中缀 后缀表达式求值

一.中缀转后缀

1.遇到操作数：直接输出（添加到后缀表达式中）
2.栈为空时，遇到运算符，直接入栈
3.遇到左括号：将其入栈
4.遇到右括号：执行出栈操作，并将出栈的元素输出，直到弹出栈的是左括号，左括号不输出。
5.遇到其他运算符：例如加减乘除：弹出所有优先级大于或者等于该运算符的栈顶元素，然后将该运算符入栈。
6.最终将栈中的元素依次出栈，输出。

二.由后缀表达式得到表达式树

三.对表达式树的根节点调用cal()虚函数就能算出表达式的值

代码

#include<iostream>#include<string>#include<map>#include<stack>using namespace std;map<char, int> m{{'*', 3}, {'/', 3},{'+', 4}, {'-', 4},{'(', 99}};//定义优先级 class node{public:virtual double cal() const = 0;virtual ~node () {}}; class numnode : public node{public:numnode(double d):number(d){}virtual double cal() const;private:double number;};class binarynode : public node{protected:node* _left;node* _right;public:binarynode(node* left, node* right):_left(left),_right(right){}~binarynode();};class addnode : public binarynode{public:addnode(node* left, node* right):binarynode(left, right){};virtual double cal() const;};class mutinode : public binarynode{public:mutinode(node* left, node* right):binarynode(left, right){};virtual double cal() const;};inline double numnode::cal() const{return number;}binarynode::~binarynode() {delete _left;delete _right;}double addnode::cal() const{return _left->cal() + _right->cal();}double mutinode::cal() const{return _left->cal() * _right->cal();}string suffix(const string& str) //得到后缀表达式{stack<char> sta;string ret;for(int i=0; i<str.size(); i++){if( str[i]=='.' || (str[i]>='0' && str[i]<='9') ){ret += str[i];}else{if(ret.back() != ' ')ret += " " ;if( sta.empty() || str[i]=='(' )sta.push(str[i]);else if(str[i] == ')'){while(sta.top()!='('){ret.push_back(sta.top());ret.push_back(' '); sta.pop();}sta.pop();}else {while( !sta.empty() && m[str[i]]>=m[sta.top()] ){ret = ret + sta.top()+" ";sta.pop();}sta.push(str[i]);}}//cout<<i+1<<" "<<ret<<endl;}ret += " ";//确保每个数后边都有个空格 while(!sta.empty()){ret = ret + sta.top()+" ";sta.pop();}return ret;}node* suffix_tree(const string& str)//生成后缀表达式树{stack<node*> sta;string temp;node* left;node* right;for(int i=0; i<str.size(); i++){//cout<<i<<endl;if( str[i]=='.' || (str[i]>='0' && str[i]<='9') ){temp += str[i];//cout<<"temp"<<temp<<endl;}else if(str[i]==' ' && str[i-1]>='0' && str[i-1]<='9' ){double d = stod(temp);node *pnode = new numnode(d);sta.push(pnode);temp = "";}else if(str[i]==' ')continue;else switch(str[i]){case '+':right = sta.top();sta.pop();left = sta.top();sta.pop();sta.push(new addnode(left,right));break;case '*':right = sta.top();sta.pop();left = sta.top();sta.pop();sta.push(new mutinode(left,right));break;}}return sta.top();}int main(){string temp = "11.0+22*33+(44.0*55+66)*77";cout<<"11.0+22*33+(44.0*55+66)*77的后缀表达式：";//11.0 22 33 * + 44.0 55 * 66 + 77 * +string sur = suffix(temp);cout<<sur<<endl;node* root = suffix_tree(sur);double x = root->cal();cout << x << endl;//192159delete root;}

还有一种不面向对象的。

一.中缀转后缀

二.由后缀直接得到结果

#include<iostream>#include<string>#include<map>#include<stack>using namespace std;map<char, int> m{{'*', 3}, {'/', 3},{'+', 4}, {'-', 4},{'(', 99}};string suffix(const string& str){stack<char> sta;string ret;for(int i=0; i<str.size(); i++){if(str[i]>='0' && str[i]<='9'){ret += str[i];}else{if(ret.back() != ' ')ret += " " ;if( sta.empty() || str[i]=='(' )sta.push(str[i]);else if(str[i] == ')'){while(sta.top()!='('){ret = ret + sta.top()+" ";sta.pop();}sta.pop();}else {while( !sta.empty() && m[str[i]]>=m[sta.top()] ){ret = ret + sta.top()+" ";sta.pop();}sta.push(str[i]);}}//cout<<i+1<<" "<<ret<<endl;}ret += " ";//确保每个数后边都有个空格 while(!sta.empty()){ret = ret + sta.top()+" ";sta.pop();}return ret;}int cal(const string &str){stack<int> sta;string temp;int left = 0;int right = 0;for(int i=0; i<str.size(); i++){//cout<<i<<endl;if(str[i]>='0' && str[i]<='9'){temp += str[i];//cout<<"temp"<<temp<<endl;}else if(str[i]==' ' && str[i-1]>='0' && str[i-1]<='9' ){sta.push(stoi(temp));temp = "";}else if(str[i]==' ')continue;else switch(str[i]){case '+':right = sta.top();//cout<<"right"<<right<<endl;sta.pop();left = sta.top();//cout<<"left"<<left<<endl;sta.pop();sta.push(left+right);//cout<<"jia"<<sta.top() <<endl;break;case '*':right = sta.top();//cout<<"right"<<right<<endl;sta.pop();left = sta.top();//cout<<"left"<<left<<endl;sta.pop();sta.push(left*right);//cout<<"cheng"<<sta.top() <<endl;break;}}return sta.top();}int main(){string temp = "11+22*33+(44*55+66)*77";cout<<"11+22*33+(44*55+66)*77的后缀表达式：";//11 22 33 *+ 44 55 *66 + 77 *+string sur = suffix(temp);cout<<sur<<endl;cout<<"表达式的和：";int sum = cal(sur);cout<<sum<<endl;}

参考：http://www.cnblogs.com/Solstice/archive/2012/07/06/learncpp.html
http://www.relisoft.com/book/lang/poly/3tree.html