本博客前面文章已对树与二叉树有过简单的介绍，本文主要是重点介绍有关二叉树的一些具体操作与应用

阅读本文前，可以先参考本博客 各种基本算法实现小结（三）—— 树与二叉树   和  各种基本算法实现小结（二）—— 堆 栈

二叉树

深度层数、叶子数、节点数和广度优先算法

以及树的先序、中序、后序的递归与非递归（深度优先）

测试环境：VS2008（C）

#include "stdafx.h" #include <stdlib.h> #include <malloc.h> #define DataType char int d_tree=0; /* tree's depth */ int l_tree=0; /* tree's leaf */ int n_tree=0; /* tree's node */ /**************************************/ /******** 树的结构定义 ********/ /**************************************/ struct _tree { DataType data; struct _tree *lchild; struct _tree *rchild; }; typedef struct _tree tree, *ptree; /**************************************/ /******** 栈的结构定义 ********/ /**************************************/ struct _node { ptree pt; struct _node *next; }; typedef struct _node node, *pnode; struct _stack { int size; pnode ptop; }; typedef struct _stack stack, *pstack; /**************************************/ /******** 堆的结构定义 ********/ /**************************************/ struct _queue { pnode front; pnode rear; }; typedef struct _queue queue, *pqueue; /**************************************/ /******** 栈的数据操作 ********/ /**************************************/ pstack init_stack() { pnode pn=NULL; pstack ps=NULL; pn=(pnode)malloc(sizeof(node)); ps=(pstack)malloc(sizeof(stack)); pn->pt=NULL; pn->next=NULL; ps->ptop=pn; return ps; } int empty_stack(pstack ps) { if(ps->ptop->next==NULL) return 1; else return 0; } void push_stack(pstack ps, ptree pt) /* flag for post tree: 0 for lchild; 1 for rchild */ { pnode pn=NULL; pn=(pnode)malloc(sizeof(node)); pn->pt=pt; pn->next=ps->ptop; ps->ptop=pn; } ptree pop_stack(pstack ps) { ptree pt=NULL; pnode pn=NULL; if(!empty_stack(ps)) { pn=ps->ptop; ps->ptop=ps->ptop->next; pt=pn->pt; free(pn); } return pt; } ptree gettop_stack(pstack ps) { if(!empty_stack(ps)) return ps->ptop->pt; } /**************************************/ /******** 堆的数据操作 ********/ /**************************************/ queue init_queue() { pnode pn=NULL; queue qu; pn=(pnode)malloc(sizeof(node)); pn->pt=NULL; pn->next=NULL; qu.front=qu.rear=pn; /* init: pn is header */ return qu; } int empty_queue(queue &qu) { if(qu.front==qu.rear) return 1; else return 0; } void en_queue(queue &qu, ptree pt) { pnode pn=NULL; pn=(pnode)malloc(sizeof(node)); pn->pt=pt; pn->next=qu.rear->next; qu.rear->next=pn; qu.rear=qu.rear->next; } ptree de_queue(queue &qu) { ptree pt=NULL; pnode pn=NULL; if(!empty_queue(qu)) { pn=qu.front->next; if(pn==qu.rear) /* qu is null: qu.front==qu.rear */ qu.rear=qu.front; else qu.front->next=qu.front->next->next; pt=pn->pt; free(pn); } return pt; } /**************************************/ /******** 树的数据操作 ********/ /**************************************/ ptree init_tree() { ptree pt=NULL; pt=(ptree)malloc(sizeof(tree)); pt->data='0'; pt->lchild=NULL; pt->rchild=NULL; return pt; } ptree create_tree() { char ch; ptree pt=NULL; scanf("%c", &ch); getchar(); if(ch==' ') return NULL; else { pt=(ptree)malloc(sizeof(tree)); pt->data=ch; pt->lchild=create_tree(); pt->rchild=create_tree(); } return pt; } int depth_tree(ptree pt) { int l_len, r_len; ptree p=pt; if(p==NULL) return 0; else { l_len=depth_tree(p->lchild); r_len=depth_tree(p->rchild); return l_len>r_len?(l_len+1):(r_len+1); } } void leaf_tree(ptree pt) { ptree p=pt; if(p->lchild==NULL && p->rchild==NULL) l_tree++; else { leaf_tree(p->lchild); leaf_tree(p->rchild); } } void node_tree(ptree pt) { ptree p=pt; if(p!=NULL) { n_tree++; node_tree(p->lchild); node_tree(p->rchild); } } void print_pretree(ptree pt) { if(pt!=NULL) { printf("%3c", pt->data); print_pretree(pt->lchild); print_pretree(pt->rchild); } } void print_pretree2(ptree pt) { pstack ps=NULL; ptree p=NULL; ps=init_stack(); p=pt; while(p!=NULL || !empty_stack(ps)) { while(p!=NULL) { printf("%3c", p->data); push_stack(ps, p); p=p->lchild; } if(!empty_stack(ps)) { p=pop_stack(ps); p=p->rchild; } } } void print_midtree(ptree pt) { if(pt!=NULL) { print_midtree(pt->lchild); printf("%3c", pt->data); print_midtree(pt->rchild); } } void print_midtree2(ptree pt) { pstack ps=NULL; ptree p=NULL; ps=init_stack(); p=pt; while (p!=NULL || !empty_stack(ps)) { while(p!=NULL) { push_stack(ps, p); p=p->lchild; } if(!empty_stack(ps)) { p=pop_stack(ps); printf("%3c", p->data); p=p->rchild; } } } void print_posttree(ptree pt) { if(pt!=NULL) { print_posttree(pt->lchild); print_posttree(pt->rchild); printf("%3c", pt->data); } } void print_posttree2(ptree pt) { pstack ps=NULL; ptree p=NULL; ptree p2=NULL; ptree lastvisit=NULL; ps=init_stack(); p=pt; while (p!=NULL || !empty_stack(ps)) { while(p!=NULL) { push_stack(ps, p); p=p->lchild; } p2=gettop_stack(ps); /* top: rchild==null or sub_root */ if(p2->rchild==NULL || p2->rchild==lastvisit) { printf("%3c", p2->data); lastvisit=pop_stack(ps); /* pop */ } else p=p2->rchild; } } void bfs_tree(ptree pt) { ptree p=NULL; queue qu; qu=init_queue(); p=pt; if(p!=NULL) { en_queue(qu, p); while (!empty_queue(qu)) { p=de_queue(qu); printf("%3c", p->data); if(p->lchild!=NULL) en_queue(qu, p->lchild); if(p->rchild!=NULL) en_queue(qu, p->rchild); } } } int _tmain(int argc, _TCHAR* argv[]) { ptree pt=NULL; /*pt=init_tree();*/ printf("Create tree:/n"); pt=create_tree(); /************ recursion ************/ printf("/n/nrecursion..."); printf("/npre tree.../n"); print_pretree(pt); printf("/nmid tree.../n"); print_midtree(pt); printf("/npost tree.../n"); print_posttree(pt); /************ stack ************/ printf("/n/nstack, non recursion:"); printf("/npre tree.../n"); print_pretree2(pt); printf("/nmid tree.../n"); print_midtree2(pt); printf("/npost tree.../n"); print_posttree2(pt); /********** bfs tree **********/ printf("/n/nbfs_tree:/n"); bfs_tree(pt); /********* tree operation ********/ printf("/n/ntree operation:"); d_tree=depth_tree(pt); leaf_tree(pt); node_tree(pt); printf("/ntree's depth: %d", d_tree); printf("/ntree's leaf: %d", l_tree); printf("/ntree's node: %d", n_tree); printf("/n"); return 0; }

运行结果：

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