【数据结构】二叉树

二叉树的建立和遍历

使用前序+左右孩子标志#的方式输入；
输出依次为先序遍历、中序遍历、后序遍历、层次遍历、树的深度、树是否为完全二叉树。

#include 
#include
using namespace std;
#define maxn 2000
#define error 1
#define ok 0
#define no 1
typedef int status;
char str[2000];
typedef struct node
{
    char val;
    node *lson, *rson;
}node,*lnode;//链式树 
typedef lnode elem;
typedef struct qnode
{
    elem data;
    struct qnode *next;
}qnode,*queueptr;//链式队列 
typedef struct
{
    queueptr front;
    queueptr rear;
}linkqueue;//链式队列的头和尾节点 
status init_queue(linkqueue &q)
{
    q.front=q.rear=(queueptr)malloc(sizeof(qnode));
    q.rear->next=NULL;
    return ok;
}
status push_queue(linkqueue &q,elem e)
{
    q.rear->data=e;
    queueptr s;
	s=(queueptr)malloc(sizeof(qnode));
	q.rear->next=s;
	q.rear=s;
	q.rear->next=NULL;
	return ok;
}
queueptr pop_queue(linkqueue &q)
{
	queueptr p=q.front;
	queueptr t;
	t=q.front->next;
	q.front=t;
	return p;
}
void levelorder(lnode node)
{
	linkqueue q;
    init_queue(q);
    if(node!=NULL)
    {
    	push_queue(q,node);
    	while(q.front!=q.rear)
		{
    		queueptr p;
			p=pop_queue(q);
    		printf("%c",p->data->val);
    		if(p->data->lson!=NULL)
    			push_queue(q,p->data->lson);
    		if(p->data->rson!=NULL)
    			push_queue(q,p->data->rson);
		}
	}
}//层次遍历 
int complete(lnode T)
{
	if(T==NULL)
	return ok;
	linkqueue q;
    init_queue(q);
    push_queue(q,T);
    queueptr p;
	while(q.front!=q.rear)
	{
		p=pop_queue(q);
		if(p->data)
		{
			push_queue(q,p->data->lson);
			push_queue(q,p->data->rson);
		}
		else
		{
			while(q.front!=q.rear)
			{
				p=pop_queue(q);
				if(p->data)
				return no;
			}
		}//找到一个空结点之后判断后面是否是非空元素，如果是，一定不是完全二叉树
	}
	return ok;
}
void create1(lnode* T,string s1,string s2)
{
    *T = (lnode)calloc(1,sizeof(node));
    (*T)->val=s1[0];
    if(s1.size() == 1)
	{
        return;
    }
    int index;
    for(index = 0; index < s2.size(); index++)
	{
        if(s2[index] == s1[0])
			break;
    }
    int left_length = index;
    int right_length = s1.size() - left_length - 1;
    if(left_length > 0)
	{
        create1(&(*T)->lson, s1.substr(1, left_length), s2.substr(0, left_length));
    }
    if(right_length > 0)
	{
        create1(&(*T)->rson, s1.substr(1 + left_length, right_length), s2.substr(1 + left_length, right_length));
    }
}//已知前序和中序建立二叉树 
void create2(lnode &T,int &i,int n)
{
	if(i==n)
	return;
	if(str[i]=='#')
	{
		T=NULL;
		i++;
	}
	else
	{
		T=new node;
		T->val=str[i];
		i++;
		create2(T->lson,i,n);
		create2(T->rson,i,n);
	}
}//已知先序遍历序建立二叉树 
void preorder(lnode T)
{
    if(T!=NULL)
	{
		printf("%c",T->val);
		preorder(T->lson);
		preorder(T->rson);
	}
}//先序遍历 
void inorder(lnode T)
{
    if(T!=NULL)
	{
		inorder(T->lson);
		printf("%c",T->val);
		inorder(T->rson);
	}
}//中序遍历 
void postorder(lnode T)
{
    if(T!=NULL)
	{
		postorder(T->lson);
		postorder(T->rson);
		printf("%c",T->val);
	}
}//后序遍历 
int getdepth(lnode T)
{
	int ld,rd;
	if(T==NULL)
	return 0;
	else
	{
		ld=getdepth(T->lson);
		rd=getdepth(T->rson);
		if(ld>rd)
		return (ld+1);
		else
		return (rd+1);
	}
}//求二叉树的深度 
int main()
{
	int depth;
    while(scanf("%s",str)!=EOF) 
    {
	    lnode T=NULL;
	    int i=0;
	    create2(T,i,strlen(str));
	    /*printf("preorder:");
	    preorder(T);
	    printf("\ninorder:");
	    inorder(T);
	    printf("\npostorder:");
	    postorder(T);
	    printf("\nlevelorder:");
	    levelorder(T);
	    printf("\ndepth:");
	    depth=getdepth(T);
		printf("%d\ncomplete:",depth);*/
		if(complete(T)==ok)
		printf("Yes\n");
		else
		printf("No\n");
	}
    return 0;
}

已知前序中序二叉树的建立

输入为二叉树的先序和中序遍历；
输出为二叉树的后序遍历。

#include 
#include
using namespace std;
#define maxn 2000
#define error 1
#define ok 0
#define no 1
typedef int status;
char str[2000];
typedef struct node
{
    char val;
    node *lson, *rson;
}node,*lnode;//链式树 
typedef lnode elem;
typedef struct qnode
{
    elem data;
    struct qnode *next;
}qnode,*queueptr;//链式队列 
typedef struct
{
    queueptr front;
    queueptr rear;
}linkqueue;//链式队列的头和尾节点 
status init_queue(linkqueue &q)
{
    q.front=q.rear=(queueptr)malloc(sizeof(qnode));
    q.rear->next=NULL;
    return ok;
}
status push_queue(linkqueue &q,elem e)
{
    q.rear->data=e;
    queueptr s;
	s=(queueptr)malloc(sizeof(qnode));
	q.rear->next=s;
	q.rear=s;
	q.rear->next=NULL;
	return ok;
}
queueptr pop_queue(linkqueue &q)
{
	queueptr p=q.front;
	queueptr t;
	t=q.front->next;
	q.front=t;
	return p;
}
void levelorder(lnode node)
{
	linkqueue q;
    init_queue(q);
    if(node!=NULL)
    {
    	push_queue(q,node);
    	while(q.front!=q.rear)
		{
    		queueptr p;
			p=pop_queue(q);
    		printf("%c",p->data->val);
    		if(p->data->lson!=NULL)
    			push_queue(q,p->data->lson);
    		if(p->data->rson!=NULL)
    			push_queue(q,p->data->rson);
		}
	}
}//层次遍历 
int complete(lnode T)
{
	if(T==NULL)
	return ok;
	linkqueue q;
    init_queue(q);
    push_queue(q,T);
    queueptr p;
	while(q.front!=q.rear)
	{
		p=pop_queue(q);
		if(p->data)
		{
			push_queue(q,p->data->lson);
			push_queue(q,p->data->rson);
		}
		else
		{
			while(q.front!=q.rear)
			{
				p=pop_queue(q);
				if(p->data)
				return no;
			}
		}//找到一个空结点之后判断后面是否是非空元素，如果是，一定不是完全二叉树
	}
	return ok;
}
void create1(lnode* T,string s1,string s2)
{
    *T = (lnode)calloc(1,sizeof(node));
    (*T)->val=s1[0];
    if(s1.size() == 1)
	{
        return;
    }
    int index;
    for(index = 0; index < s2.size(); index++)
	{
        if(s2[index] == s1[0])
			break;
    }
    int left_length = index;
    int right_length = s1.size() - left_length - 1;
    if(left_length > 0)
	{
        create1(&(*T)->lson, s1.substr(1, left_length), s2.substr(0, left_length));
    }
    if(right_length > 0)
	{
        create1(&(*T)->rson, s1.substr(1 + left_length, right_length), s2.substr(1 + left_length, right_length));
    }
}//已知前序和中序建立二叉树 
void create2(lnode &T,int &i,int n)
{
	if(i==n)
	return;
	if(str[i]=='#')
	{
		T=NULL;
		i++;
	}
	else
	{
		T=new node;
		T->val=str[i];
		i++;
		create2(T->lson,i,n);
		create2(T->rson,i,n);
	}
}//已知先序遍历序建立二叉树 
void preorder(lnode T)
{
    if(T!=NULL)
	{
		printf("%c",T->val);
		preorder(T->lson);
		preorder(T->rson);
	}
}//先序遍历 
void inorder(lnode T)
{
    if(T!=NULL)
	{
		inorder(T->lson);
		printf("%c",T->val);
		inorder(T->rson);
	}
}//中序遍历 
void postorder(lnode T)
{
    if(T!=NULL)
	{
		postorder(T->lson);
		postorder(T->rson);
		printf("%c",T->val);
	}
}//后序遍历 
int getdepth(lnode T)
{
	int ld,rd;
	if(T==NULL)
	return 0;
	else
	{
		ld=getdepth(T->lson);
		rd=getdepth(T->rson);
		if(ld>rd)
		return (ld+1);
		else
		return (rd+1);
	}
}//求二叉树的深度 
int main()
{
	int depth;
    string str_1, str_2;
	lnode T=NULL;
	while(cin>>str_1>>str_2)
	{
		create1(&T,str_1,str_2);
		postorder(T);
		printf(" ");
		levelorder(T);
		printf("\n");
	}
    return 0;
}

平衡二叉树的判断

#include 
#include
using namespace std;
#define maxn 2000
#define error 1
#define ok 0
#define no 1
typedef int status;
char str[2000];
typedef struct node
{
    char val;
    node *lson, *rson;
}node,*lnode;//链式树
void create2(lnode &T,int &i,int n)
{
	if(i==n)
	return;
	if(str[i]=='#')
	{
		T=NULL;
		i++;
	}
	else
	{
		T=new node;
		T->val=str[i];
		i++;
		create2(T->lson,i,n);
		create2(T->rson,i,n);
	}
}//已知先序遍历序建立二叉树 
void preorder(lnode T)
{
    if(T!=NULL)
	{
		printf("%c",T->val);
		preorder(T->lson);
		preorder(T->rson);
	}
}//先序遍历
int getdepth(lnode T)
{
	int ld,rd;
	if(T==NULL)
	return 0;
	else
	{
		ld=getdepth(T->lson);
		rd=getdepth(T->rson);
		if(ld>rd)
		return (ld+1);
		else
		return (rd+1);
	}
}//求二叉树的深度 
status balance(lnode T)
{
	if(T==NULL)
	return 1;
	int lefthight=getdepth(T->lson);
	int righthight=getdepth(T->rson);
	int diff=lefthight-righthight;
	if(diff>1||diff<-1)
		return 0;
	else 
	return (balance(T->lson)&&balance(T->rson));
}
int main()
{
	int depth;
    while(scanf("%s",str)!=EOF) 
    {
	    lnode T=NULL;
	    int i=0;
	    create2(T,i,strlen(str));
	    if(balance(T)==0)
	    	printf("No\n");
	    else 
	    printf("Yes\n");
	}
    return 0;
}