中缀表达式表示成二叉树

将一个中缀表达式表示成二叉树的形式，相关提示如下：（1）基本思路：中缀先转换成后缀，然后再表示成二叉树。

这样做起来要方便的多；（2）打印二叉树时，可以用课件上的逆时针旋转90度打印方式。

#include<iostream>#include<string>#include"d_except.h"using namespace std;#ifndef STACK#define STACKconst MAXSTACKSIZE=50;template<typename T>class stack //有限栈{public:stack();void push(const T& item);void pop();T& top();const T& top() const;bool empty() const;bool full() const;int size() const;private:T stackList[MAXSTACKSIZE];int topIndex;};template <typename T>stack<T>::stack(){topIndex=-1;}template <typename T>void stack<T>::push(const T& item){if(full())throw underflowError("miniStack top():stack empty");//exit(1);topIndex++;stackList[topIndex]=item;}template <typename T>void stack<T>::pop(){if (empty())throw underflowError("miniStack top(): stack empty");topIndex--;}template <typename T>T& stack<T>::top(){if (empty()) throw underflowError("miniStack top(): stack empty");return stackList[topIndex];}template <typename T>const T& stack<T>::top() const{if (empty()) throw underflowError("miniStack top(): stack empty");return stackList[topIndex];}template <typename T>bool stack<T>::empty() const{return topIndex == -1;}template <typename T>bool stack<T>::full() const{return topIndex==MAXSTACKSIZE-1;}template <typename T>int stack<T>::size() const{return topIndex+1;}#endif#include<string>#include"stack.h"using namespace std;class expressionSymbol{public:expressionSymbol();expressionSymbol(char ch);friend bool operator>= (const expressionSymbol& left, const expressionSymbol& right ) {return left.stackPrecedence >= right.inputPrecedence;}char getOp() const;private:char op;int inputPrecedence;int stackPrecedence;};expressionSymbol::expressionSymbol(){}expressionSymbol::expressionSymbol(char ch) { op = ch;switch(op){ case '+':case '-': inputPrecedence = 1;stackPrecedence = 1; break;case '*':case '%':case '/': inputPrecedence = 2;stackPrecedence = 2; break;case '^': inputPrecedence = 4;stackPrecedence = 3; break;case '(': inputPrecedence = 5;stackPrecedence = -1; break;case ')': inputPrecedence = 0;stackPrecedence = 0; break;}}char expressionSymbol::getOp() const{return op;}class infix2Postfix{public:infix2Postfix();infix2Postfix(const string& infixExp);void setInfixExp(const string& infixExp);string postfix();private:string infixExpression;string postfixExpression;stack<expressionSymbol> operatorStack;void outputHigherOrEqual(const expressionSymbol& op);bool isOperator(char ch) const;// ch is one of '+','-','*','/','%','^'};void infix2Postfix::outputHigherOrEqual(const expressionSymbol& op) {expressionSymbol op2;while(!operatorStack.empty() &&(op2 = operatorStack.top()) >= op){operatorStack.pop();postfixExpression += op2.getOp();postfixExpression += ' ';}}bool infix2Postfix::isOperator(char ch) const{return ch == '+' || ch == '-' || ch == '*' ||ch == '%' || ch == '/' || ch == '^';}infix2Postfix::infix2Postfix(){}infix2Postfix::infix2Postfix(const string& infixExp):infixExpression(infixExp){}void infix2Postfix::setInfixExp(const string& infixExp){infixExpression = infixExp;postfixExpression = "";}string infix2Postfix::postfix(){expressionSymbol op;int rank = 0, i;char ch;for (i=0; i < infixExpression.length(); i++){ch = infixExpression[i];if (isdigit(ch)){postfixExpression += ch;// postfixExpression += ' ';rank++;if (rank > 1)throw expressionError("infix2Postfix:Operator expected");}else if (isOperator(ch) || ch == '('){if (ch != '(') rank--;if (rank < 0)throw expressionError("infix2Postfix:Operand expected");else{op = expressionSymbol(ch);outputHigherOrEqual(op);operatorStack.push(op);}}else if (ch == ')'){op = expressionSymbol(ch);outputHigherOrEqual(op);if(operatorStack.empty())throw expressionError("infix2Postfix: Missing '('");elseoperatorStack.pop();}else if (!isspace(ch))throw expressionError("infix2Postfix: Invalid input");}if (rank != 1)throw expressionError("infix2Postfix: Operand expected");else{while (!operatorStack.empty()){op = operatorStack.top();operatorStack.pop();if (op.getOp() == '(')throw expressionError("infix2Postfix: Missing ')'");else{postfixExpression += op.getOp();//postfixExpression += ' ';}}}return postfixExpression;}#include<iostream>#include<iomanip>#include<string>#include"stack.h"using namespace std;class tnode{public:char nodeValue;tnode *left, *right;tnode(){}tnode (const char& item, tnode *lptr = NULL,tnode *rptr = NULL):nodeV alue(item), left(lptr), right(rptr){}tnode* buildtree(string str);int depth(tnode *root);void print(tnode *node_ptr, int depth);};//根据后缀表达式生成二叉树tnode* tnode::buildtree(string n){tnode *ptr;stack<tnode*> nodeStack;char c;int i=0;c=n[i++];while(c!='\0'){//如果不是运算符，则进栈if(c!='+' && c!='-' && c!='*' && c!='/'){ptr=new tnode(c);nodeStack.push(ptr);c=n[i++];}else{ptr=new tnode(c);if(!nodeStack.empty()){ptr->right=nodeStack.top();nodeStack.pop();}if(!nodeStack.empty()){ptr->left=nodeStack.top();nodeStack.pop();}nodeStack.push(ptr);c=n[i++];}}return ptr;}int tnode::depth(tnode *root){int depthval,depthleft,depthright;if(root==NULL)depthval=-1;else{depthleft=depth(root->left);depthright=depth(root->right);depthval=1+(depthleft>depthright?depthleft:depthright);}return depthval;}void tnode::print(tnode *node_ptr, int depth){if (node_ptr != NULL){print(node_ptr->right, depth+1);cout << setw(4*depth) << " ";cout << node_ptr->nodeValue << endl;print(node_ptr->left, depth+1);}}#include<iostream>#include<string>#include"stack.h"#include"expression.h"#include"tree.h"using namespace std;void main(){string p;cout<<"请输入表达式:"<<endl;cin>>p;infix2Postfix A(p);string q=A.postfix();cout<<"后缀表达式为:"<<endl;cout<<q<<endl;cout<< "二叉树为:"<<endl;tnode tree(' ');tnode *root;int depth;root=tree.buildtree(q);depth=tree.depth(root);tree.print(root,depth);}。