1.直接求解

遇到数字直接放入操作数栈,遇到操作符则根据规则进行操作

#include<bits/stdc++.h>
using namespace std;
unordered_map<char,int>priority{{'+',1},{'-',1},{'*',2},{'/',2}};
stack<int>num;
stack<char>op;
void eval()
{
    int res=0;
    int a=num.top();
    num.pop();
    int b=num.top();
    num.pop();
    char x=op.top();
    op.pop();
    if(x=='+')res=b+a;
    if(x=='-')res=b-a;
    if(x=='*')res=b*a;
    if(x=='/')res=b/a;
    num.push(res);
}
int main()
{
    string s;
    cin>>s;
    for(int i=0;i<s.size();i++)
    {
        if(isdigit(s[i]))
        {
            int j=i,x=0;
            while(j<s.size()&&isdigit(s[j]))
            {
                x=10*x+s[j]-'0';
                j++;
            }
            num.push(x);
            i=j-1;
        }
        else if(s[i]=='(')
            op.push(s[i]);
        else if(s[i]==')')
        {
            while(op.top()!='(')
                eval();
            op.pop();
        }
        else
        {
            while(op.size()&&priority[op.top()]>=priority[s[i]])
                eval();
            op.push(s[i]);
        }
    }
    while(op.size())eval();
    cout<<num.top();
    return 0;
}

2.将中缀表达式转换为后缀表达式后进行解决

(1)中缀转后缀:遇到数字直接加入后缀表达式,遇到操作符则根据规则进行操作

(2)后缀表达式求值:从左到右扫描,遇到数字入操作数栈,遇到操作符操作离它最近的两个操作数,再入栈

数字

#include<bits/stdc++.h>
using namespace std;
unordered_map<char,int>priority{{'+',1},{'-',1},{'*',2},{'/',2}};
string infixToPostfix(string infix)
{
    string postfix;
    stack<char>op;
    for(int i=0;i<infix.size();i++)
    {
        if(isdigit(infix[i]))postfix+=infix[i];
        else if(infix[i]=='(')op.push(infix[i]);
        else if(infix[i]==')')
        {
            while(!op.empty()&&op.top()!='(')
            {
                postfix+=op.top();
                op.pop();
            }
            if(op.empty())
                return "Invalid Expression!";
            op.pop();
        }
        else
        {
            if(!op.empty()&&priority[op.top()]>=priority[infix[i]])
            {
                postfix+=op.top();
                op.pop();
            }
            op.push(infix[i]);
        }
    }
    while(op.size())
    {
        if(op.top()=='(')
            return "Invalid Expression";
        postfix+=op.top();
        op.pop();
    }
    return postfix;
}
int get(string postfix)
{
    stack<int>num;
    for(char x : postfix)
    {
        if(isdigit(x))num.push(x-'0');
        else
        {
            int a=num.top();
            num.pop();
            int b=num.top();
            num.pop();
            if(x=='+')num.push(b+a);
            if(x=='-')num.push(b-a);
            if(x=='*')num.push(b*a);
            if(x=='/')num.push(b/a);
        }
    }
    return num.top();
}
int main(){
    string infix;
    cin>>infix;
    string postfix=infixToPostfix(infix);
    cout<<postfix<<endl;
    cout << get(postfix) << endl;
    return 0;
}

字母

#include<bits/stdc++.h>
using namespace std;
unordered_map<char,int>priority{{'+',1},{'-',1},{'*',2},{'/',2}};
string infixToPostfix(string infix)
{
    string postfix;
    stack<char>op;
    for(int i=0;i<infix.size();i++)
    {
        if((infix[i]>='a'&&infix[i]<='z')||(infix[i]>='A'&&infix[i]<='Z'))
            postfix+=infix[i];
        else if(infix[i]=='(')op.push(infix[i]);
        else if(infix[i]==')')
        {
            while(!op.empty()&&op.top()!='(')
            {
                postfix+=op.top();
                op.pop();
            }
            if(op.empty())
                return "Invalid Expression!";
            op.pop();
        }
        else
        {
            if(!op.empty()&&priority[op.top()]>=priority[infix[i]])
            {
                postfix+=op.top();
                op.pop();
            }
            op.push(infix[i]);
        }
    }
    while(op.size())
    {
        if(op.top()=='(')
            return "Invalid Expression";
        postfix+=op.top();
        op.pop();
    }
    return postfix;
}
int main(){
    string infix;
    cin>>infix;
    string postfix=infixToPostfix(infix);
    cout<<postfix<<endl;
    return 0;
}