先將中綴表達式利用棧轉換爲後綴表達式,而後再利用棧由後綴表達式計算算數表達式的值,具體代碼以下:ios
#include <iostream> using namespace std; #include <string> #include <vector> #include <stack> enum Type { OP_NUM, OP_SYMBOL, }; enum Operat { ADD, SUB, MUL, DIV, }; struct Cell { Type _type; int _num; }; //input = 1 + ((2 + 3) * 4) - 5; //中綴到後綴 string topolishNotation(const char* input) { stack<char> s1; //運算符 stack<char> s2; //數字 size_t iCount = 0; while (input[iCount] != '\0') { //是數字將其壓入s2 if (input[iCount] >= '0'&& input[iCount] <= '9') { while (input[iCount] != '\0' && input[iCount] >= '0'&& input[iCount] <= '9') { s2.push(input[iCount++]); } s2.push(' '); --iCount; //最後會統一加1,因此先減一 } //是運算符比較其與S1棧頂運算符的優先級 while (input[iCount] == '+' || input[iCount] == '-' || input[iCount] == '*' || input[iCount] == '/') { //s1爲空,或棧頂運算符爲左括號「(」,則直接將此運算符入棧 if (s1.empty() || s1.top() == '(') { s1.push(input[iCount]); break; } //不然,若優先級比棧頂運算符的高,也將運算符壓入s1 else if ((input[iCount] == '*' || input[iCount] == '/') && (s1.top() == '+' || s1.top() == '-')) { s1.push(input[iCount]); break; } //不然,將S1棧頂的運算符彈出並壓入到S2中,再次與S1中新的棧頂運算符相比較 else { s2.push(s1.top()); s1.pop(); } } //若是是左括號「(」,則直接壓入S1; if (input[iCount] == '(') { s1.push(input[iCount]); } /*若是是右括號「)」,則依次彈出S1棧頂的運算符,並壓入S2, *直到遇到左括號爲止,此時將這一對括號丟棄;*/ if (input[iCount] == ')') { while (s1.top() != '(') { s2.push(s1.top()); s1.pop(); } s1.pop(); //將'('也出棧 } ++iCount; //統一加一次 } //將S1中剩餘的運算符依次彈出並壓入S2; while (!s1.empty()) { s2.push(s1.top()); s1.pop(); } string ret; while (!s2.empty()) { ret.push_back(s2.top()); s2.pop(); } reverse(ret.begin(), ret.end()); return ret; } //後綴到數組 vector<Cell> StrBehindToVect(const string& strBehind) { vector<Cell> call; size_t iCount = 0; while (strBehind[iCount] != '\0') { if (strBehind[iCount] >= '0' && strBehind[iCount] <= '9') { int ret = 0; while (strBehind[iCount] != '\0' && strBehind[iCount] >= '0' && strBehind[iCount] <= '9') { ret = ret * 10 + strBehind[iCount] - '0'; ++iCount; } call.push_back({ OP_NUM, ret }); --iCount; } else if (strBehind[iCount] == '+') { call.push_back({ OP_SYMBOL, ADD }); } else if (strBehind[iCount] == '-') { call.push_back({ OP_SYMBOL, SUB }); } else if (strBehind[iCount] == '*') { call.push_back({ OP_SYMBOL, MUL }); } else if (strBehind[iCount] == '/') { call.push_back({ OP_SYMBOL, DIV }); } ++iCount; } return call; } //計算值 int RPNCount(const vector<Cell>& array, size_t size) { stack<int> val; for (size_t i = 0; i < size; ++i) { if (array[i]._type == OP_NUM) { val.push(array[i]._num); } else { int right = val.top(); val.pop(); switch (array[i]._num) { case ADD: val.top() += right; break; case SUB: val.top() -= right; break; case MUL: val.top() *= right; break; case DIV: if (right == 0) { throw(array[i]); } val.top() /= right; break; default: cout << "請輸入合法字符" << endl; exit(0); }/*switch*/ } } return val.top(); } int main() { string strMid = "12 * (3 + 4) - 6 + 8 / 2"; string strBehind = topolishNotation(strMid.c_str()); vector<Cell> call = StrBehindToVect(strBehind); try { int ret = RPNCount(call, call.size()); cout << ret << endl; } catch (Cell) { cout << "除數爲0!" << endl; } system("pause"); return 0; }