有向图(7)--再谈可达性&&有向图总结

顶点对的可达性。给定一幅有向图，回答“是否存在一条从一个给定的顶点v到另一个给定的顶点w的路径？”等类似问题。

可以使用深度搜索来实现，无论对于稀疏还是稠密的图，它都是理想的解决方案，但它不适用于在实际应用中可能遇到的大型有向图，因为所需的空间和V²成正比，所需时间和V(V+E)成正比。

-TransitiveClosure.h

#ifndef __TRANSITIVE_CLOSURE_H__
#define __TRANSITIVE_CLOSURE_H__

#include "Digraph.h"
#include "DirectedDFS.h"

class TransitiveClosure {
private:
DirectedDFS* all;

public:
TransitiveClosure(Digraph G);
<span style="white-space:pre">	</span>~TransitiveClosure() { delete[] all; }
bool reachable(int v, int w) { return all[v].isMarked(w); }

};

TransitiveClosure::TransitiveClosure(Digraph G) {
all = new DirectedDFS[G.getV()];
for (int v = 0; v < G.getV(); ++v)
all[v].createDFS(G, v);
}

#endif

这里我稍微对之前的DirectedDFS做了修改，还有给Digraph的构造函数添加了默认值，因为new的时候只能调用默认构造函数，所以写了新的函数来重新构造bool* marked

-DirectedDFS.h

#ifndef __DIRECTED_DFS_H__
#define __DIRECTED_DFS_H__

#include "Digraph.h"

// 解决单点可达性或者多点可达性
class DirectedDFS {
private:
bool* marked;

public:
DirectedDFS(const Digraph& G = Digraph(), int s = 0);
DirectedDFS(const Digraph& G, std::list<int> ilst);
~DirectedDFS() { delete[] marked; }

bool isMarked(int v)const { return marked[v]; }

void createDFS(Digraph G, int s);	// 为了在TransitiveClosure中重新构造

private:
void dfs(const Digraph& G, int v);
};

// constructor
DirectedDFS::DirectedDFS(const Digraph& G, int s) {
if (0 == G.getV()) return;
marked = new bool[G.getV()];
for (int i = 0; i < G.getV(); ++i)
marked[i] = false;
dfs(G, s);
}

// constructor
DirectedDFS::DirectedDFS(const Digraph& G, std::list<int> ilst) {
marked = new bool[G.getV()];
for (int i = 0; i < G.getV(); ++i)
marked[i] = false;
for (int v : ilst) {
if (!marked[v])
dfs(G, v);
}
}

void DirectedDFS::dfs(const Digraph& G, int v) {
marked[v] = true;
for (int w : G.getAdj(v)) {
if (!marked[w])
dfs(G, w);
}
}

// 重新构造DirectedDFS，和构造函数差不多了
void DirectedDFS::createDFS(Digraph G, int s) {
if(NULL == marked) delete[] marked;
marked = new bool[G.getV()];
for (int i = 0; i < G.getV(); ++i)
marked[i] = false;
dfs(G, s);
}

#endif

测试用例 -main.cpp

#include "TransitiveClosure.h"
#include "Digraph.h"
#include <iostream>
using namespace std;

int main()
{
int vNum, eNum;
cin >> vNum >> eNum;
Digraph G(vNum);

int v, w;
for (int i = 0; i < eNum; ++i) {
cin >> v >> w;
G.addEdge(v, w);
}

TransitiveClosure tc(G);

int a, b;
for (;;) {
cout << "输入起点：";
cin >> a;
cout << "输入终点：";
cin >> b;
cout << "                      "
<< a << " 到 " << b << "是";
if (!tc.reachable(a, b))
cout << "不";
cout << "可达的" << endl;
}

return 0;
}

有向图总结