实现邻接矩阵和邻接表两种不同存储结构上实现图的基本运算, 在MGraph类中扩充添加DFS()和BFS()函数.
包括的运算: 插入一条边, 删除一条边, 查询边是否存在, 图的深度优先搜索和广度优先搜索.
广度优先搜索利用队列作为辅助的数据结构, 元素类型是树的结点.
实现代码:
#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, Duplicate, Failure, Success, NotPresent };
template <class T>
class SeqQueue
{
public:
SeqQueue(int mSize);
~SeqQueue() { delete []q; }
bool IsEmpty() const { return front == rear; } // front与rear相等时循环队列为空
bool IsFull() const { return (rear + 1) % maxSize == front; } // front与(rear + 1) % maxSize相等时循环队列满
bool Front(T &x) const;
bool EnQueue(T x);
bool DeQueue();
void Clear() { front = rear = 0; }
/* data */
private:
int front, rear, maxSize; // 队头元素 队尾元素 数组最大长度
T *q;
};
template <class T>
SeqQueue<T>::SeqQueue(int mSize)
{
maxSize = mSize;
q = new T[maxSize];
front = rear = 0;
}
template <class T>
bool SeqQueue<T>::Front(T &x) const
{
if(IsEmpty()) { // 空队列处理
cout << "SeqQueue is empty" << endl;
return false;
}
x = q[(front + 1) % maxSize];
return true;
}
template <class T>
bool SeqQueue<T>::EnQueue(T x)
{
if(IsFull()) { // 溢出处理
cout << "SeqQueue is full" << endl;
return false;
}
q[(rear = (rear + 1) % maxSize)] = x;
return true;
}
template <class T>
bool SeqQueue<T>::DeQueue()
{
if(IsEmpty()) { // 空队列处理
cout << "SeqQueue is empty" << endl;
return false;
}
front = (front + 1) % maxSize;
return true;
}
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 MGraph: public Graph<T>
{
public:
MGraph(int mSize, const T& noedg);
~MGraph();
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();
void DFS();
void BFS();
protected:
T **a;
T noEdge;
int n, e;
void DFS(int v, bool *vis);
void BFS(int v, bool *vis);
/* data */
};
template <class T>
void MGraph<T>::Output()
{
for(int i = 0; i < n; ++i) {
for(int j = 0; j < n; ++j)
if(a[i][j] == noEdge) cout << "NE ";
else cout << a[i][j] << " ";
cout << endl;
}
cout << endl << endl << endl;
}
template <class T>
MGraph<T>::MGraph(int mSize, const T &noedg)
{
n = mSize, e = 0, noEdge = noedg;
a = new T *[n];
for(int i = 0; i < n; ++i) {
a[i] = new T[n];
for(int j = 0; j < n; ++j)
a[i][j] = noEdge;
a[i][i] = 0;
}
}
template <class T>
MGraph<T>::~MGraph()
{
for(int i = 0; i < n; ++i)
delete []a[i];
delete []a;
}
template <class T>
bool MGraph<T>::Exist(int u, int v) const
{
if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v || a[u][v] == noEdge) return false;
return true;
}
template <class T>
ResultCode MGraph<T>::Insert(int u, int v, T &w)
{
if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v) return Failure;
if(a[u][v] != noEdge) return Duplicate;
a[u][v] = w;
e++;
return Success;
}
template <class T>
ResultCode MGraph<T>::Remove(int u, int v)
{
if(u < 0 || v < 0 || u > n - 1 || v > n - 1 || u == v) return Failure;
if(a[u][v] == noEdge) return NotPresent;
a[u][v] = noEdge;
e--;
return Success;
}
template <class T>
void MGraph<T>::DFS()
{
bool *vis = new bool[n];
memset(vis, false, n);
for(int i = 0; i < n; ++i)
if(!vis[i]) DFS(i, vis);
delete []vis;
}
template <class T>
void MGraph<T>::DFS(int v, bool *vis)
{
vis[v] = true;
cout << ' ' << v;
for(int i = 0; i < n; ++i)
if(a[v][i] != noEdge && a[v][i] != 0 && !vis[i]) DFS(i, vis);
}
template <class T>
void MGraph<T>::BFS()
{
bool *vis = new bool[n];
memset(vis, false, n);
for(int i = 0; i < n; ++i)
if(!vis[i]) BFS(i, vis);
delete []vis;
}
template <class T>
void MGraph<T>::BFS(int v, bool *vis)
{
SeqQueue<int> q(n);
vis[v] = true;
cout << ' ' << v;
q.EnQueue(v);
while(!q.IsEmpty()) {
q.Front(v);
q.DeQueue();
for(int i = 0; i < n; ++i)
if(a[v][i] != noEdge && a[v][i] != 0 && !vis[i]) {
vis[i] = true;
cout << ' ' << i;
q.EnQueue(i);
}
}
}
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 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;
}
int main(int argc, char const *argv[])
{
int n, g;
cout << "请输入元素的个数: ";
cin >> n;
MGraph<int> A(n, INF);
LGraph<int> B(n);
cout << "请输入边的条数: ";
cin >> g;
int *a = new int[g];
int *b = new int[g];
int *w = new int[g];
for(int i = 0; i < g; ++i)
{
cout << "请输入边及权值: ";
cin>> a[i] >> b[i] >> w[i];
A.Insert(a[i], b[i], w[i]);
B.Insert(a[i], b[i], w[i]);
}
cout << "该图的深度优先遍历为:" << endl;
A.DFS();
cout << endl;
cout << "该图的广度优先遍历为:" << endl;
A.BFS();
cout << endl;
cout << "请输入要搜索的边: ";
int c, d;
cin >> c >> d;
if(A.Exist(c, d)) cout << "邻接矩阵中该边存在!" << endl;
else cout << "邻接矩阵中该边不存在!" << endl;
if(B.Exist(c, d)) cout << "邻接表中该边存在!" << endl;
else cout << "邻接表中该边不存在!" << endl;
cout << "请输入要删除的边: ";
int e, f;
cin>> e >> f;
if(A.Remove(e, f) == Success) cout << "邻接矩阵中删除该边成功!" << endl;
else if(A.Remove(e, f) == NotPresent) cout<<"邻接矩阵中该边不存在!"<<endl;
else cout<<"输入错误!"<<endl;
if(B.Remove(e, f) == Success) cout << "邻接表中删除该边成功!" << endl;
else if(B.Remove(e, f) == NotPresent) cout << "邻接表中该边不存在!" << endl;
else cout << "邻接表中输入错误!" << endl;
cout << "删除该边后该图的深度优先遍历为:" << endl;
A.DFS();
cout << endl;
cout << "删除该边后该图的广度优先遍历为:" << endl;
A.BFS();
cout << endl;
return 0;
}