深度优先实现 一
深度优先算法
- 原料：class LinkStack
; 步骤：
- 将起始顶点压入栈中
- 弹出栈顶顶点 v， 判断是否已经标记（比较：转2； 未标记：转3）
- 标记顶点， 并将顶点 v 的邻接顶点压入栈中
- 判断栈是否为空（非空：转2； 空：结束）
深度优先算法示例
编程实验：深度优先算法
文件：Graph.h
#ifndef GRAPH_H
#define GRAPH_H
#include "Object.h"
#include "SharedPointer.h"
#include "DynamicArray.h"
#include "LinkQueue.h"
#include "LinkStack.h"
namespace DTLib
{
template
struct Edge : public Object
{
int b;
int e;
E data;
Edge(int i=-1, int j=-1) : b(i), e(j)
{
}
Edge(int i, int j, const E &value) : b(i), e(j), data(value)
{
}
bool operator == (const Edge &obj)
{
return (b == obj.b) && (e == obj.e);
}
bool operator != (const Edge &obj)
{
return !(*this == obj);
}
};
template
class Graph : public Object
{
public:
virtual V getVertex(int i) const = 0;
virtual bool getVertex(int i, V &value) const = 0;
virtual bool setVertex(int i, const V &value) = 0;
virtual SharedPointer> getAdjacent(int i) const = 0;
virtual E getEdge(int i, int j) const = 0;
virtual bool getEdge(int i, int j, E &value) const = 0;
virtual bool setEdge(int i, int j, const E &value) = 0;
virtual bool removeEdge(int i, int j) = 0;
virtual int vCount() const = 0;
virtual int eCount() = 0;
virtual int OD(int i) = 0;
virtual int ID(int i) = 0;
virtual int TD(int i)
{
return OD(i) + ID(i);
}
SharedPointer> BFS(int i)
{
DynamicArray *ret = nullptr;
if ((0 <= i) && (i < vCount()))
{
LinkQueue q;
LinkQueue r;
DynamicArray visited(vCount());
for (int j=0; j 0)
{
int v = q.front();
q.remove();
if (!visited[v])
{
SharedPointer> aj = getAdjacent(v);
for (int j=0; jlength(); ++j)
{
q.add((*aj)[j]);
}
r.add(v);
visited[v] = true;
}
}
ret = toArray(r);
}
else
{
THROW_EXCEPTION(InvalidParameterExcetion, "Parameter i is invalid ...");
}
return ret;
}
SharedPointer> DFS(int i)
{
DynamicArray *ret = nullptr;
if ((0 <= i) && (i < vCount()))
{
LinkStack s;
LinkQueue r;
DynamicArray visited(vCount());
for (int j=0; j 0)
{
int v = s.top();
s.pop();
if (!visited[v])
{
SharedPointer> aj = getAdjacent(v);
for (int j=aj->length()-1; j>=0; --j)
{
s.push((*aj)[j]);
}
r.add(v);
visited[v] = true;
}
}
ret = toArray(r);
}
else
{
THROW_EXCEPTION(InvalidParameterExcetion, "Parameter i is invalid ...");
}
return ret;
}
protected:
template
DynamicArray* toArray(LinkQueue &queue)
{
DynamicArray *ret = new DynamicArray(queue.length());
if (ret != nullptr)
{
for (int i=0; ilength(); ++i, queue.remove())
{
ret->set(i, queue.front());
}
}
else
{
THROW_EXCEPTION(NoEnoughMemoryException, "No memory to create ret obj ...");
}
return ret;
}
};
}
#endif // GRAPH_H 文件：main.cpp
#include
#include "MatrixGraph.h"
using namespace std;
using namespace DTLib;
int main()
{
MatrixGraph<9, char, int> g;
const char* VD = "ABEDCGFHI";
for(int i=0; i<9; i++)
{
g.setVertex(0, VD[i]);
}
g.setEdge(0, 1, 0);
g.setEdge(1, 0, 0);
g.setEdge(0, 3, 0);
g.setEdge(3, 0, 0);
g.setEdge(0, 4, 0);
g.setEdge(4, 0, 0);
g.setEdge(1, 2, 0);
g.setEdge(2, 1, 0);
g.setEdge(1, 4, 0);
g.setEdge(4, 1, 0);
g.setEdge(2, 5, 0);
g.setEdge(5, 2, 0);
g.setEdge(3, 6, 0);
g.setEdge(6, 3, 0);
g.setEdge(4, 6, 0);
g.setEdge(6, 4, 0);
g.setEdge(6, 7, 0);
g.setEdge(7, 6, 0);
g.setEdge(7, 8, 0);
g.setEdge(8, 7, 0);
SharedPointer> sa = g.DFS(0);
for (int i=0; ilength(); ++i)
{
cout << (*sa)[i] << " ";
}
cout << endl;
return 0;
}; 输出：
0 1 2 5 4 6 3 7 8深度优先实现 二
问题： 如何使用二叉树先序遍历的思想遍历图？
递归深度优先
G = v0 + G'
DFG(G) = visited(v0) + DFS(G')
(G'不为空，且 v0 到 G' 有连接)
定义功能： DFS(graph, vex)
- 以顶点 vex 为起始顶点深度优先遍历 graph
编程实验：递归版深度优先算法
文件：main.cpp
#include
#include "BTreeNode.h"
#include "ListGraph.h"
#include "MatrixGraph.h"
using namespace std;
using namespace DTLib;
template
void DFP(Graph &graph, int i, DynamicArray &visited)
{
if (!visited[i])
{
cout << i << " ";
visited[i] = true;
SharedPointer> aj = graph.getAdjacent(i);
for (int j=0; jlength(); ++j)
{
DFP(graph, (*aj)[j], visited);
}
}
}
template
void DFP(Graph &graph, int i)
{
if ((0 <= i) && (i < graph.vCount()))
{
DynamicArray visited(graph.vCount());
for (int j=0; j g;
const char* VD = "ABEDCGFHI";
for(int i=0; i<9; i++)
{
g.setVertex(0, VD[i]);
}
g.setEdge(0, 1, 0);
g.setEdge(1, 0, 0);
g.setEdge(0, 3, 0);
g.setEdge(3, 0, 0);
g.setEdge(0, 4, 0);
g.setEdge(4, 0, 0);
g.setEdge(1, 2, 0);
g.setEdge(2, 1, 0);
g.setEdge(1, 4, 0);
g.setEdge(4, 1, 0);
g.setEdge(2, 5, 0);
g.setEdge(5, 2, 0);
g.setEdge(3, 6, 0);
g.setEdge(6, 3, 0);
g.setEdge(4, 6, 0);
g.setEdge(6, 4, 0);
g.setEdge(6, 7, 0);
g.setEdge(7, 6, 0);
g.setEdge(7, 8, 0);
g.setEdge(8, 7, 0);
SharedPointer< Array > sa = g.DFS(0);
for(int i=0; ilength(); i++)
{
cout << (*sa)[i] << " ";
}
cout << endl;
DFP(g, 0);
return 0;
} 输出：
0 1 2 5 4 6 3 7 8
0 1 2 5 4 6 3 7 8小结
- 深度优先按照"先序遍历的方式"对顶点进行访问
- 深度优先算法的核心是栈的使用
- 深度优先和广度优先的唯一不同在于栈或队列的使用
- 深度优先算法可以使用递归的方式实现
以上内容整理于狄泰软件学院系列课程，请大家保护原创！
[添加递归版深度优先算法]文件：Grap.h
#ifndef GRAPH_H
#define GRAPH_H
#include "Object.h"
#include "SharedPointer.h"
#include "DynamicArray.h"
#include "LinkQueue.h"
#include "LinkStack.h"
namespace DTLib
{
template
struct Edge : public Object
{
int b;
int e;
E data;
Edge(int i=-1, int j=-1) : b(i), e(j)
{
}
Edge(int i, int j, const E &value) : b(i), e(j), data(value)
{
}
bool operator == (const Edge &obj)
{
return (b == obj.b) && (e == obj.e);
}
bool operator != (const Edge &obj)
{
return !(*this == obj);
}
};
template
class Graph : public Object
{
public:
virtual V getVertex(int i) const = 0;
virtual bool getVertex(int i, V &value) const = 0;
virtual bool setVertex(int i, const V &value) = 0;
virtual SharedPointer> getAdjacent(int i) const = 0;
virtual E getEdge(int i, int j) const = 0;
virtual bool getEdge(int i, int j, E &value) const = 0;
virtual bool setEdge(int i, int j, const E &value) = 0;
virtual bool removeEdge(int i, int j) = 0;
virtual int vCount() const = 0;
virtual int eCount() = 0;
virtual int OD(int i) = 0;
virtual int ID(int i) = 0;
virtual int TD(int i)
{
return OD(i) + ID(i);
}
SharedPointer> BFS(int i)
{
DynamicArray *ret = nullptr;
if ((0 <= i) && (i < vCount()))
{
LinkQueue q;
LinkQueue r;
DynamicArray visited(vCount());
for (int j=0; j 0)
{
int v = q.front();
q.remove();
if (!visited[v])
{
SharedPointer> aj = getAdjacent(v);
for (int j=0; jlength(); ++j)
{
q.add((*aj)[j]);
}
r.add(v);
visited[v] = true;
}
}
ret = toArray(r);
}
else
{
THROW_EXCEPTION(InvalidParameterExcetion, "Parameter i is invalid ...");
}
return ret;
}
#ifdef DFS_R
SharedPointer> DFS(int i) // 递归版深度优先遍历
{
DynamicArray *ret = nullptr;
if ((0 <= i) && (i < vCount()))
{
LinkQueue r;
DynamicArray visited(vCount());
for (int j=0; j> DFS(int i)
{
DynamicArray *ret = nullptr;
if ((0 <= i) && (i < vCount()))
{
LinkStack s;
LinkQueue r;
DynamicArray visited(vCount());
for (int j=0; j 0)
{
int v = s.top();
s.pop();
if (!visited[v])
{
SharedPointer> aj = getAdjacent(v);
for (int j=aj->length()-1; j>=0; --j)
{
s.push((*aj)[j]);
}
r.add(v);
visited[v] = true;
}
}
ret = toArray(r);
}
else
{
THROW_EXCEPTION(InvalidParameterExcetion, "Parameter i is invalid ...");
}
return ret;
}
#endif
protected:
template
DynamicArray* toArray(LinkQueue &queue)
{
DynamicArray *ret = new DynamicArray(queue.length());
if (ret != nullptr)
{
for (int i=0; ilength(); ++i, queue.remove())
{
ret->set(i, queue.front());
}
}
else
{
THROW_EXCEPTION(NoEnoughMemoryException, "No memory to create ret obj ...");
}
return ret;
}
#ifdef DFS_R
void DFP(int i, DynamicArray &visited, LinkQueue& queue)
{
if (!visited[i])
{
queue.add(i);
visited[i] = true;
SharedPointer> aj = getAdjacent(i);
for (int j=0; jlength(); ++j)
{
DFP((*aj)[j], visited, queue);
}
}
}
#endif
};
}
#endif // GRAPH_H