Thank you for the inspiration of this article. If you don't want to change the suffix expression, you can read this article and write it in detail
https://www.cnblogs.com/chenying99/p/3675876.html
The source code is at the bottom!
1. Supported functions
Logical expression:>, <, = = (note double equal sign), < =, > =, & (and), | (or), ~ (not)
Mathematical operators:+, -, *, /,% (modulus), ^ (power),! (factorial), ා (minus sign, generally it will automatically distinguish the minus sign from the minus sign)
Symbol:Parenthesis, comma
Function:Trigonometric function sin(x) cos(x) tan(x) asin(x) acos(x) atan(x)
0 if no domain is defined
Random number rand (x,y) (return integer between [x,y], srand required)
Radian rotation angle deg(x) angle rotation radian rad(x)
Conditional expression if (condition, x,y), where when x is not 0, the value of expression x is returned, otherwise the value of expression y is returned
Logarithm log(x,y) returns logarithm based on X and Y ln(x) returns natural logarithm based on e
n power exp(x) of natural number, return e^x
max(x,y) returns the larger one of expression X and expression y, min is the opposite
Take sign(x) if x is greater than or equal to 0, return 1, otherwise return - 1
round(x) round down floor(x)
Absolute value abs(x) returns the absolute value of X
Open square sqrt(x) returns the value of X open square
The operator "^" can be used instead of the open n power
2. Usage
#include<eval.c>
It's very simple, just one line
Call double eval(char* str) directly;
Where str is the expression, ending with '\ 0'
3. Effect
The result of 0.5 + 6 + 3 * 5 is 21.5
The middle two lines are infix expression and suffix expression respectively
The result of calculating sin (1.57) + cos (if (1 > 0,0,1)) is 2.0 (the accuracy of trigonometric function is not very good, make do with it)
The if (1 > 0,0,1) function takes three parameters. The first parameter is the condition. Obviously, the condition holds. The value of the result of the second parameter (expression) is 0, that is, sin(1.57)+cos(0) is calculated
Note that sin is replaced with J in infix and suffix expressions
cos is replaced by K.
Because of the convenience of a single character, replace it with a single character uppercase character using the replaceString() function. So, be careful not to let users enter capital letters!
The middle two lines of output can be commented out in the code.
Attached are several effect pictures of analytic string transplanted to calculator
(drawing the image of complex functions, such as the function of sin (x) < cos (y))
4. Thinking
Here I'll explain with examples.
If the user input "- sin(12.57)-cos(-6)"
Rule: if the minus sign "-" appears after the symbol (excluding the closing bracket) or at the beginning of the string, replace it with the minus sign "ා", the minus sign is a unary operator, and the minus sign is a binary operator, so it is necessary to distinguish.
Therefore, the original string is replaced with "ාsin (12.57) - cos (ා6)"
Since sin and cos are not easy to process, they are replaced with single characters (here I use A-Z), so they are replaced with "ාj (12.57) - K (ා6)"
Next you just need to distinguish between symbols and numbers.
Read in the symbol
Read J as a symbol
Read in (it's a symbol (all the above are standard operations for postfix expressions, no more details, see the blog recommended at the beginning)
Read in 1 is a number. If you are not sure if it is a complete number, it exists in number,
Read in 2 as a number, and change the original number*10+2.
Read in. Indicates that the next number is a decimal part.
Read in 5, number+=pow(10,-1)*5
Read in 7, number+=pow(10,-2)*7
When a symbol is read in or at the end of a string, the stored number is saved and cleared.
and so on
In this way, the sub symbol and the number are distinguished and converted to a suffix expression.
Next, you just need to run the evaluation of the suffix expression and control the priority.
Because of the particularity of my algorithm, the following wonderful writing method can also calculate the correct result:
sin7
7sin
(7)sin
If necessary, please write your own grammar analysis.
5. Source code (c98 compliant)
Read the comments in the code for details
#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 arguments char 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 error typedef struct sign{ int isOperator;//If isOperator == 0 use the num, else use the opera double 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 stack operatorS[++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 s2 int i; char s2[1000]; int lenS1 = (int)strlen(s1); int lenS = (int)strlen(s); int j; //copy s to s2 and clear the s for (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 factor if (n < 0) return -1; if (n > 1) return fact(n - 1) * n; else return n; } double calculate(double *n, char op, int num){//Arguments are in *n. op is the operator. num is the number of arguments switch (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 operator isError = 6; return 0.0f; } } void calculateOpera(char op, int pos){//Change the reverseSigns(stack) when calculating int 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 stack for(i = 0; i < signsSize; i++){ SIGN sign = signs[i]; if(sign.isOperator != 1){ //is number pushReverseNum(sign.num); }else{ //is operator if(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) expression while(!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; }
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