表达式的转换----->中缀表达式转后缀表达式

要做该题的基础可以参考：https://blog.csdn.net/mhxy199288/article/details/38025319

题目链接：http://www.noobdream.com/DreamJudge/Issue/page/1063/

通过代码：

#include <iostream>
#include <stack>
#include <string>
#include <queue>
#include <vector>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#define ll long long

using namespace std;

string expr;

struct Priority{
    int p;// 表示优先级
    char op;// 操作运算符 
};

Priority ps[5] = {{1,'+'},{1,'-'},{2,'*'},{2,'/'},{3,'^'}}; 

// 比较运算符优先级 
int getPriority(char a, char b) {
    int a1, b1;
    
    for (int i = 0; i < 5; i++) {
        if (ps[i].op == a) {
            a1 = ps[i].p;
        }
        if (ps[i].op == b) {
            b1 = ps[i].p;
        }
    }
    return a1 > b1 ? 1 : 0;
} 

// 把表达式(中缀表达式)转成后缀表达式 
stack<char> parsing(string &expr) {
    stack<char> ret;// 存放最终结果 
    stack<char> opr;// 存放运算符 
    // 开始转换 
    for (int i = 0; i < expr.size(); i++) {
        char ch = expr[i];
        if (ch == ' ') continue;
        if (ch >= '0' && ch <= '9') {
            ret.push(ch);
        }else {
            if (opr.empty() || ch == '(') {
                opr.push(ch);
            }else if (ch ==')') {
                while(!opr.empty() && opr.top() != '(') {
                    ret.push(opr.top());
                    opr.pop();
                }
                opr.pop(); 
            }else {
                while((!opr.empty()) && (opr.top() != '(')) {
                    if (getPriority(ch, opr.top()) == 0) {
                        ret.push(opr.top());
                        opr.pop();
                    }else break;
                }
                
                opr.push(ch);
            }
        }
    }
    
    // 把最后的运算符放到栈中 
    while(!opr.empty()) {
        ret.push(opr.top());
        opr.pop();
    }
    return ret;
}

ll cal(ll a, ll b, char op) {
    switch(op) {
        case '+': return a+b; break;
        case '-': return a-b; break;
        case '*': return a*b; break;
        case '/': return a/b; break;
        case '^': return pow(a, b); break;
        default: break;
    }
}

void print(stack<ll> s, string &str, int start) {
    
    vector<ll> ans;
    int i = 1;
    while(!s.empty()) {
        ans.push_back(s.top());
        s.pop();
    }
    for (i = ans.size()-1; i >= 0; i--)
        cout << ans[i] << " ";
    for (i = start; i < str.size(); i++)
        cout << str[i] << " ";
    cout << endl;
}

// 求后缀表达式的值 
void getRes(string &expr) {
    stack<char> bls = parsing(expr);
    stack<ll> s;
    string str = "";
    char ch;
    int a, b, res = 0;
    while(!bls.empty()) {
        str = bls.top() + str;
        bls.pop();
    }
    if (str.size() == 1) res = str[0]-'0';// 如果只有一位运算数 
    else {
        for (int i = 0; i < str.size(); i++) {
            ch = str[i];
            if (ch >= '0' && ch <= '9')
                s.push(ch-'0');
            else {
                print(s, str, i);//打印 
                b = s.top(); s.pop();
                a = s.top(); s.pop();
                res = cal(a,b,ch);
                s.push(res); 
            }
        }
    }
    cout << res << endl;
}

int main() {
    while(cin >> expr) {
        getRes(expr);
    }
    return 0;
}

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