前中后缀表达式与表达式树

[code]#include <string>
#include <iostream>
#include <iomanip>
#include <stack>

using namespace std;

//表达式树的节点类
typedef struct _node_{
    union{
        char opt;
        double value;
    };
    _node_ *left, *right;
}node;

//为了非递归实现中缀直接转树的算法，模拟系统调用栈的历史记录写的record
struct record{
    node *root;
    int left, right;
    record(node *root, int left, int right){
        this->root = root;
        this->left = left;
        this->right = right;
    }
};

//表达式树类
class exptree{
public:
    //运算符最高优先级
    static const int max_priority = 20;
    //是运算符
    static int is_operator(char c)
    {
        if (c == '+' || c == '-' || c == '*' || c == '/' || c == '%' || c == '^' || c == 'e' || c == 'E') return 1;
        return 0;
    }
    //返回运算符优先级
    static int get_priority(char c)
    {
        switch (c)
        {
        case '+':
        case '-':return 1;
        case '*':
        case '/':
        case '%':return 2;
        case 'e':
        case 'E':return 3;
        case '^':return 4;
        default:return -1;
        }
    }
    //数字串转double
    static double get_double(char *mid, int left, int right)
    {
        int nfloat = right;
        double dtemp = 0;
        for (int i = left; i <= right; i++)
        {
            if (mid[i] == ' ')continue;
            if (mid[i] == '.'){
                nfloat = i;
                continue;
            }
            dtemp = 10 * dtemp + mid[i] - '0';
        }//求得itemp
        nfloat = right - nfloat;
        while (nfloat-- != 0)dtemp /= 10.0;//算得实际大小
        return dtemp;
    }
    //返回a，b运算的结果
    static double calculate(char c, double a, double b)
    {
        switch (c)
        {
        case '+':return a + b;
        case '-':return a - b;
        case '*':return a * b;
        case '/':return a / b;
        case '%':return (int)a % (int)b;
        case 'e':
        case 'E':return a*pow(10, b);
        default:
            break;
        }
        return -1;
    }
    //前缀建表达式树算法，root是表达式树根结点
    static void pre_to_tree(char *pre, node *root)
    {
        int left, right;//数字串的左右边界
        stack<node*> tstack;
        //前缀表达式转树，逆序建树
        for (int pos = strlen(pre) - 1; pos > -1; pos--)
        {
            if (isdigit(pre[pos]))
            {
                right = pos;//数字串右端点
                while (isdigit(pre[pos]) || pre[pos] == '.')pos--;
                left = pos + 1;//数字串左端点
                node *child = new node();
                child->value = get_double(pre, left, right);
                child->left = child->right = nullptr;
                tstack.push(child);
            }//数字节点入栈
            if (is_operator(pre[pos]))
            {
                node *root = new node();
                root->opt = pre[pos];
                root->left = tstack.top();
                tstack.pop();
                root->right = tstack.top();
                tstack.pop();
                tstack.push(root);
            }//是运算符，出栈左右操作数，建新树
        }
        root = tstack.top();//返回栈顶指针地址
    }//前缀建树
    //中缀直接转树的分治递归算法，mid是中缀表达式
    //root是表达式树根，left，right是左右端点
    static void mid_to_tree(char *mid, node *root, int left, int right)
    {
        int power = 1;//计算当前所在括号的层数，最外层为1
        int position = -1;//最低优先级运算符的位置
        //为寻找低优先级，运算符，需要设当前优先级为最高优先级
        int priority = 0x0FFFFFFF;
        for (int pos = left; pos <= right; pos++)
        {
            if (mid[pos] == '(')power++;//括号内优先级高
            if (mid[pos] == ')')power--;//括号外优先级低
            if (is_operator(mid[pos]))
            {
                if (max_priority * power + get_priority(mid[pos]) <= priority)
                {
                    priority = max_priority * power + get_priority(mid[pos]);//记录当前优先级
                    position = pos;//记录运算符位置
                }//power + get_priority(mid[pos])为全局优先级
            }//是运算符
        }//寻找全局最低优先级运算符
        if (position != -1)
        {
            root->opt = mid[position];
            root->left = new node();//创建左子结点
            root->right = new node();//创建右子节点
            mid_to_tree(mid, root->left, left, position - 1);//递归左表达式
            mid_to_tree(mid, root->right, position + 1, right);//递归右表达式
        }//有运算符
        else
        {
            //分段递归边界未考虑左右括号，需要处理数字段左右的括号空格
            while (mid[left] == '(' || mid[left] == ' ')left++;
            while (mid[right] == ')' || mid[right] == ' ')right--;
            //根据数字串的左右边界计算数字串的值
            root->value = get_double(mid, left, right);
            root->left = root->right = nullptr;
        }//无运算符，是数字
    }
    //中缀表达式直接转树的非递归算法（非递归前序遍历二叉树）
    static void mid_to_tree(char *mid, node *root)
    {
        int count = 0;
        root = new node();
        stack<record*> tstack;
        record *rec = new record(root, 0, strlen(mid) - 1);
        tstack.push(nullptr);//栈底监视哨
        while (!tstack.empty()){
            int power = 1;//计算当前所在括号的层数，最外层为1
            int position = -1;//最低优先级运算符的位置
            //为寻找低优先级，运算符，需要设当前优先级为最高优先级
            int priority = INT_MAX;
            for (int pos = rec->left; pos <= rec->right; pos++)
            {
                if (mid[pos] == '(')power++;//括号内优先级高
                if (mid[pos] == ')')power--;//括号外优先级低
                if (is_operator(mid[pos]))
                {
                    if (max_priority * power + get_priority(mid[pos]) <= priority)
                    {
                        //记录当前优先级
                        priority = max_priority * power + get_priority(mid[pos]);
                        position = pos;//记录运算符位置
                    }//power + get_priority(mid[pos])为全局优先级
                }//是运算符
            }//寻找全局最低优先级运算符
            if (position != -1)
            {
                //建立根结点
                rec->root->opt = mid[position];
                rec->root->left = new node();
                rec->root->right = new node();
                //右子树入栈
                tstack.push(new record(rec->root->right, position + 1, rec->right));
                //左子树下降
                rec = new record(rec->root->left, rec->left, position - 1);
            }//有运算符，是新树根
            else
            {
                //去掉数字两边的括号和空格
                while (mid[rec->left] == '(' || mid[rec->left] == ' ')rec->left++;
                while (mid[rec->right] == ')' || mid[rec->right] == ' ')rec->right--;
                //取得数字段的值赋给root->value
                rec->root->value = get_double(mid, rec->left, rec->right);
                rec->root->left = rec->root->right = nullptr;
                //左子树访问完毕，转右子树
                rec = tstack.top();
                tstack.pop();
            }//无运算符，是数字节点
        }
    }
    //后缀建表达式树算法
    static void pst_to_tree(char *pst, node *root)
    {
        int left, right;//数字串的左右边界
        stack<node*> tstack;//表达式树栈
        for (int pos = 0; pos < strlen(pst); pos++){
            if (isdigit(pst[pos])){
                node *child = new node();
                child->value = 0;
                left = pos;
                while (isdigit(pst[++pos]));
                right = pos - 1;
                child->value = get_double(pst, left, right);
                child->left = child->right = nullptr;
                tstack.push(child);
            }//是数字，建立数字节点
            if (is_operator(pst[pos])){
                node *root = new node();
                root->opt = pst[pos];
                root->right = tstack.top();
                tstack.pop();
                root->left = tstack.top();
                tstack.pop();
                tstack.push(root);
            }//是运算符，出栈，建立子树压入栈
        }
        root = tstack.top();//返回栈顶指针地址
    }//后缀建树
    //前中后序递归遍历表达式树
    static void pre_traverse_tree(node *root, int pos)
    {
        if (root)
        {
            if (root->left&&root->right)
                cout << setw(pos * 5) << root->opt << endl;
            else
                cout << setw(pos * 5) << root->value << endl;
            pre_traverse_tree(root->left, pos + 1);
            pre_traverse_tree(root->right, pos + 1);
        }
    }
    static void mid_traverse_tree(node *root, int pos)
    {
        if (root)
        {
            mid_traverse_tree(root->left, pos + 1);
            if (root->left&&root->right)
                cout << setw(pos * 5) << root->opt << endl;
            else
                cout << setw(pos * 5) << root->value << endl;
            mid_traverse_tree(root->right, pos + 1);
        }
    }
    static void pst_traverse_tree(node *root, int pos)
    {
        if (root)
        {
            pst_traverse_tree(root->left, pos + 1);
            pst_traverse_tree(root->right, pos + 1);
            if (root->left&&root->right)
                cout << setw(pos * 5) << root->opt << endl;
            else
                cout << setw(pos * 5) << root->value << endl;
        }
    }
    //表达式树转前中后缀表达式
    static void tree_to_pre(node *root)
    {
        if (root){
            if (root->left&&root->right)
                cout << root->opt << " ";
            else
                cout << root->value << " ";
            tree_to_pre(root->left);
            tree_to_pre(root->right);
        }
    }
    static void tree_to_mid(node *root)
    {
        if (root)
        {
            if (root->left){
                if (root->left->left&&root->left->right){
                    if (get_priority(root->opt) > get_priority(root->left->opt)){
                        cout << "(";
                    }
                }
            }//左子树加左括号
            tree_to_mid(root->left);
            if (root->left){
                if (root->left->left&&root->left->right){
                    if (get_priority(root->opt) > get_priority(root->left->opt)){
                        cout << ")";
                    }
                }
            }//左子树加右括号
            if (root->left&&root->right)
                cout << root->opt;
            else
                cout << root->value;
            if (root->right){
                if (root->right->left&&root->right->right){
                    if (get_priority(root->opt) > get_priority(root->right->opt)){
                        cout << "(";
                    }
                }
            }//右子树加左括号
            tree_to_mid(root->right);
            if (root->right){
                if (root->right->left&&root->right->right){
                    if (get_priority(root->opt) > get_priority(root->right->opt)){
                        cout << ")";
                    }
                }
            }//右子树加右括号
        }
    }
    static void tree_to_pst(node *root)
    {
        if (root)
        {
            tree_to_pst(root->left);
            tree_to_pst(root->right);
            if (root->left&&root->right)
                cout << root->opt << " ";
            else
                cout << root->value << " ";
        }
    }
    //计算表达式值
    static double calculate(node *root)
    {
        if (!root->left&&!root->right)return root->value;
        return calculate(root->opt, calculate(root->left), calculate(root->right));
    }
};//所有成员方法都是静态的，相当于一个建表达式树的函数库