数据结构 -- 算术运算器设计

这是数据结构的实验~~

由于某些实验要上交，所以一部分的程序的代码改为英语注释了

这是实现中缀表达式求解，根据用户输入的算术表达式，求解表达式的值。

这里支持括号()，小数，多位数。

采用栈实现，采用了C++STL的stack类。

代码可能有点繁杂，因为也进行了对一些输入错误的判断。

 

Experiment.h 算术运算器的基本算法

/* Experiment.h */// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - // 实验题 2.1 ：算术运算器设计． // 问题描述 :// 设计一个模拟计算器功能的程序，它读入一个表达式，// 如果是一个正确的表达式（即它由操作数、圆括号 和+ 、 - 、 * 、 / 四种运算符组成），// 则求出该表达式的值；否则给出某种错误信息。 // // 提示：// 读入一个以字符序列形式给出的以等号（ = ）结尾的表达式；// 程序中应考虑运算符的优先级、运算的合法性。 // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #include <cstdio>#include <stack>using namespace std;// - - - - base constant value - - - - - const int ERROR = 0x7f800000;// infiniteinline int NUMBER(char a)// translate the char to number{return (a - '0');}// - - - - data structure - - - - - //Operator setconst char OP[7] = {'+', '-', '*', '/', '(', ')', '='};//Operand setconst char NUM[11] = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '.'};//Priority tableconst char PRI[7][7] = {//'+' '-' '*' '/' '(' ')' '='{'>', '>', '<', '<', '<', '>', '>'}, // '+'{'>', '>', '<', '<', '<', '>', '>'}, // '-'{'>', '>', '>', '>', '<', '>', '>'}, // '*'{'>', '>', '>', '>', '<', '>', '>'}, // '/'{'<', '<', '<', '<', '<', '=', '~'}, // '('{'>', '>', '>', '>', '~', '>', '>'}, // ')'{'<', '<', '<', '<', '<', '~', '='}, // '='};// - - - - - - base functions - - - - - - bool IsOperator (const char c, const char OP[7]);bool IsNumber (const char num, const char NUM[11]);int Pos (const char op, const char OP[7]);char Precede (const char op1, const char op2, const char PRI[7][7]);float Operate (const float a, const char op, const float b);float EvaluateExpression();// evaluate the arithmetic expressionfloat EvaluateExpression(){// operator stack: OPND; operand stack: OPTRstack<float> OPND;stack<char>OPTR;// push the finishing char '='OPTR.push('=');char op;float a;float b;//IsExtend: true if the number is a long number//fractionNumber: the decimal numbersbool IsExtend;int fractionNumber;IsExtend = false;// c used to read the expressionchar c;c = getchar();// end when OPTR is empty and the expression is empty toowhile (c != '=' || OPTR.top() != '='){// - - - - - deal with the operand - - - - - - - - -IsExtend = false;while (IsNumber(c, NUM)){// deal with the first char of a numberif (!IsExtend){if(c == '.'){//error: '.' is ahead of the number return ERROR;}OPND.push(NUMBER(c));c = getchar();}// deal with the other char of a numberelse{// deal with the decimal fraction partif (c == '.'){c = getchar();b = 0;fractionNumber = 0;while(IsNumber(c, NUM)){if (c == '.'){//error: multi '.' in one numberreturn ERROR;}b = b *10 + NUMBER(c);c = getchar();fractionNumber++;}while (fractionNumber > 0){b = b / 10;fractionNumber--;}a = OPND.top();OPND.pop();OPND.push(a + b);}// deal with the non-decimal fraction partelse{a = OPND.top();OPND.pop();if (a == 0.0){//error: number start with a zeroreturn ERROR;}OPND.push(a * 10 + NUMBER(c));c = getchar();}}IsExtend = true;}// - - - - - deal with the operator - - - - - - - - -if(IsOperator(c, OP)){// compare the priorityswitch(Precede(OPTR.top(), c, PRI)){// push the operatorcase '<':OPTR.push(c);c = getchar();break;// pop a operatorcase '=':OPTR.pop();c = getchar();break;// pop tow operands and a operator, operate them with the operator case '>':op = OPTR.top();OPTR.pop();b = OPND.top();OPND.pop();a = OPND.top();OPND.pop();OPND.push(Operate(a, op, b)); break;// '~' means an errorcase '~':return ERROR; break;default:return ERROR; break;}}else{//error: illegal letter in the expressionreturn ERROR;}}return OPND.top();}//return true when c is in the operator set OP[7]bool IsOperator(const char c, const char OP[7]){int i;for (i=0; i<7; i++){if (c == OP[i]){return true;}}return false;}//return true when num is in the operand set NUM[11]bool IsNumber(const char num, const char NUM[11]){int i;for (i=0; i<11; i++){if (num == NUM[i]){return true;}}return false;}// return the operator op's position in the operator setint Pos(const char op, const char OP[7]){int i;for (i=0; i<7; i++){if (op == OP[i]){return i;}}return -1;}//return the priority of op1 and op2char Precede(const char op1, const char op2, const char PRI[7][7]){if (!IsOperator(op1, OP) || !IsOperator(op2, OP)){return '~';}int i;int j;i = Pos(op1, OP);j = Pos(op2, OP);return PRI[i][j];}//return the result of a operate b with operator op float Operate(const float a, const char op, const float b){if (!IsOperator(op, OP)){return ERROR;}switch(op){case '+':return a + b;break;case '-':return a - b;break;case '*':return a * b; break;case '/':if (b == 0.0){return ERROR;}else{return a / b;} break;default:return ERROR; break;}}

 

test.cpp 应用算术运算器求解用户输入表达式

/* test.cpp */#include "Experiment2_1.h"#include <iostream>using namespace std;int main(){cout<<"/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /"<<endl;cout<<"/ - 实验题2.1：算术运算器设计． - /"<<endl;cout<<"/ - - /"<<endl;cout<<"/ - 运算数规定： - /"<<endl;cout<<"/ - 支持浮点数的运算，运算数可以多位 - /"<<endl;cout<<"/ - - /"<<endl;cout<<"/ - 输入规则： - /"<<endl;cout<<"/ - 中缀表达式输入，输入过程中不能输入空格，回车，制表符 - /"<<endl;cout<<"/ - 表达式以‘=’为结束符，输入完成后按回车 - /"<<endl;cout<<"/ - 例：1.5*2+(12-8/6)= - /"<<endl;cout<<"/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /"<<endl;cout<<endl;float result;cout<<"/ - 请输入表达式：";result = EvaluateExpression();cout<<endl;if (result == ERROR){cout<<"/ - 表达式不正确，请修正表达式。"<<endl;}else{cout<<"/ - 表达式的值 = "<<result<<endl;}cout<<endl;return 0;}