假设表达式中的数都是1位正整数。
#include <iostream>
#include <string>
#include <stack>
#include <cctype>
using namespace std;
void infixToPostfix(string &infix, string &postfix);
int isp(char c);
int icp(char c);
double calPostfix(string &postfix);
int main(){
string infix, postfix;
cin>>infix;
infixToPostfix(infix, postfix);
cout<<postfix<<endl<<calPostfix(postfix);
return 0;
}
void infixToPostfix(string &infix, string &postfix){
infix.push_back('#');
stack<char> s;
s.push('#');
for(char c:infix){
if(c==' ') continue;
if(isalnum(c)) postfix.push_back(c);
else{
if(icp(c)==isp(s.top())) s.pop(); //()，##相遇直接退栈
else if(icp(c)<isp(s.top())){
//退栈并输出，直到isp(栈顶)<=scp(c)
while(icp(c)<isp(s.top())){
postfix.push_back(s.top());
s.pop();
}
if(icp(c)==isp(s.top())) s.pop();
else s.push(c);
}
else{
//入栈
s.push(c);
}
}
}
}
int isp(char c){
if(c=='#') return 0;
if(c=='(') return 1;
if(c=='+' || c=='-') return 3;
if(c=='*' || c=='/') return 5;
if(c==')') return 6;
return -1;
}
int icp(char c){
if(c=='#') return 0;
if(c=='(') return 6;
if(c=='+' || c=='-') return 2;
if(c=='*' || c=='/') return 4;
if(c==')') return 1;
return -1;
}
double calPostfix(string &postfix){
stack<double> operands;
for(char c:postfix){
if(isdigit(c)) operands.push(double(c-'0'));
else{
double a = operands.top();
operands.pop();
double b = operands.top();
operands.pop();
if(c=='+') operands.push(b+a);
else if(c=='-') operands.push(b-a);
else if(c=='*') operands.push(b*a);
else operands.push(b/a);
}
}
return operands.top();
}
进阶版：支持超过1位的正整数的运算。转出的后缀表达式以空格分隔。
#include <iostream>
#include <string>
#include <stack>
#include <cctype>
using namespace std;
void infixToPostfix(string &infix, string &postfix);
int isp(char c);
int icp(char c);
double calPostfix(string &postfix);
int main(){
string infix, postfix;
getline(cin, infix);
infixToPostfix(infix, postfix);
cout<<postfix<<endl<<calPostfix(postfix);
return 0;
}
void infixToPostfix(string &infix, string &postfix){
infix.push_back('#');
stack<char> s;
s.push('#');
int infix_len = infix.length();
for(int i=0; i<infix_len; ){
if(infix[i]==' '){
i++;
continue;
}
if(isdigit(infix[i])){
while(isdigit(infix[i])) postfix.push_back(infix[i++]);
postfix.push_back(' ');
}
else{
if(icp(infix[i])==isp(s.top())) s.pop(); //()，##相遇直接退栈
else if(icp(infix[i])<isp(s.top())){
//退栈并输出，直到isp(栈顶)<=scp(infix[i])
while(icp(infix[i])<isp(s.top())){
postfix.push_back(s.top());
postfix.push_back(' ');
s.pop();
}
if(icp(infix[i])==isp(s.top())) s.pop();
else s.push(infix[i]);
}
else{
//入栈
s.push(infix[i]);
}
i++;
}
}
}
int isp(char c){
if(c=='#') return 0;
if(c=='(') return 1;
if(c=='+' || c=='-') return 3;
if(c=='*' || c=='/') return 5;
if(c==')') return 6;
return -1;
}
int icp(char c){
if(c=='#') return 0;
if(c=='(') return 6;
if(c=='+' || c=='-') return 2;
if(c=='*' || c=='/') return 4;
if(c==')') return 1;
return -1;
}
double calPostfix(string &postfix){
stack<double> operands;
int postfix_len = postfix.length();
for(int i=0; i<postfix_len; ){
if(postfix[i]==' '){
i++;
continue;
}
if(isdigit(postfix[i])){
double c = 0;
while(isdigit(postfix[i])){
c = c * 10 + (postfix[i] - '0');
i++;
}
operands.push(c);
}
else{
double a = operands.top();
operands.pop();
double b = operands.top();
operands.pop();
if(postfix[i]=='+') operands.push(b+a);
else if(postfix[i]=='-') operands.push(b-a);
else if(postfix[i]=='*') operands.push(b*a);
else operands.push(b/a);
i++;
}
}
return operands.top();
}