_TopoSort