表达式二叉树的C++实现

这篇博客详细介绍了如何使用C++实现表达式二叉树。通过建立优先级数组和操作符栈,将表达式转化为二叉树,并进行后序遍历。代码中包含了从输入读取表达式,构建、遍历和释放二叉树节点的过程。

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#include <iostream>
#include 
<stack>
#include 
<string>
using namespace std;

int prior[1000]={0};
char oper[]={'(',')','+','-','*','/','^'};
int testcase;
string expr;
char tmpchr,c;


class Node{
public:
    
char oper;
    Node 
* left;
    Node 
* right;
    Node()
{left=right=NULL;};
    Node(
char op){left=right=NULL;oper=op;}
}
;

stack
<char>operStack;
stack
<Node *>dataStack;

void generateTree(Node * &p,int idx)
{
   
    tmpchr
=expr[idx];
    
while(!(operStack.top()=='#' && tmpchr=='#')){
        
if(!prior[tmpchr]){
            p
=new Node(tmpchr);
            dataStack.push(p);
        }

        
else {
            
switch(tmpchr){
            
case '(':
                operStack.push(
'(');
                
break;
            
case ')':
                c
=operStack.top(); operStack.pop();
                
while(c!='('){
                    p
=new Node(c);
                    p
->right=dataStack.top(); dataStack.pop();
                    p
->left=dataStack.top(); dataStack.pop();
                    dataStack.push(p);
                    c
=operStack.top(); operStack.pop();
                }

                
break;
            
default:
                
while(operStack.size() && prior[operStack.top()]>prior[tmpchr]){
                    p
=new Node(operStack.top());
                    p
->oper=operStack.top();
                    
if(dataStack.size()){p->right=dataStack.top(); dataStack.pop();}
                    
if(dataStack.size()){p->left=dataStack.top(); dataStack.pop();}
                    dataStack.push(p);
                    operStack.pop();
                }

                
if(tmpchr!='#')operStack.push(tmpchr);
                
break;
            }

        }

        
if(tmpchr!='#')tmpchr=expr[++idx];
    }

    p
=dataStack.top(); dataStack.pop();
}


inline 
void freeTree(Node * p)
{
    
if(p->left!=NULL)freeTree(p->left);
    
if(p->right!=NULL)freeTree(p->right);
    delete(p);
}


void postOrderTraverse(Node * p)
{
    
if(p){
        postOrderTraverse(p
->left);
        postOrderTraverse(p
->right);
        cout
<<p->oper;
    }

}


Node 
* tree;

int main()
{
    cin
>>testcase;
    
for(int i=0;i<7;i++)prior[oper[i]]=i+2;
    prior[
'#']=1;
    
while(testcase--){
        cin
>>expr;
        
while(operStack.size())operStack.pop();
        operStack.push(
'#');
        
while(dataStack.size())dataStack.pop();
        generateTree(tree,
1);
        postOrderTraverse(tree);
        cout
<<endl;
        freeTree(tree);
    }

}

 
// 输入格式 #表达式#
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