数据结构上机实验

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01 约瑟夫环问题

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#include<stdio.h>
#include<stdlib.h>

typedef struct node
{
	int data;
	struct node *next;
}node;
node *creat(node *head, int n)
{
	int i = 1;
	node *s, *p = head;
	while (i <= n) {
		s = (node *)malloc(sizeof(node));
		s->data = i++;
		p->next = s;
		p = p->next;
	}
	p->next = head->next;
	free(head);
	return p->next;
}
int main()
{
	int i, n, m;
	node *head, *newstart, *h, *t;
	head = (node *)malloc(sizeof(node));
	printf("请输入数据长度n，数据间隔m\n");
	scanf("%d %d", &n, &m);
	newstart = creat(head, n);
	h = newstart;
	while (h != h->next)
	{
		for (i = 1; i<m; i++) {
			h = h->next;
		}
		t = h->next;
		printf("%d->\n", h->next->data);
		h->next = t->next;
		h = t->next;
		free(t);
	}
	printf("%d\n", h->data);
	return 0;
}


Markdown
02 一元多项式相加

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#include<iostream>
using namespace std;
 struct Node
{
	double coe;//系数
	int exp;//指数
	Node *next;
};
//创建链表，节点数为一元多项式的项数
void CreatPoly(Node *&head,int n)//写成*head报错 为什么？
{
	head=(Node *)new Node;
	head->coe=0;
	head->exp=0;
	head->next=NULL;//初始化头节点
	Node *p=head;
	for(int i=0;i<n;i++){
		p->next=(Node *)new Node;//尾插法建表
		p=p->next;
		cin>>p->coe>>p->exp;
		p->next=NULL;
	}
}
//打印表
void ShowPoly(Node *head)
{
	if(head->next == NULL)
	putchar('0');
	else{
		for(Node *p=head->next;p!=NULL;p=p->next){//遍历所有节点
			if(p!=head->next&&p->coe>0)putchar('+');
			if(p->coe==1){
				if(p->exp==0)putchar('1');
			}
			if(p->coe==1&&p->exp==0)putchar('1');
			else if(p->coe==-1)putchar('-');
			else  cout<<p->coe;
			//指数为0，1时特殊处理
			switch(p->exp){
				case 0:break;
				case 1:putchar('X');break;
				default:
				p->exp<0?printf("x^(%d)",p->exp):printf("x^%d",p->exp);break;//看不懂
				break;
			}

		}
	}
	cout<<endl;
}
char comp(int a,int b)
{
	if(a>b)return '>';
	if(a<b)return '<';
	return '=';
}
//相加
void AddPoly(Node *&pA, Node *&pB) // 传进两个链表的头指针
{
Node *ha = pA;
Node *hb = pB;
Node *qa = ha->next; // ha, hb分别跟在qa, qb的后一位置
Node *qb = hb->next; // qa, qb分别指向Pa, Pb中当前比较元素
while(qa && qb)
{
double sum = 0;
int a = qa->exp;
int b = qb->exp;
switch( comp(a, b) ) {
case '<':
ha = qa;
qa = qa->next; // 非ha = ha->next;
break;
case '=':
sum = qa->coe + qb->coe;
if(sum != 0.0) {
qa->coe = sum;
ha = qa;
}
else {
if(ha->next != qa)
cout << "Error: ha->next != qa" << endl;
ha->next = ha->next->next; // 删除和为0的结点，ha不变，还在qa后一位置

}
if(hb->next != qb)
cout << "Error: hb->next != qb" << endl;
hb->next = hb->next->next;

qb = hb->next;
qa = ha->next;
break;
case '>':
hb->next = hb->next->next; // 删除qb指向的结点
qb->next = ha->next; // 将qb插入ha后qa前
ha->next = qb;
qb = hb->next; // not qb = ha->next
ha = ha->next;
break;
default:
cout << "Error!" << endl;
break;
}
}
if(qb)
ha->next = qb;

}

int  main()
{
	Node *A=NULL;
	Node *B=NULL;
	int countA;
	int countB;
	cout<<"输入A的项数"<<endl;cin>>countA;
	cout<<"输入B的项数"<<endl;cin>>countB;
	CreatPoly(A,countA);
	CreatPoly(B,countB);
	cout<<"A="<<endl;
	ShowPoly(A);
	cout<<"B="<<endl;
	ShowPoly(B);
	AddPoly(A,B);
	cout<<"A+B="<<endl;
	ShowPoly(A);
	delete(A);

}

03 栈 正则表达式运算

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#include<stdio.h>
#include<stdlib.h>
#include<iostream>
using namespace std;
#define maxsize 1000
//中则表达式str转换为后缀表达式
void trans(char str[], char exp[])
{
	struct
	{
		char data[maxsize];
		int top;
	}op;
	char ch;
	int i = 0, t = 0;
	op.top = -1;
	ch = str[i];
	i++;
	while (ch != '\0')
	{
		switch (ch)
		{
		case '(':
			op.top++;
			op.data[op.top] = ch;
			break;
		case ')':
			while (op.data[op.top] != '(')
			{
				exp[t] = op.data[op.top];
				op.top--;
				t++;

			}
			op.top--;
			break;
		case '+':
		case '-':
			while (op.top != -1 && op.data[op.top] != '(')
			{
				exp[t] = op.data[op.top];
				op.top--;
				t++;
			}
			op.top--;
			op.data[op.top] = ch;
			break;
		case '*':
		case '/':
			while (op.data[op.top] == '*' || op.data[op.top] == '/')
			{
				exp[t] = op.data[op.top];
				op.top--;
				t++;
			}
			op.top++;
			op.data[op.top] = ch;
			break;
		case ' ':
			break;
		default:
			while (ch >= '0'&&ch <= '9')
			{
				exp[t] = ch;
				t++;
				ch = str[i];
				i++;
			}
			i--;
			exp[t] = '#';
			t++;
		}
		ch = str[i];
		i++;
	}
	while (op.top != -1)
	{
		exp[t] = op.data[op.top];
		t++;
		op.top--;
	}
	exp[t] = '\0';
}
//后缀表达式的求值
float compvalue(char exp[])
{
	struct
	{
		float data[maxsize];
		int top;
	}st;
	float d;
	char ch;
	int t = 0;
	st.top = -1;
	ch = exp[t];
	t++;
	while (ch != '\0')
	{
		switch (ch)
		{
		case '+':
			st.data[st.top - 1] = st.data[st.top - 1] + st.data[st.top];
			st.top--;
			break;
		case '-':
			st.data[st.top - 1] = st.data[st.top - 1] - st.data[st.top];
			st.top--;
			break;
		case '*':
			st.data[st.top - 1] = st.data[st.top - 1] * st.data[st.top];
			st.top--;
			break;
		case '/':
			if (st.data[st.top] != 0)
				st.data[st.top - 1] = st.data[st.top - 1] / st.data[st.top];
			else
			{
				printf("\nerror! \n");
				exit(0);
			}
			st.top--;
			break;
		default: d = 0;
			while (ch >= '0'&&ch <= '9')
			{
				d = 10 * d + ch - '0';
				ch = exp[t];
				t++;
			}
			st.top++;
			st.data[st.top] = d;
		}
		ch = exp[t];
		t++;
	}
	return st.data[st.top];
}

int main()
{
	char str[maxsize], exps[maxsize];

	printf("please input a expressions,just include +,-,*,/and integers:");
	cin >> str;//输入一个中缀表达式
	printf("old is: %s\n", str);  trans(str, exps);//转换
	printf("after is: %s\n", exps);
	printf("the result is: %g\n", compvalue(exps)); //求值并输出
	return 0;
}

![])(http://i1.piimg.com/567571/a11fae0ace0176df.png)

04 车厢排序问题

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#include <iostream>  
using namespace std;

template<class T>
class My_queue;

template<class T>
class Node
{
private:
	T data;
	Node<T> *next;
public:
	Node()
	{
		next = 0;
	}
	Node(T d)
	{
		data = d;
		next = 0;
	}
	friend My_queue<T>;
};

template<class T>
class My_queue
{
private:
	Node<T> *tail;
public:
	My_queue()
	{
		tail = new Node<T>();
		tail->next = tail;
	}

	bool empty()
	{
		return (tail->next == tail);
	}

	void push(T d)
	{
		Node<T> *p = new Node<T>(d);
		p->next = tail->next;
		tail->next = p;
		tail = p;
	}

	T front()
	{
		if (empty())
		{
			cout << "queue is empty!" << endl;
			exit(0);
		}
		Node<T> *p = tail->next;
		T data = p->next->data;
		return data;
	}

	T back()
	{
		if (empty())
		{
			cout << "queue is empty!" << endl;
			exit(0);
		}
		T data = tail->data;
		return data;
	}

	void pop()
	{
		Node<T> *p = tail->next;
		Node<T> *q = p->next;
		p->next = q->next;
		if (q == tail)
			tail = p;
		delete q;
	}

};

void OutPut(int& minH, int& minQ, My_queue<int> H[], int k, int n);
bool Hold(int c, int& minH, int& minQ, My_queue<int> H[], int k);

bool Rail_Road(int p[], int n, int k)
{
	//k个缓冲轨，车厢初始排序为p[1...n]  

	//创建与缓冲轨对应的队列  
	My_queue<int> *H;
	H = new My_queue<int>[k];

	int NowOut = 1; //下一次要出轨的车厢  
	int minH = n + 1; //缓冲轨中编号最小的车厢  
	int minQ = k; //编号最小的车厢所在缓冲轨的编号  

				  //车厢重排序  
	for (int i = 0; i<n; i++)
	{
		if (p[i] == NowOut)
		{
			cout << "Move car " << p[i] << " from input to output" << endl;
			NowOut++;

			//从缓冲轨中输出  
			while (minH == NowOut)
			{
				OutPut(minH, minQ, H, k, n);
				NowOut++;
				if (NowOut == n + 1) //输出全部车厢后返回  
					return true;
			}
		}
		else
		{
			//将p[i]放入某个缓冲轨  
			if (!Hold(p[i], minH, minQ, H, k))
				return false;
		}
	}
	return true;
}

void OutPut(int& minH, int& minQ, My_queue<int> H[], int k, int n)
{
	//该函数实现把一节车厢从缓冲轨送至出轨处  
	//同时修改minH minQ的值  

	int c;

	//从队列中pop掉编号最小的车厢minH  
	c = H[minQ].front();
	H[minQ].pop();

	cout << "Move car " << c << " from holding queue " << minQ + 1 << " to output " << endl;

	//检查所有队列，搜索新的minH minQ  
	minH = n + 1;

	for (int i = 0; i<k; i++)
		if ((!H[i].empty()) && (H[i].front()<minH))
		{
			minH = H[i].front();
			minQ = i;
		}

}

bool Hold(int c, int& minH, int& minQ, My_queue<int> H[], int k)
{
	//该函数是将车厢c放入缓冲轨中  

	//为车厢c寻找最优缓冲轨  
	int BestQueue = k;//初始化缓冲轨的编号  
	int BestLast = 0; //最优缓冲轨的队尾车厢编号  

	int x;

	//扫描缓冲轨  
	for (int i = 0; i<k; i++)
	{
		if (!H[i].empty())
		{
			x = H[i].back();
			if (c>x && x>BestLast)
			{
				BestLast = x;
				BestQueue = i;
			}
		}
		else
		{
			//H[i]为空时  
			if (BestQueue == k)
				BestQueue = i;
		}
	}

	if (BestQueue == k) //没有可用的缓冲轨  
		return false;

	H[BestQueue].push(c);
	cout << "Move car " << c << " from input to holding queue " << BestQueue + 1 << endl;

	//必要时修改minH和minS  
	if (c<minH)
	{
		minH = c;
		minQ = BestQueue;
	}

	return true;
}
int main()
{
	int p[9] = { 3,6,9,2,4,7,1,8,5 };
	if (Rail_Road(p, 9, 3))
		cout << "车厢重排序成功" << endl;
	else
		cout << "车厢重排序失败" << endl;
	getchar();



}


05 三元组实现稀疏矩阵的转置

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#include<iostream>
using namespace std;

struct node{
	int r;//行标
	int c;//列标
	double dat;//数据

};
class triple
{
private:
	int row;//行数
	int col;//列数
	int num;//非零个数
	node *ptr;//存放数组的首地址
public:
	triple(int co,int ro,int nu):col(co),row(ro),num(nu)
	{
		ptr=new node[num];//分配num，盛放num个元素
		cout<<"请输入"<<num<<"个三元组元素\n"<<"格式为：2 3 6.7\n其中2为行标，3为列标，6.7为数据元素"<<endl;
		for(int i=0;i<num;i++)
		{
			cin>>ptr[i].r;
			cin>>ptr[i].c;
			cin>>ptr[i].dat;

		}
	}
	~triple(){delete[]ptr;}

void print()
{
	int flag=ptr[0].r;
	cout<<"第"<<flag<<"行元素为：";
	for(int i=0;i<num;i++)
	{
		if(ptr[i].r!=flag)
		{
			cout<<"\n";
			flag=ptr[i].r;
			cout<<endl;
			cout<<"第"<<flag<<"行元素为：";
		}
		cout<<"("<<ptr[i].r<<","<<ptr[i].c<<","<<ptr[i].dat<<")";
	}
}

void transpose()
{
	int flag=0;
	for(int i=1;i<=col;i++)
	{
		for(int j=0;j<num;j++)
		{
			if(ptr[j].c==i)
			{
				if(flag!=ptr[j].c)
				{
					flag=ptr[j].c;
					cout<<"\n第"<<ptr[j].c<<"行为：";
				}
      cout<<"("<<ptr[j].c<<","<<ptr[j].r<<","<<ptr[j].dat<<")";
			}
		}
	}
}
};



int main()
{
   cout<<"请输入数组的行列和元素个数:\n";
	 int a[3];
	 for(int i=0;i<3;i++)
	 {
		 cin>>a[i];
	 }
	 triple t(a[0],a[1],a[2]);
	 t.print();//输出原矩阵
	 cout<<"转制后的矩阵为:\n";
	 t.transpose();
}

06 二叉树后序遍历的非递归算法

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#define _CRT_SECURE_NO_DEPRECATE
//转载请标明出处，原文地址：http://blog.csdn.net/hackbuteer1/article/details/6583988
#include<iostream>  
#include<queue>  
#include<stack>  
using namespace std;

//二叉树结点的描述  
typedef struct BiTNode
{
	char data;
	struct BiTNode *lchild, *rchild;      //左右孩子  
}BiTNode, *BiTree;

//按先序遍历创建二叉树  
//BiTree *CreateBiTree()     //返回结点指针类型  
//void CreateBiTree(BiTree &root)      //引用类型的参数  
void CreateBiTree(BiTNode **root)    //二级指针作为函数参数  
{
	char ch; //要插入的数据  
	scanf("\n%c", &ch);
	//cin>>ch;  
	if (ch == '#')
		*root = NULL;
	else
	{
		*root = (BiTNode *)malloc(sizeof(BiTNode));
		(*root)->data = ch;
		printf("请输入%c的左孩子：", ch);
		CreateBiTree(&((*root)->lchild));
		printf("请输入%c的右孩子：", ch);
		CreateBiTree(&((*root)->rchild));
	}
}

//前序遍历的算法程序  
void PreOrder(BiTNode *root)
{
	if (root == NULL)
		return;
	printf("%c ", root->data); //输出数据  
	PreOrder(root->lchild); //递归调用，前序遍历左子树  
	PreOrder(root->rchild); //递归调用，前序遍历右子树  
}

//中序遍历的算法程序  
void InOrder(BiTNode *root)
{
	if (root == NULL)
		return;
	InOrder(root->lchild); //递归调用，前序遍历左子树  
	printf("%c ", root->data); //输出数据  
	InOrder(root->rchild); //递归调用，前序遍历右子树  
}

//后序遍历的算法程序  
void PostOrder(BiTNode *root)
{
	if (root == NULL)
		return;
	PostOrder(root->lchild);      //递归调用，前序遍历左子树  
	PostOrder(root->rchild);      //递归调用，前序遍历右子树  
	printf("%c ", root->data);    //输出数据    
}

/*
二叉树的非递归前序遍历，前序遍历思想：先让根进栈，只要栈不为空，就可以做弹出操作，
每次弹出一个结点，记得把它的左右结点都进栈，记得右子树先进栈，这样可以保证右子树在栈中总处于左子树的下面。
*/
void PreOrder_Nonrecursive(BiTree T)     //先序遍历的非递归    
{
	if (!T)
		return;

	stack<BiTree> s;
	s.push(T);

	while (!s.empty())
	{
		BiTree temp = s.top();
		cout << temp->data << " ";
		s.pop();
		if (temp->rchild)
			s.push(temp->rchild);
		if (temp->lchild)
			s.push(temp->lchild);
	}
}

void PreOrder_Nonrecursive1(BiTree T)     //先序遍历的非递归
{
	if (!T)
		return;
	stack<BiTree> s;
	BiTree curr = T;
	while (curr != NULL || !s.empty())
	{
		while (curr != NULL)
		{
			cout << curr->data << "  ";
			s.push(curr);
			curr = curr->lchild;
		}
		if (!s.empty())
		{
			curr = s.top();
			s.pop();
			curr = curr->rchild;
		}
	}
}

void PreOrder_Nonrecursive2(BiTree T)     //先序遍历的非递归  
{
	if (!T)
		return;

	stack<BiTree> s;
	while (T)          // 左子树上的节点全部压入到栈中  
	{
		s.push(T);
		cout << T->data << "  ";
		T = T->lchild;
	}

	while (!s.empty())
	{
		BiTree temp = s.top()->rchild;  // 栈顶元素的右子树  
		s.pop();                        // 弹出栈顶元素  
		while (temp)          // 栈顶元素存在右子树，则对右子树同样遍历到最下方  
		{
			cout << temp->data << "  ";
			s.push(temp);
			temp = temp->lchild;
		}
	}
}

void InOrderTraverse1(BiTree T)   // 中序遍历的非递归  
{
	if (!T)
		return;
	BiTree curr = T;    // 指向当前要检查的节点  
	stack<BiTree> s;
	while (curr != NULL || !s.empty())
	{
		while (curr != NULL)
		{
			s.push(curr);
			curr = curr->lchild;
		}//while
		if (!s.empty())
		{
			curr = s.top();
			s.pop();
			cout << curr->data << "  ";
			curr = curr->rchild;
		}
	}
}

void InOrderTraverse(BiTree T)   // 中序遍历的非递归  
{
	if (!T)
		return;
	stack<BiTree> s;
	BiTree curr = T->lchild;    // 指向当前要检查的节点  
	s.push(T);
	while (curr != NULL || !s.empty())
	{
		while (curr != NULL)    // 一直向左走  
		{
			s.push(curr);
			curr = curr->lchild;
		}
		curr = s.top();
		s.pop();
		cout << curr->data << "  ";
		curr = curr->rchild;
	}
}

void PostOrder_Nonrecursive1(BiTree T)  // 后序遍历的非递归    
{
	stack<BiTree> S;
	BiTree curr = T;           // 指向当前要检查的节点  
	BiTree previsited = NULL;    // 指向前一个被访问的节点  
	while (curr != NULL || !S.empty())  // 栈空时结束    
	{
		while (curr != NULL)            // 一直向左走直到为空  
		{
			S.push(curr);
			curr = curr->lchild;
		}
		curr = S.top();
		// 当前节点的右孩子如果为空或者已经被访问，则访问当前节点  
		if (curr->rchild == NULL || curr->rchild == previsited)
		{
			cout << curr->data << "  ";
			previsited = curr;
			S.pop();
			curr = NULL;
		}
		else
			curr = curr->rchild;      // 否则访问右孩子  
	}
}

void PostOrder_Nonrecursive(BiTree T)  // 后序遍历的非递归     双栈法  
{
	stack<BiTree> s1, s2;
	BiTree curr;           // 指向当前要检查的节点  
	s1.push(T);
	while (!s1.empty())  // 栈空时结束    
	{
		curr = s1.top();
		s1.pop();
		s2.push(curr);
		if (curr->lchild)
			s1.push(curr->lchild);
		if (curr->rchild)
			s1.push(curr->rchild);
	}
	while (!s2.empty())
	{
		printf("%c ", s2.top()->data);
		s2.pop();
	}
}


int visit(BiTree T)
{
	if (T)
	{
		printf("%c ", T->data);
		return 1;
	}
	else
		return 0;
}

void LeverTraverse(BiTree T)   //方法一、非递归层次遍历二叉树   
{
	queue <BiTree> Q;
	BiTree p;
	p = T;
	if (visit(p) == 1)
		Q.push(p);
	while (!Q.empty())
	{
		p = Q.front();
		Q.pop();
		if (visit(p->lchild) == 1)
			Q.push(p->lchild);
		if (visit(p->rchild) == 1)
			Q.push(p->rchild);
	}
}
void LevelOrder(BiTree BT)     //方法二、非递归层次遍历二叉树   
{
	BiTNode *queue[10];//定义队列有十个空间  
	if (BT == NULL)
		return;
	int front, rear;
	front = rear = 0;
	queue[rear++] = BT;
	while (front != rear)//如果队尾指针不等于对头指针时  
	{
		cout << queue[front]->data << "  ";  //输出遍历结果  
		if (queue[front]->lchild != NULL)  //将队首结点的左孩子指针入队列  
		{
			queue[rear] = queue[front]->lchild;
			rear++;    //队尾指针后移一位  
		}
		if (queue[front]->rchild != NULL)
		{
			queue[rear] = queue[front]->rchild;    //将队首结点的右孩子指针入队列  
			rear++;   //队尾指针后移一位  
		}
		front++;    //对头指针后移一位  
	}
}

int depth(BiTNode *T)   //树的深度  
{
	if (!T)
		return 0;
	int d1, d2;
	d1 = depth(T->lchild);
	d2 = depth(T->rchild);
	return (d1>d2 ? d1 : d2) + 1;
	//return (depth(T->lchild)>depth(T->rchild)?depth(T->lchild):depth(T->rchild))+1;  
}
int CountNode(BiTNode *T)
{
	if (T == NULL)
		return 0;
	return 1 + CountNode(T->lchild) + CountNode(T->rchild);
}

int main(void)
{
	BiTNode *root = NULL; //定义一个根结点  
	int flag = 1, k;
	printf("                     本程序实现二叉树的基本操作。\n");
	printf("可以进行建立二叉树，递归先序、中序、后序遍历，非递归先序、中序遍历及非递归层序遍历等操作。\n");

	while (flag)
	{
		printf("\n");
		printf("|--------------------------------------------------------------|\n");
		printf("|                    二叉树的基本操作如下:                     |\n");
		printf("|                        0.创建二叉树                          |\n");
		printf("|                        1.递归先序遍历                        |\n");
		printf("|                        2.递归中序遍历                        |\n");
		printf("|                        3.递归后序遍历                        |\n");
		printf("|                        4.非递归先序遍历                      |\n");
		printf("|                        5.非递归中序遍历                      |\n");
		printf("|                        6.非递归后序遍历                      |\n");
		printf("|                        7.非递归层序遍历                      |\n");
		printf("|                        8.二叉树的深度                        |\n");
		printf("|                        9.二叉树的结点个数                    |\n");
		printf("|                        10.退出程序                            |\n");
		printf("|--------------------------------------------------------------|\n");
		printf("                        请选择功能：");
		scanf("%d", &k);
		switch (k)
		{
		case 0:
			printf("请建立二叉树并输入二叉树的根节点：");
			CreateBiTree(&root);
			break;
		case 1:
			if (root)
			{
				printf("递归先序遍历二叉树的结果为：");
				PreOrder(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 2:
			if (root)
			{
				printf("递归中序遍历二叉树的结果为：");
				InOrder(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 3:
			if (root)
			{
				printf("递归后序遍历二叉树的结果为：");
				PostOrder(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 4:
			if (root)
			{
				printf("非递归先序遍历二叉树：");
				PreOrder_Nonrecursive1(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 5:
			if (root)
			{
				printf("非递归中序遍历二叉树：");
				InOrderTraverse1(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 6:
			if (root)
			{
				printf("非递归后序遍历二叉树：");
				PostOrder_Nonrecursive(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 7:
			if (root)
			{
				printf("非递归层序遍历二叉树：");
				//LeverTraverse(root);  
				LevelOrder(root);
				printf("\n");
			}
			else
				printf("          二叉树为空！\n");
			break;
		case 8:
			if (root)
				printf("这棵二叉树的深度为：%d\n", depth(root));
			else
				printf("          二叉树为空！\n");
			break;
		case 9:
			if (root)
				printf("这棵二叉树的结点个数为：%d\n", CountNode(root));
			else
				printf("          二叉树为空！\n");
			break;
		default:
			flag = 0;
			printf("程序运行结束，按任意键退出！\n");
		}
	}
	system("pause");
	return 0;
}

07 图的两种遍历方法及对应的生成树

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#define _CRT_SECURE_NO_WARNINGS
//图的遍历是指按某条搜索路径访问图中每个结点，使得每个结点均被访问一次，而且仅被访问一次。图的遍历有深度遍历算法和广度遍历算法，程序如下：
#include <iostream>
#include<stdio.h>
#define INFINITY 32767
#define MAX_VEX 20 //最大顶点个数
#define QUEUE_SIZE (MAX_VEX+1) //队列长度
using namespace std;
bool *visited;  //访问标志数组
				//图的邻接矩阵存储结构
typedef struct {
	char *vexs; //顶点向量
	int arcs[MAX_VEX][MAX_VEX]; //邻接矩阵
	int vexnum, arcnum; //图的当前顶点数和弧数
}Graph;


//队列类
class Queue {
public:
	void InitQueue() {
		base = (int *)malloc(QUEUE_SIZE * sizeof(int));
		front = rear = 0;
	}
	void EnQueue(int e) {
		base[rear] = e;
		rear = (rear + 1) % QUEUE_SIZE;
	}
	void DeQueue(int &e) {
		e = base[front];
		front = (front + 1) % QUEUE_SIZE;
	}
public:
	int *base;
	int front;
	int rear;
};


//图G中查找元素c的位置
int Locate(Graph G, char c) {
	for (int i = 0; i<G.vexnum; i++)
		if (G.vexs[i] == c) return i;
	return -1;
}


//创建无向网
void CreateUDN(Graph &G) {
	int i, j, w, s1, s2;
	char a, b, temp;
	printf("输入顶点数和弧数:");
	scanf("%d%d", &G.vexnum, &G.arcnum);
	temp = getchar(); //接收回车
	G.vexs = (char *)malloc(G.vexnum * sizeof(char)); //分配顶点数目
	printf("输入%d个顶点.\n", G.vexnum);
	for (i = 0; i<G.vexnum; i++) { //初始化顶点
		printf("输入顶点%d:", i);
		scanf("%c", &G.vexs[i]);
		temp = getchar(); //接收回车
	}
	for (i = 0; i<G.vexnum; i++) //初始化邻接矩阵
		for (j = 0; j<G.vexnum; j++)
			G.arcs[i][j] = INFINITY;
	printf("输入%d条弧.\n", G.arcnum);
	for (i = 0; i<G.arcnum; i++) { //初始化弧
		printf("输入弧%d:", i);
		scanf("%c %c %d", &a, &b, &w); //输入一条边依附的顶点和权值
		temp = getchar(); //接收回车
		s1 = Locate(G, a);
		s2 = Locate(G, b);
		G.arcs[s1][s2] = G.arcs[s2][s1] = w;
	}
}


//图G中顶点k的第一个邻接顶点
int FirstVex(Graph G, int k) {
	if (k >= 0 && k<G.vexnum) { //k合理
		for (int i = 0; i<G.vexnum; i++)
			if (G.arcs[k][i] != INFINITY) return i;
	}
	return -1;
}


//图G中顶点i的第j个邻接顶点的下一个邻接顶点
int NextVex(Graph G, int i, int j) {
	if (i >= 0 && i<G.vexnum && j >= 0 && j<G.vexnum) { //i,j合理
		for (int k = j + 1; k<G.vexnum; k++)
			if (G.arcs[i][k] != INFINITY) return k;
	}
	return -1;
}


//深度优先遍历
void DFS(Graph G, int k) {
	int i;
	if (k == -1) { //第一次执行DFS时,k为-1
		for (i = 0; i<G.vexnum; i++)
			if (!visited[i]) DFS(G, i); //对尚未访问的顶点调用DFS
	}
	else {
		visited[k] = true;
		printf("%c ", G.vexs[k]); //访问第k个顶点
		for (i = FirstVex(G, k); i >= 0; i = NextVex(G, k, i))
			if (!visited[i]) DFS(G, i); //对k的尚未访问的邻接顶点i递归调用DFS
	}
}


//广度优先遍历
void BFS(Graph G) {
	int k;
	Queue Q; //辅助队列Q
	Q.InitQueue();
	for (int i = 0; i<G.vexnum; i++)
		if (!visited[i]) { //i尚未访问
			visited[i] = true;
			printf("%c ", G.vexs[i]);
			Q.EnQueue(i); //i入列
			while (Q.front != Q.rear) {
				Q.DeQueue(k); //队头元素出列并置为k
				for (int w = FirstVex(G, k); w >= 0; w = NextVex(G, k, w))
					if (!visited[w]) { //w为k的尚未访问的邻接顶点
						visited[w] = true;
						printf("%c ", G.vexs[w]);
						Q.EnQueue(w);
					}
			}
		}
}


//主函数
void main() {
	int i;
	Graph G;
	CreateUDN(G);
	visited = (bool *)malloc(G.vexnum * sizeof(bool));
	printf("\n深度优先遍历: ");
	for (i = 0; i<G.vexnum; i++)
		visited[i] = false;
	DFS(G, -1);
	printf("\n广度优先遍历: ");
	for (i = 0; i<G.vexnum; i++)
		visited[i] = false;
	BFS(G);
	printf("\n程序结束.\n");
	getchar();
}

08 给定一个有向图，对其拓扑排序

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#include <cstdlib>
#include <iostream>
#include <stack>
#define Maxsize 30
#define INFINITY 99999
using namespace std;
typedef struct ArcNode
{
	int adjvex;
	struct ArcNode *nextarc;
}ArcNode;
typedef struct adjlist
{
	char name[10];
	int indegree;
	ArcNode *firstarc;
}adjlist;
typedef struct
{
	int vexnum, arcnum;
	adjlist ver[Maxsize];
}ALGraph;
int Locatecity(ALGraph G, char v[]);
void createGraph();
void output(ALGraph G);
void FindInDegree(ALGraph &G);
void TopologicalSort(ALGraph &G);

void TopologicalSort(ALGraph &G)
{
	int i, j, e, count;
	stack<int> s;
	ArcNode *p;
	FindInDegree(G);
	for (i = 0; i<G.vexnum; i++)
		if (!G.ver[i].indegree)
			s.push(i);
	count = 0;  //对顶点进行计数
	cout << "拓扑排序的结果如下: \n";
	while (!s.empty())
	{
		e = s.top();
		cout << G.ver[e].name << " ";
		count++;
		s.pop();
		for (p = G.ver[e].firstarc; p; p = p->nextarc)
		{
			if (!(--G.ver[p->adjvex].indegree))
				s.push(p->adjvex);
		}//for
	}//while
	cout << endl;
	if (count<G.vexnum)
	{
		cout << "该有向图有回路\n";
		return;
	}//if
}
void FindInDegree(ALGraph &G)
{
	int indeg, i, j;
	ArcNode *p;
	for (i = 0; i<G.vexnum; i++)
	{
		indeg = 0;
		for (j = 0; j<G.vexnum; j++)
		{
			if (G.ver[j].firstarc != NULL)
			{
				p = G.ver[j].firstarc;
				while (p)
				{
					if (p->adjvex == i)
						indeg++;
					p = p->nextarc;
				}//while
			}//if
		}//for
		G.ver[i].indegree = indeg;
	}//for
}
void createGraph()
{
	ALGraph G;
	cout << "请输入图的顶点个数: \n";
	cin >> G.vexnum;
	cout << "请输入弧数:\n";
	cin >> G.arcnum;
	for (int i = 0; i<G.vexnum; i++)
	{
		cout << "第 " << i + 1 << " 个顶点的名称\n";
		cin >> G.ver[i].name;
		G.ver[i].indegree = 0;  //都初始化为零
		G.ver[i].firstarc = NULL;
	}//for
	int n, m;
	char v1[10], v2[10];
	for (int j = 0; j<G.arcnum; j++)
	{
		cout << "请输入第 " << j + 1 << " 条弧的弧尾与弧头" << endl;
		cin >> v1 >> v2;
		n = Locatecity(G, v1); m = Locatecity(G, v2);
		ArcNode *p, *q, *t;
		p = (ArcNode*)malloc(sizeof(ArcNode));
		p->adjvex = m;
		p->nextarc = NULL;
		if (G.ver[n].firstarc == NULL)
			G.ver[n].firstarc = p;
		else
		{
			q = G.ver[n].firstarc;
			while (q->nextarc)
				q = q->nextarc;
			q->nextarc = p;
		}//else
	}//for
	output(G);
	TopologicalSort(G);
}
void output(ALGraph G)
{
	int i, j;
	ArcNode *p;
	cout << "有向图的邻接边的对应关系为:\n";
	for (i = 0; i<G.vexnum; i++)
	{

		if (G.ver[i].firstarc != NULL)
		{
			p = G.ver[i].firstarc;
			while (p)
			{
				cout << p->adjvex << "  ";
				p = p->nextarc;
			}//while
		}//if
		cout << endl;
	}//for
}
int Locatecity(ALGraph G, char v[])  //定位v在G中的位置的函数
{
	int i;
	for (i = 0; i<G.vexnum; i++)
		if (!strcmp(G.ver[i].name, v))
			break;
	return i;
}
int main()
{

	createGraph();
	system("PAUSE");
	return 0;
}


09 二叉排序树的建立，删除，插入节点，查找

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#include<iostream>
#include<stdio.h>
using namespace std;
#include<malloc.h>
#define MaxSize 100
typedef int KeyType;
typedef char InfoType;
typedef struct node
{
	KeyType key;
	InfoType data;
	struct node *lchild, *rchild;
}BSTNode;
int path[MaxSize];
void DispBST(BSTNode *b);
int InsetBST(BSTNode *&p, KeyType k)
{
	if (p == NULL)
	{
		p = (BSTNode *)malloc(sizeof(BSTNode));
		p->key = k; p->lchild = p->rchild = NULL;
		return 1;
	}
	else if (k == p->key)
		return 0;
	else if (k < p->key)
		return InsetBST(p->lchild, k);
	else
		return InsetBST(p->rchild, k);
}
BSTNode *CreatBST(KeyType A[], int n)
{
	BSTNode *bt = NULL;
	int i = 0;
	while (i<n)
	{
		if (InsetBST(bt, A[i]) == 1)
		{
			printf("第%d步 插入%d:", i + 1, A[i]);
			DispBST(bt); i++;
		}
	}
	return bt;
}
void Delete1(BSTNode *p, BSTNode *&r)
{
	BSTNode *q;
	if (r->rchild != NULL)
		Delete1(p, r->rchild);
	else
	{
		p->key = r->key;
		q = r;
		r = r->lchild;
		free(q);
	}
}
void Delete(BSTNode *&p)
{
	BSTNode *q;
	if (p->rchild == NULL)
	{
		q = p;
		p = p->lchild;
		free(q);
	}
	else if (p->lchild == NULL)
	{
		q = p;
		p = p->rchild;
		free(q);
	}
	else
		Delete1(p, p->lchild);
}
int DeleteBST(BSTNode *&bt, KeyType k)
{
	if (bt == NULL)
		return 0;
	else
	{
		if (k < bt->key)
			return DeleteBST(bt->lchild, k);
		else if (k > bt->key)
			return DeleteBST(bt->rchild, k);
		else
		{
			Delete(bt);
			return 1;
		}
	}
}
void SearchBST(BSTNode *bt, KeyType k, KeyType path[], int i)
{
	int j;
	if (bt == NULL)
		return;
	else if (k == bt->data)
	{
		path[i + 1] = bt->key;
		for (j = 0; j <= i + 1; j++)
		{
			printf("%3d", path[j]);
		}
	}
	else
	{
		path[i + 1] = bt->key;
		if (k < bt->key)
			SearchBST(bt->lchild, k, path, i + 1);
		else
			SearchBST(bt->rchild, k, path, i + 1);
	}
}
int SearchBST2(BSTNode *bt, KeyType k)
{
	if (bt == NULL)
		return 0;
	else if (k == bt->key)
	{
		printf("%3d", bt->data);
		return 1;
	}
	else if (k < bt->key)
		SearchBST2(bt->lchild, k);
	else
		SearchBST2(bt->rchild, k);
	printf("%3d", bt->key);
}
void DispBST(BSTNode *bt)
{
	if (bt != NULL)
	{
		printf("%d", bt->key);
		if (bt->lchild != NULL || bt->rchild != NULL)
		{
			printf("(");
			DispBST(bt->lchild);
			if (bt->rchild != NULL)
				printf(",");
			DispBST(bt->rchild);
			printf(")");
		}
	}
}
KeyType predt = -32767;
int JundgBST(BSTNode *bt)
{
	int b1, b2;
	if (bt == NULL)
		return 1;
	else
	{
		b1 = JundgBST(bt->lchild);
		if (b1 == 0 || predt >= bt->key)
			return 0;
		predt = bt->key;
		b2 = JundgBST(bt->rchild);
		return b2;
	}
}
void main()
{
	BSTNode *bt;
	KeyType k = 6;
	int a[] = { 4,9,3,8,7,0,1,2,5,6 }, n = 10;
	printf("创建一颗BST树");
	bt = CreatBST(a, n);
	printf("BST："); DispBST(bt);
	printf("bt%s\n", (JundgBST(bt) ? "是一颗树" : "不是一颗树"));
	printf("查找%d关键字(递归，顺序)", k); SearchBST(bt, k, path, -1);
	printf("查找%d关键字(非递归，逆序)", k); SearchBST2(bt, k);
	printf("删除操作：\n");
	printf("原BST："); DispBST(bt); printf("\n");
	printf("删除节点4");
	DeleteBST(bt, 4);
	DispBST(bt);
	getchar();

}

Markdown

10 希尔排序 与 快速排序的比较

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#define _CRT_SECURE_NO_DEPRECATE
#include<stdio.h>
#define Max 30
typedef struct
{
	int key;

}RecType;
RecType R[Max], S[Max];
void ShellSort(RecType R[], int n)
{
	int i, j, gap;
	RecType tmp;
	gap = n / 2;
	while (gap>0)
	{
		for (i = gap; i < n; i++)
		{
			tmp = R[i];
			j = i - gap;
			while (j >= 0 && tmp.key<R[j].key)
			{
				R[j + gap] = R[j];
				j = j - gap;
			}
			R[j + gap] = tmp;
		}
		gap = gap / 2;
	}
}
void QuickSort(RecType R[], int s, int t)
{
	int i = s, j = t;
	RecType tmp;
	if (s < j)
	{
		tmp = R[s];
		while (i != j)
		{
			while (j > i&&R[j].key > tmp.key)
				j--;
			R[i] = R[j];
			while (i < j&&R[i].key < tmp.key)
				i++;
			R[j] = R[i];
		}
		R[i] = tmp;
		QuickSort(R, s, i - 1);
		QuickSort(R, i + 1, t);
	}
}

void main()
{
	int n, i;
	printf("请输入关键字个数：\n");
	scanf("%d", &n);
	printf("请输入关键字序列：\n");
	for (int i = 0; i < n; i++)
	{
		scanf("%d", &R[i].key);
		S[i].key = R[i].key;
	}
	ShellSort(R, n);
	printf("希尔排序结果为：");
	for (i = 0; i < n; i++)
		printf("%d", R[i].key);
	printf("\n");
	QuickSort(S, 0, n - 1);
	printf("快速排序结果为：");
	for (i = 0; i < n; i++)
		printf("%d", S[i].key);

}

Markdown

11

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#include<stdio.h>
int tile = 0;//L型骨牌数量
int Matrix[100][100];//定义数据结构
void ChessBoard(int tr, int tc, int dr, int dc, int size)
{
	//tr tc 行号 列号
	if (size == 1) return;
	int t = tile++;//L型骨牌号
	int s = size / 2;//分割棋盘
	if (dr < tr + s&&dc < tc + s)//用L型骨牌覆盖左上角棋盘
		ChessBoard(tr, tc, dr, dc, s);//特殊方格在此棋盘中
	else
	{
		//特殊方格不在此棋盘中，t号L型骨牌覆盖右下角
		Matrix[tr + s - 1][tc + s - 1];//覆盖本子棋盘其余方格
		ChessBoard(tr, tc, tr + s - 1, tc + s - 1, s);
	}
	if (dr < tr + s&&dc >= tc + s)//用L型骨牌号覆盖右上角棋盘
		ChessBoard(tr, tc, dr, dc, s);
	else
	{
		//特殊方格不在此棋盘中，t号L型骨牌覆盖左下角
		Matrix[tr + s - 1][tc + s] = t;//覆盖本子棋盘其余方格
		ChessBoard(tr, tc + s, tr + s - 1, tc + s, s);
	}
	if (dr >= tr + s&&dc<tc + s)//用L型骨牌覆盖左下角子棋盘
		ChessBoard(tr + s, tc, dr, dc, s);
	else
	{
		//特殊方格不在此棋盘中，t号L型骨牌覆盖右上角
		Matrix[tr + s][tc + s] = t;//覆盖本子棋盘其余方格
		ChessBoard(tr, tc + s, tr + s - 1, tc + s, s);
	}
	if (dr >= tr + s&&dc >= tc + s)//用L骨牌覆盖右上角子棋盘
		ChessBoard(tr + s, tc + s, dr, dc, s);
	else
	{
		//特殊方格不在此棋盘中，t号L型骨牌覆盖右上角
		Matrix[tr + s][tc + s] = t;//覆盖本子棋盘其余方格
		ChessBoard(tr, tc + s, tr + s, tc + s, s);
	}
}

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