C語言 利用后綴表達式解析字符串（符合c98標準，很容易移植到計算器上）

最近用98標準的C語言寫了個解析字符串，類似于JavaScript中的eval函數，感覺挺實用（移植到了計算器上，可以畫F(X,Y)==0這種圖像了），特此分享一下，大家可以使用。

有了這個函數，就能像js，python那樣輕松解析字符串，移植到計算器上就能實現更好玩的功能了，更方便，特此分享。

感謝這篇文章給的啟發，不會轉后綴表達式的可以看看這篇，寫的很詳細
波蘭式、逆波蘭式與表達式求值 - 刺猬的溫馴 - 博客園

源代碼在最底下！

1、支持的函數

邏輯表達式：
>,<,==(注意是雙等于號),<=,>=,&(and),|(or),~(not)
注意，在本解析字符串程序中，用戶輸入值0代表邏輯false，非0代表邏輯true（true默認為1，也就是2==2返回的值是1）
數學運算符：
+,-,*,/,%(求模),^(乘方),!(階乘),#(負號，一般會自動區分負號和減號)
符號：
括號，逗號
函數：
三角函數 sin(x) cos(x) tan(x) asin(x) acos(x) atan(x)
如果不在定義域則返回0
隨機數 rand(x,y)(返回[x,y]間的整數，需要srand)
弧度轉角度 deg(x) 角度轉弧度 rad(x)
條件表達式 if(條件,x,y),其中當條件計算結果非0，則返回表達式x的值，否則返回表達式y的值
對數 log(x,y)返回以x為底y的對數 ln(x)返回以e為底的自然對數
自然數的n次方 exp(x),返回e^x
最大最小值 max(x,y)返回表達式x和表達式y的較大的一個，min相反
取符號 sign(x) 如果x大于等于0，返回1，否則返回-1
四舍五入 round(x) 向下取整 floor(x)
絕對值 abs(x) 返回x的絕對值
開平方 sqrt(x) 返回x開平方的值
開n次方可以用運算符“ ^ ”代替

2、用法

#include<eval.c>

很簡單，就一行：

直接調用

double eval(char* str);

其中str為表達式，以’ 0 '結束

3、效果

計算0.5+6+3*5的結果為21.5

中間兩行分別是中綴表達式和后綴表達式

計算sin(1.57)+cos(if(1>0,0,1))的結果為2.0（三角函數的精度不太好，湊合吧）

其中if(1>0,0,1)，if函數接受3個參數，第一個參數是條件，顯然條件成立，返回第二個參數（表達式）的結果的值，就是0，即計算sin(1.57)+cos(0)

注意到：sin在中綴表達式和后綴表達式被替換為了J

cos被替換為了K。

因為注意到單字符的方便性，就用replaceString()函數替換為單字符大寫字符。所以，要注意不要讓用戶輸入大寫字母！

圖中間兩行輸出可以在代碼中注釋掉。

附幾張移植到計算器上的解析字符串效果圖

（畫復雜函數圖像的，例如sin(X)<cos(Y)這種函數的圖像）

4、思路

這里我用例子解釋。

假如用戶輸入“-sin(12.57)-cos(-6)”

規定：如果減號“-”出現在符號后面（不包括右括號）或者出現在字符串開頭，就替換為負號“#”，負號是一元運算符，減號是二元運算符，所以有必要區分。

故原字符串被替換為“#sin(12.57)-cos(#6)”

由于sin，cos是多字符不好處理，則替換為單字符（這里我用A-Z）,故替換為“#J(12.57)-K(#6)”

接下來只需要區分是符號還是數字即可。

讀入#是符號
讀入J是符號
讀入(是符號（以上都是轉后綴表達式的標準操作，不再贅述，詳細可見開頭推薦的博客）
讀入1是數字，不確定是不是一個完整的數字，則存在number里，
讀入2是數字，將原來的number*10+2。
讀入.表明接下來的數字是小數部分了。
讀入5，number+=pow(10,-1)*5
讀入7，number+=pow(10,-2)*7
當讀入符號或者到字符串末尾時，講存的數字保存下來，并且清空。
以此類推

這樣子符號和數字就被區分開了，并且轉為后綴表達式了。

接下來就只需要運行后綴表達式的求值和控制好優先級了。

因為我這個算法的特殊性，以下的奇葩寫法也能計算出正確結果：

sin7
7sin
(7)sin

如有需要，請讀者自行編寫語法分析。

5、源代碼（符合c98標準）

詳細請閱讀代碼中的注釋

#include <stdio.h> #include <math.h> #include <string.h> #include <stdlib.h>/*** Developed by sandyz987* Function 'eval'* @param Expression string (chars' length <= MAX_SIZE)* @return Answer : double* @isError 0:no error 1:wrong number of decimal points 2:can't get top item at an empty stack 3:can't pop item at an empty stack(number of brackets is invalid?)* 4:can't get priority 5:too many arguments 6:unexpect character 7:wrong number of arguments 8:math error*/#define PI 3.141592653 #define MAX_SIZE 1024 #define MAX_SIGN_NUM 26 #define MIN_NUM 1.0e-7 char *functionName[MAX_SIGN_NUM] = {">=", "<=", "!=", "==", ">", "<", "asin", "acos", "atan","sin", "cos", "tan", "rand", "deg", "if", "rad", "log", "ln", "exp", "min", "max", "sign", "round", "floor", "abs", "sqrt"}; char nameTran[MAX_SIGN_NUM] = {'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'}; int namePriority[MAX_SIGN_NUM] = {2,2,2,2,2,2,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8};//function's priority int nameArgNum[MAX_SIGN_NUM] = {2,2,2,2,2,2,1,1,1,1,1,1,2,1,3,1,2,1,1,2,2,1,1,1,1,1};//Number of argumentschar operator[] = {'+','-','*','/','^','!','%','(',')',',','&','|','~','#'}; int priority[] = {3,3,4,4,5,5,5,-4,-5,-1,1,0,5,8};//Operator' priority int operatorArgNum[] = {2,2,2,2,2,1,2,0,0,1,2,2,1,1};//Number of arguments//I didn't use the struct to build a stack because pointer can reduce readability. char operatorS[MAX_SIZE] = {0};//Operator stack int operatorSTop = -1; int isError = 0;//0=no errortypedef struct sign{int isOperator;//If isOperator == 0 use the num, else use the operadouble num;char opera; } SIGN; SIGN signs[MAX_SIZE];int signsSize = 0;//To save the "infix expression" by using "struct SIGN" SIGN reverseSigns[MAX_SIZE];int reverseSignsSize = 0;//To save the "Postfix Expression" /** Example:* if user input str = "1+2*3"* the signs(Stack) store 5 item : [isOperator=0,num=1,opera='0'],[isOperator=1,num=0,opera='+'],[isOperator=0,num=2,opera='0'],[isOperator=1,num=0,opera='*'],[isOperator=0,num=3,opera='0']* the reverseSigns(Stack) store 5 item : [isOperator=0,num=2,opera='0'],[isOperator=0,num=3,opera='0'],[isOperator=1,num=0,opera='*'],[isOperator=0,num=1,opera='0'],[isOperator=1,num=0,opera='+']*/int getPriority(char c){int i;for(i = 0; i < sizeof(operator); i++){if(operator[i] == c){return priority[i];}}for(i = 0; i < sizeof(nameTran); i++){if(nameTran[i] == c){return namePriority[i];}}isError = 4;return 0; }void pushSignOpera(char c){signs[signsSize].isOperator = 1;signs[signsSize].opera = c;signsSize++; }void pushSignNum(double n){signs[signsSize].isOperator = 0;signs[signsSize].num = n;signsSize++; }void pushReverseOpera(char c){reverseSigns[reverseSignsSize].isOperator = 1;reverseSigns[reverseSignsSize].opera = c;reverseSignsSize++; }void pushReverseNum(double n){reverseSigns[reverseSignsSize].isOperator = 0;reverseSigns[reverseSignsSize].num = n;reverseSignsSize++; }void deleteReverseItem(int pos){int i;for (i = pos + 1; i < reverseSignsSize; i++) {reverseSigns[i-1] = reverseSigns[i];}reverseSignsSize--; }void insertReverseNum(int pos, double n){int i;for (i = reverseSignsSize - 1; i >= pos; i--) {reverseSigns[i+1] = reverseSigns[i];}reverseSigns[pos].isOperator = 0;reverseSigns[pos].num = n;reverseSignsSize++; }int isNumber(char c){return (c>='0'&&c<='9')||(c=='.'); }int isOperator(char c){int flag = 0,i;for(i = 0; i<sizeof(operator); i++){if (c == operator[i]){flag = 1;}}for(i = 0; i<sizeof(nameTran); i++){if (c == nameTran[i]){flag = 1;}}return flag; }void pushOpera(char opera){//Operator stackoperatorS[++operatorSTop] = opera; }int isNotEmptyOperaS(){return operatorSTop != -1; }char popOpera(){return operatorS[operatorSTop--]; }char getTopOpera(){if (operatorSTop != -1){return operatorS[operatorSTop];} else{isError = 2;return '0';} }void replaceString(char s[], int pos, int len, char s1[]){//Replace the s from pos to len with s2int i;char s2[1000];int lenS1 = (int)strlen(s1);int lenS = (int)strlen(s);int j;//copy s to s2 and clear the sfor (i = 0; i < lenS; i++) {s2[i] = s[i];}memset(s,'0',sizeof(*s));for (i = 0; i < pos; ++i) {s[i] = s2[i];}for (i = pos; i < pos + lenS1; i++) {s[i] = s1[i - pos];}j = pos + lenS1;for (i = pos + len; i < lenS; i++){s[j++] = s2[i];}s[j] = '0'; }void tranString(char s[]){//Format string. For example "sin(3.14)+abs(-1)" is format to "J(3.14)+Y(-1)"int pos = 0;int i;while (pos < strlen(s)){for (i = 0; i < MAX_SIGN_NUM; i++) {if(pos + (int)strlen(functionName[i]) <= (int)strlen(s)){char tmp[20];memset(tmp,'0',sizeof(tmp));strncpy(tmp,s + pos ,strlen(functionName[i]));if(strcmp(functionName[i], tmp) == 0){char tmpChar[2] = {'0', '0'};tmpChar[0] = nameTran[i];replaceString(s, pos, (int)strlen(functionName[i]), tmpChar);}}}pos++;}if(s[0] == '-'){//decide whether the '-' is '#'char tmpChar[2] = {'#', '0'};replaceString(s, 0, 1, tmpChar);}pos = 1;while (pos < strlen(s)){//decide whether the '-' is '#'if(isOperator(s[pos - 1]) && s[pos] == '-' && s[pos-1]!=')'){char tmpChar[2] = {'#', '0'};replaceString(s, pos, 1, tmpChar);}pos++;} }int getOperaArgNum(char op){//Get operator's number of arguments.int i;for (i = 0; i < sizeof(nameTran); ++i) {if(nameTran[i] == op){return nameArgNum[i];}}for (i = 0; i < sizeof(operator); ++i) {if(operator[i] == op){return operatorArgNum[i];}}isError = 6;return 0; }int long fact(int n){//return the number's factorif (n < 0)return -1;if (n > 1)return fact(n - 1) * n;elsereturn n; }double calculate(double *n, char op, int num){//Arguments are in *n. op is the operator. num is the number of argumentsswitch (op) {case ',':return n[num - 1];case '#':return -n[num - 1];case '+':return n[num - 1] + n[num - 2];case '-':return n[num - 1] - n[num - 2];case '*':return n[num - 1] * n[num - 2];case '/':return n[num - 2] != 0 ? n[num - 1] / n[num - 2] : (isError = 8, 0);case '%':return (double)((int)n[num - 1] % (int)n[num - 2]);case '^':return pow(n[num - 1] , n[num - 2]);case '!':return fact((int)n[num - 1]);case '&':return fabs(n[num - 1]) >= MIN_NUM && fabs(n[num - 2]) >= MIN_NUM;case '|':return fabs(n[num - 1]) >= MIN_NUM || fabs(n[num - 2]) >= MIN_NUM;case '~':return fabs(n[num - 1]) <= MIN_NUM;case 'A':return n[num - 1] >= n[num - 2];case 'B':return n[num - 1] <= n[num - 2];case 'C':return fabs(n[num - 1] - n[num - 2]) >= MIN_NUM;case 'D':return fabs(n[num - 1] - n[num - 2]) <= MIN_NUM;case 'E':return n[num - 1] > n[num - 2];case 'F':return n[num - 1] < n[num - 2];case 'G':return n[num - 1] <= 1 && n[num - 1] >= -1 ? asin(n[num - 1]) : (isError = 8, 0);case 'H':return n[num - 1] <= 1 && n[num - 1] >= -1 ? acos(n[num - 1]) : (isError = 8, 0);case 'I':return atan(n[num - 1]);case 'J':return sin(n[num - 1]);case 'K':return cos(n[num - 1]);case 'L':return tan(n[num - 1]);case 'M':return n[num - 1] >= 0 && n[num - 2] >= 0 && n[num - 2] - n[num - 1] >= 1 ? (rand() % ((int)n[num - 2] - (int)n[num - 1]) + 1) + (int)n[num - 1] : (isError = 8, 0);case 'N':return n[num - 1] / PI * 180.0;case 'O':return fabs(n[num - 1]) >= MIN_NUM ? n[num - 2] : n[num - 3] ;case 'P':return n[num - 1] / 180.0 * PI;case 'Q':return n[num - 1] != 1 && n[num - 1] > 0 && n [num - 2] > 0 ? log(n[num - 2]) / log(n[num - 1]) : (isError = 8, 0);case 'R':return n[num - 1] > 0 ? log(n[num - 1]) : (isError = 8, 0);case 'S':return exp(n[num - 1]);case 'T':return n[num - 1] <= n[num - 2] ? n[num - 1] : n[num - 2];case 'U':return n[num - 1] <= n[num - 2] ? n[num - 2] : n[num - 1];case 'V':return n[num - 1] >= 0 ? 1 : -1;case 'W':return (double)(int)(n[num - 1] + 0.5);case 'X':return (double)(int)(n[num - 1]);case 'Y':return n[num - 1] >= 0 ? n[num - 1] : - n[num - 1];case 'Z':return n[num - 1] >= 0 ? sqrt(n[num - 1]) : (isError = 8, 0) ;default://not find the operatorisError = 6;return 0.0f;} }void calculateOpera(char op, int pos){//Change the reverseSigns(stack) when calculatingint num = getOperaArgNum(op);int i;double n[10] = {0};int size = 0;double ans;if (pos >= num){for (i = 0; i < num; ++i) {if(reverseSigns[pos - 1 - i].isOperator != 1){n[size++] = reverseSigns[pos - 1 - i].num;} else{isError = 7;break;}deleteReverseItem(pos - i);}deleteReverseItem(pos - i);ans = calculate(n, op, num);insertReverseNum(pos - num, ans);}else {isError = 7;} }double eval(char s[]){double number = 0;int numberUsed = 0;int numberPoint = 0;int i;operatorSTop = -1;signsSize = 0;reverseSignsSize = 0;srand(0);//set srand!isError = 0;//tranString(s); !!!!You must decide whether use "tranString" function here or before eval() execute. Because tranString() use too much time.while(*s != '0'){if (isNumber(*s)){numberUsed = 1;if (*s == '.'){if (numberPoint != 0){isError = 1;}numberPoint = 1;s++;continue;}if(numberPoint == 0){number *= 10.0;number += *s - '0';}else{number += pow(10,-(numberPoint++)) * (*s - '0');}}if (isOperator(*s)){if (numberUsed == 1){numberUsed = 0;pushSignNum(number);number = 0;numberPoint = 0;}pushSignOpera(*s);}s++;}if(numberUsed != 0){pushSignNum(number);}if(isError){return 0.0f;}//start calculating the sign stackfor(i = 0; i < signsSize; i++){SIGN sign = signs[i];if(sign.isOperator != 1){//is numberpushReverseNum(sign.num);}else{//is operatorif(sign.opera == '('){pushOpera(sign.opera);}else if(sign.opera == ')'){while(getTopOpera() != '('){if(isNotEmptyOperaS()){pushReverseOpera(popOpera());} else{isError = 3;break;}}if(isNotEmptyOperaS()){popOpera();}}else{while(isNotEmptyOperaS() && getPriority(getTopOpera()) >= getPriority(sign.opera)){pushReverseOpera(popOpera());}pushOpera(sign.opera);}}}while (isNotEmptyOperaS()){char tmp = popOpera();if(tmp != '(' && tmp != ')'){pushReverseOpera(tmp);}}//===========================up --This code block is to test print the "infix expression" and the "Postfix Expression" // for(i = 0; i < signsSize; i++){ // if(!signs[i].isOperator){ // printf("%f,",signs[i].num); // }else{ // printf("%c,",signs[i].opera); // } // } // printf("n"); // for(i = 0; i < reverseSignsSize; i++){ // if(!reverseSigns[i].isOperator){ // printf("%f,",reverseSigns[i].num); // }else{ // printf("%c,",reverseSigns[i].opera); // } // } // printf("n"); //============================down --This code block is to test print the "infix expression" and the "Postfix Expression"//start calculate the expression by reverse (Postfix) expressionwhile(!isError){int pos = -1;for (i = 0; i < reverseSignsSize; i++) {if(reverseSigns[i].isOperator == 1){pos = i;break;}}if(pos == -1){break;}else{calculateOpera(reverseSigns[i].opera, pos);}}if(isError){return 0.0f;}if(reverseSignsSize != 1){isError = 5;return 0.0f;} else{return reverseSigns[0].num;}}int main(){char s[100];scanf("%s",s);tranString(s);printf("%f",eval(s));return 0; }

原文鏈接：C語言 科學計算器 仿JS的eval函數 解析字符串 后綴表達式

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