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表达式求解程序(CPP实现)
/**
* This is a program for solve mathematical expression. Just like:
* "1+4*3/2+22*(3+2*(3-4))"
*
* To solve this problem, Let us see it by a view of priority. The rules as following:
* 1). the priority of plus sign is 1, and minus sign too.
* 2). the priority of product sign and sign of division is 2.
* 3). the priority of bracket is 3.
*
* so, we can convert the expression above to:
*
*
* [1]
* .
* -------------
* [2] . .
* [1] . . .
* . . . .
* --------------------------------
* [2] [2] [2] . .
* [1] . . [1] . . .
* . . . . . . .
* " 1 + 4 * 3 / 2 + 22 * ( 3 + 2 * ( 3 - 4 ) ) "
*
* It is easy to know, we can‘t compute a sign in rising edge. And on the other way, we could dispose those brackets by a special way. that‘s means we could get a more
* simple expression without bracket
*
* [1] [2] [2] [1] [2] [4] [5] [7]
* " 1 + 4 * 3 / 2 + 22 * 3 + 2 * 3 - 4"
*
* and then what we should to do is just as follow:
*
* step 1: get a operator .
* step 2: compare the priority with it‘s last one‘s.
* -- ‘>=‘ , compute it.
* -- ‘<‘ , return to the step above.
*
* if arrvied the end , we will get a new expression. The priority of totally expression is increase by degree.
*
* [1] [1] [2] [4] [5] [7]
* " 1 + 6 + 22 * 3 + 2 * 3 - 4 "
*
* In the last, what we need is compute all operator by inverted order.
*
*/
#include <iostream>#include <stdio.h>#include "../stack.h"#define NUMS_DEP 20#define SYMS_DEP 20/*** All input symbol must be one of the types. we will deal those symbol* with a corresponding operation. Need to say, number is also belong to* symbol.*/enum SYMBOL { S_NUM, S_PLUS, S_SUB, S_MUL, //multiply S_DIV, //division S_BRAL, //left bracket S_BRAR, //right bracket S_INVAID, S_END, // the end of expression S_MAX,};/*** All symbols have a priority for operation.*/enum SYM_PRI { PR_NUM = 0, PR_INVALID = 0, PR_PLUS = 1, PR_SUB = 1, PR_MUL = 2, PR_DIV = 2, PR_MAX,};/*** record information about symbol. */struct OperatorS { //what's type? SYMBOL sym; //priority int prior; //used to record the value of number. int val;};class Calculater { public: Calculater( ); ~Calculater( ); //initialize the environment bool set( char *expr); //solve bool work( void); //show the result void show( void); private: //deal with symbol bool dwItem( OperatorS &item); //get a symbol from the expression string bool getItem( OperatorS &item); //deal with bracket, bool adjustPri( OperatorS &item); //modify the priority of a symbol bool calcuPri( OperatorS &item); //calculate the value of a symbol with its' corresponding values. bool calcuSym( OperatorS &sym); //convert a string to a interger bool str2Inter( char *begin, int &val, int &len); /* * when deal with a symbol, we found it have a feature, first-in last-out. * that is same as the feature of the stack. */ //stack for save symbol STACK<OperatorS> sym_s; //stack for save number STACK<int> num_s; //mathematical expression char * expr; //current position int cur_ind; /* * current priority. if encounter a bracket, this value will change for * revise the priority of symbol after it. */ int cur_pri; // the result will be restore in here. int sum;};Calculater::Calculater( ):num_s(NUMS_DEP),sym_s(SYMS_DEP){ this->expr = NULL; this->cur_ind = 0; this->cur_pri = 0; this->sum = 0;}Calculater::~Calculater( ){}bool Calculater::set(char * expr){ this->expr = expr; this->cur_ind = 0; this->cur_pri = 0; this->sum = 0; return true;}/*** core function, work for solve the mathematical expression.*/bool Calculater::work( void){ OperatorS item;/** untill all of symbols be computed.*/ while( ('\0'!=this->expr[this->cur_ind]) ||(this->num_s.getEleNum( )!=1) ) { //get a symbol //Y: continue //N: remain the last symbol if( !this->getItem( item) ) return false; //deal with symbol this->dwItem( item); } this->num_s.pop( this->sum); return true;}/*** get a item from the string, and build a symbol.*/bool Calculater::getItem( OperatorS & item){ char firstc = this->expr[this->cur_ind]; this->cur_ind ++; OperatorS tmp; switch( firstc) { case '+': tmp.sym = S_PLUS; tmp.prior = PR_PLUS; tmp.val = 0; break; case '-': tmp.sym = S_SUB; tmp.prior = PR_SUB; tmp.val = 0; break; case '*': tmp.sym = S_MUL; tmp.prior = PR_MUL; tmp.val = 0; break; case '/': tmp.sym = S_DIV; tmp.prior = PR_DIV; tmp.val = 0; break; case '(': tmp.sym = S_BRAL; tmp.prior = PR_MAX; tmp.val = 0; break; case ')': tmp.sym = S_BRAR; tmp.prior = PR_MAX; tmp.val = 0; break; case '0'...'9': { int len = 0; tmp.sym = S_NUM; tmp.prior = PR_INVALID; this->str2Inter( this->expr + this->cur_ind - 1, tmp.val, len); this->cur_ind += len-1; break; } /* * when arrived the end, create a end sign. */ case '\0': { tmp.sym = S_END; tmp.prior = PR_INVALID; tmp.val = 0; break; } default : return false; break; } item = tmp; return true;}/*** get a number from the string. if success, the value will* be store in @val, and the length of reading will be store* in @len.*/bool Calculater::str2Inter(char * begin,int & val,int & len){ int tmp_val = 0; int tmp_len = 0; while( (begin[tmp_len]>='0') &&(begin[tmp_len]<='9')) { tmp_val = tmp_val*10 + begin[tmp_len] - '0'; tmp_len++; } val = tmp_val ; len = tmp_len ; return true;}//deal with symbolbool Calculater::dwItem( OperatorS & item){ printf("sym: %x, prior: %x, val: %d\n", item.sym, item.prior, item.val); switch( item.sym) { //case 1: symbol is a number. //push in @num_s. case S_NUM : this->num_s.push( item.val); break; //case 2: symbol is a operator. case S_END: case S_PLUS...S_DIV : { //compute priority, cur + = () this->calcuPri( item); //compare with the last operator. // <= , compute the last operator with the last two numbers. //do the compare above untill the new operator greater than the last one. // > , do nothing. // * , push the new operator in @sym_s. //printf("sym: %x, prior: %x, val: %d\n", item.sym, item.prior, item.val); OperatorS last; do{ if(!this->sym_s.pop( last)) break; //there is no symbol if( item.prior<=last.prior) { this->calcuSym( last); continue; } this->sym_s.push( last); } while( item.prior <= last.prior); this->sym_s.push( item); break; } //deal with bracket case S_BRAL...S_BRAR: { this->adjustPri( item); break; } default : return false; } return true;}bool Calculater::adjustPri(OperatorS & item){ switch( item.sym) { case S_BRAL: this->cur_pri += item.prior; break; case S_BRAR: this->cur_pri -= item.prior; break; default : return false; break; } return true;}/*** compute the priority of this symbol.*/bool Calculater::calcuPri( OperatorS & item){ switch( item.sym) { case S_END: break; default : item.prior += this->cur_pri; break; } return true;}bool Calculater::calcuSym(OperatorS & sym){ int val1, val2, sum; this->num_s.pop( val1); this->num_s.pop( val2); sum = 0; switch( sym.sym) { case S_PLUS: sum = val2 + val1; break; case S_SUB: sum = val2 - val1; break; case S_MUL: sum = val2 * val1; break; case S_DIV: sum = val2/val1;; break; default : return false; break; } this->num_s.push( sum); return true;}void Calculater::show(void){ printf(" %s = %d\n", this->expr, this->sum);}#define EXPR "1+24*3/12-4*(5+6-7*2*(2+3*4))*22"int main(){ Calculater cal; cal.set( EXPR); cal.work( ); cal.show( ); return 0;}