构造一颗表达式树

数据结构与算法分析——c语言描述 第四章树 构造一颗表达式树

输入一个表达式，程序转换成逆序，再然后根据逆序构建表达式树，然后再用中序遍历输出表达式。

以前的文章也实现的用逆序转表达式，用栈来实现。这个用树来实现。树更加万能吧，逆序，中序，前序什么的都有。

tree.h

#include<string>
typedef std::string ElementType;
#ifndef _Tree_H
#define _Tree_H

struct TreeNode;
typedef struct TreeNode *Position;
typedef struct TreeNode *Tree;

Tree createSearchTree();
void makeEmpty(Tree t);
Tree insert(ElementType X, Tree t);
void  PrintinOrder(Tree t);
#endif

tree.cpp

#include"tree.h"
#include"fatal.h"

extern double operatorPriority(char c);
extern double operatorCmp(char c1, char c2);

struct TreeNode {
ElementType element;
Tree left;
Tree right;
};

Tree createSearchTree()
{
return NULL;
}

void makeEmpty(Tree t) {
if (t) {
makeEmpty(t->left);
makeEmpty(t->right);
free(t);
}
}

Tree insert(ElementType X, Tree t) {
if (t == NULL) {//包含树没有初始化
t = new TreeNode;
if (t == NULL)
Error("out of memory");
t->element = X;
t->left = NULL;
t->right = NULL;
}
else {
if (X < t->element)
t->left = insert(X, t->left);
else if (X>t->element)
t->right = insert(X, t->right);
}
return t;//两种情况
}

void PrintinOrder(Tree t)
{
if (t->left)
{
if (operatorCmp(t->element[0], t->left->element[0]) > 0)
{
printf("(");
PrintinOrder(t->left);
printf(")");
}
else
PrintinOrder(t->left);
}
printf("%s", t->element.c_str());
if (t->right)
{
if (operatorCmp(t->element[0], t->right->element[0]) > 0)
{
printf("(");
PrintinOrder(t->right);
printf(")");
}
else
PrintinOrder(t->right);
}

}

infixToSuffix.h

#pragma once
#include<ctype.h>
#include<string>
#include<stack>
using namespace std;
#define MAXN 100

char expression[MAXN];//输入的表达式
string postfix[MAXN];//转换成的逆序表达式

int i = 0, j = 0;//i是expression的游标，postfix是逆序表达式的游标

double operatorCmp(char c1, char c2);//c1为将要插入栈的运算符，c2为栈顶运算符,1表示c1优先级大于c2,0为相等，-1为小于
#define putNum()  postfix[j++] = num,num.clear();//把数字输出到逆序表达式
#define putOperator() oper= operator_stack.top(),operator_stack.pop(),postfix[j++] = oper;//把符号输出到逆序表达式

double operatorPriority(char c) {//运算符优先级比较
if (c == '^')
return 3;
else if (c == '*' || c == '/')
return 2;
else if (c == '+' || c == '-')
return  1;
}

void ProcessingOperator(char &c, char &oper, string &num, stack<char>&operator_stack) {//i指向的表达是为运算符字符处理
if (!num.empty())
putNum();
if (operator_stack.empty())
operator_stack.push(c);
else if (operatorCmp(c, operator_stack.top()) >0) {
operator_stack.push(c);
}
else {
while (1) {
putOperator();
if (operatorCmp(c, oper) >0 || operator_stack.empty()) {
operator_stack.push(c);
break;
}
}
}
}

int midToPostfix() {//中缀转后缀，返回int是指括号后面是否直接是数字
int flag = 0;
stack<char>operator_stack;
string num;
char c, oper;
for (; expression[i] != '\0'; i++) {
c = expression[i];
if (c == '(') {
if (isdigit(expression[i - 1]) || expression[i - 1] == ')')//遇到3（4）(3)的情况，要在括号前自行处理省去的*
{
c = '*';
ProcessingOperator(c, oper, num, operator_stack);
}
i++;
if (midToPostfix())//处理(4)4的情况
{
c = '*';
ProcessingOperator(c, oper, num, operator_stack);
}
continue;
}
else if (c == ')') {
if (isdigit(expression[i + 1]))
flag = 1;
break;
}
else if (isdigit(c) || c == '.')
num += c;
else {//运算符
ProcessingOperator(c, oper, num, operator_stack);
}
}
if (!num.empty())//处理表达式最后的数字
postfix[j++] = num;
while (!operator_stack.empty()) {//处理留在栈的运算符
postfix[j++] = operator_stack.top();
operator_stack.pop();
}
if (flag)
return 1;
else
return 0;
}

double operatorCmp(char c1, char c2) {
double t1, t2;
t1 = operatorPriority(c1);
t2 = operatorPriority(c2);
return t1 - t2;
}

main.cpp

#include"tree.h"
#include"fatal.h"

extern double operatorPriority(char c);
extern double operatorCmp(char c1, char c2);

struct TreeNode {
ElementType element;
Tree left;
Tree right;
};

Tree createSearchTree()
{
return NULL;
}

void makeEmpty(Tree t) {
if (t) {
makeEmpty(t->left);
makeEmpty(t->right);
free(t);
}
}

Tree insert(ElementType X, Tree t) {
if (t == NULL) {//包含树没有初始化
t = new TreeNode;
if (t == NULL)
Error("out of memory");
t->element = X;
t->left = NULL;
t->right = NULL;
}
else {
if (X < t->element)
t->left = insert(X, t->left);
else if (X>t->element)
t->right = insert(X, t->right);
}
return t;//两种情况
}

void PrintinOrder(Tree t)
{
if (t->left)
{
if (operatorCmp(t->element[0], t->left->element[0]) > 0)
{
printf("(");
PrintinOrder(t->left);
printf(")");
}
else
PrintinOrder(t->left);
}
printf("%s", t->element.c_str());
if (t->right)
{
if (operatorCmp(t->element[0], t->right->element[0]) > 0)
{
printf("(");
PrintinOrder(t->right);
printf(")");
}
else
PrintinOrder(t->right);
}

}