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/*---------------------------------------
函数型计算器(VC++6.0,Win32 Console)程序由 yu_hua 于2007-07-27设计完成
功能:
目前提供了10多个常用数学函数:
⑴正弦sin
⑵余弦cos
⑶正切tan
⑷开平方sqrt
⑸反正弦arcsin
⑹反余弦arccos
⑺反正切arctan
⑻常用对数lg
⑼自然对数ln
⑽e指数exp
⑾乘幂函数∧
用法:
如果要求2的32次幂,可以打入2^32<回车>
如果要求30度角的正切可键入tan(Pi/6)<回车>
注意不能打入:tan(30)<Enter>
如果要求1.23弧度的正弦,有几种方法都有效:
sin(1.23)<Enter>
sin 1.23 <Enter>
sin1.23 <Enter>
如果验证正余弦的平方和公式,可打入sin(1.23)^2+cos(1.23)^2 <Enter>或sin1.23^2+cos1.23^2 <Enter>
此外两函数表达式连在一起,自动理解为相乘如:sin1.23cos0.77+cos1.23sin0.77就等价于sin(1.23)*cos(0.77)+cos(1.23)*sin(0.77)
当然你还可以依据三角变换,再用sin(1.23+0.77)也即sin2验证一下。
本计算器充分考虑了运算符的优先级因此诸如:2+3*4^2 实际上相当于:2+(3*(4*4))
另外函数名前面如果是数字,那么自动认为二者相乘.
同理,如果某数的右侧是左括号,则自动认为该数与括弧项之间隐含一乘号。
如:3sin1.2^2+5cos2.1^2 相当于3*sin2(1.2)+5*cos2(2.1)
又如:4(3-2(sqrt5-1)+ln2)+lg5 相当于4*(3-2*(√5 -1)+loge(2))+log10(5)
此外,本计算器提供了圆周率 Pi键入字母时不区分大小写,以方便使用。
----------------------------------------*/
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <stdio.h>
#include <string.h>
#include <windows.h>
using namespace std;
const char Tab=0x9;
const int DIGIT=1;
const int MAXLEN=16384;
char s[MAXLEN],*endss;
int pcs=15;
double fun(double x,char op[],int *iop) {
while (op[*iop-1]<32) //本行使得函数嵌套调用时不必加括号,如 arc sin(sin(1.234)) 只需键入arc sin sin 1.234<Enter>
switch (op[*iop-1]) {
case 7: x=sin(x); (*iop)--;break;
case 8: x=cos(x); (*iop)--;break;
case 9: x=tan(x); (*iop)--;break;
case 10: x=sqrt(x); (*iop)--;break;
case 11: x=asin(x); (*iop)--;break;
case 12: x=acos(x); (*iop)--;break;
case 13: x=atan(x); (*iop)--;break;
case 14: x=log10(x);(*iop)--;break;
case 15: x=log(x); (*iop)--;break;
case 16: x=exp(x); (*iop)--;break;
}
return x;
}
double calc(char *expr,char **addr) {
static int deep; //递归深度
static char *fname[]={ "sin","cos","tan","sqrt","arcsin","arccos","arctan","lg","ln","exp",NULL};
double ST[10]={0.0}; //数字栈
char op[10]={'+'}; //运算符栈
char c,*rexp,*pp,*pf;
int ist=1,iop=1,last,i;
if (!deep) {
pp=pf=expr;
do {
c = *pp++;
if (c!=' '&& c!=Tab)
*pf++ = c;
} while (c!='\0');
}
pp=expr;
if ((c=*pp)=='-'||c=='+') {
op[0] = c;
pp++;
}
last = !DIGIT;
while ((c=*pp)!='\0') {
if (c=='(') {//左圆括弧
deep++;
ST[ist++]=calc(++pp,addr);
deep--;
ST[ist-1]=fun(ST[ist-1],op,&iop);
pp = *addr;
last = DIGIT;
if (*pp == '('||isalpha(*pp) && strnicmp(pp,"Pi",2)) {//目的是:当右圆括弧的右恻为左圆括弧或函数名字时,默认其为乘法
op[iop++]='*';
last = !DIGIT;
c = op[--iop];
goto operate ;
}
}
else if (c==')') {//右圆括弧
pp++;
break;
} else if (isalpha(c)) {
if (!strnicmp(pp,"Pi",2)) {
if (last==DIGIT) {
cout<< "π左侧遇)" <<endl;exit(1);
}
ST[ist++]=3.14159265358979323846264338328;
ST[ist-1]=fun(ST[ist-1],op,&iop);
pp += 2;
last = DIGIT;
if (!strnicmp(pp,"Pi",2)) {
cout<< "两个π相连" <<endl;exit(2);
}
if (*pp=='(') {
cout<< "π右侧遇(" <<endl;exit(3);
}
} else {
for (i=0; (pf=fname[i])!=NULL; i++)
if (!strnicmp(pp,pf,strlen(pf))) break;
if (pf!=NULL) {
op[iop++] = 07+i;
pp += strlen(pf);
} else {
cout<< "陌生函数名" <<endl;exit(4);
}
}
} else if (c=='+'||c=='-'||c=='*'||c=='/'||c=='^') {
char cc;
if (last != DIGIT) {
cout<< "运算符粘连" <<endl;exit(5);
}
pp++;
if (c=='+'||c=='-') {
do {
cc = op[--iop];
--ist;
switch (cc) {
case '+': ST[ist-1] += ST[ist];break;
case '-': ST[ist-1] -= ST[ist];break;
case '*': ST[ist-1] *= ST[ist];break;
case '/': ST[ist-1] /= ST[ist];break;
case '^': ST[ist-1] = pow(ST[ist-1],ST[ist]);break;
}
} while (iop);
op[iop++] = c;
} else if (c=='*'||c=='/') {
operate: cc = op[iop-1];
if (cc=='+'||cc=='-') {
op[iop++] = c;
} else {
--ist;
op[iop-1] = c;
switch (cc) {
case '*': ST[ist-1] *= ST[ist];break;
case '/': ST[ist-1] /= ST[ist];break;
case '^': ST[ist-1] = pow(ST[ist-1],ST[ist]);break;
}
}
} else {
cc = op[iop-1];
if (cc=='^') {
cout<< "乘幂符连用" <<endl;exit(6);
}
op[iop++] = c;
}
last = !DIGIT;
} else {
if (last == DIGIT) {
cout<< "两数字粘连" <<endl;exit(7);
}
ST[ist++]=strtod(pp,&rexp);
ST[ist-1]=fun(ST[ist-1],op,&iop);
if (pp == rexp) {
cout<< "非法字符" <<endl;exit(8);
}
pp = rexp;
last = DIGIT;
if (*pp == '('||isalpha(*pp)) {
op[iop++]='*';
last = !DIGIT;
c = op[--iop];
goto operate ;
}
}
}
*addr=pp;
if (iop>=ist) {
cout<< "表达式有误" <<endl;exit(9);
}
while (iop) {
--ist;
switch (op[--iop]) {
case '+': ST[ist-1] += ST[ist];break;
case '-': ST[ist-1] -= ST[ist];break;
case '*': ST[ist-1] *= ST[ist];break;
case '/': ST[ist-1] /= ST[ist];break;
case '^': ST[ist-1] = pow(ST[ist-1],ST[ist]);break;
}
}
return ST[0];
}
int main(int argc,char **argv) {
//1 2 3 4 5 6 7 8 9 =110 中间可以挿+ - 或者不挿 如果1 2 不挿的话 就是12
char op[4]=" +-";
int g1;
int g2;
int g3;
int g4;
int g5;
int g6;
int g7;
int g8;
for (g1=0;g1<3;g1++)
for (g2=0;g2<3;g2++)
for (g3=0;g3<3;g3++)
for (g4=0;g4<3;g4++)
for (g5=0;g5<3;g5++)
for (g6=0;g6<3;g6++)
for (g7=0;g7<3;g7++)
for (g8=0;g8<3;g8++) {
strcpy(s,"1 2 3 4 5 6 7 8 9");
s[ 1]=op[g1];
s[ 3]=op[g2];
s[ 5]=op[g3];
s[ 7]=op[g4];
s[ 9]=op[g5];
s[11]=op[g6];
s[13]=op[g7];
s[15]=op[g8];
if (110.0==calc(s,&endss)) printf("%s=110\n",s);
}
/*
if (argc<=1) {
if (GetConsoleOutputCP()!=936) system("chcp 936>NUL");//中文代码页
cout << "计算函数表达式的值。"<<endl<<"支持(),+,-,*,/,^,Pi,sin,cos,tan,sqrt,arcsin,arccos,arctan,lg,ln,exp"<<endl;
while (1) {
cout << "请输入表达式:";
gets(s);
if (s[0]==0) break;//
cout << s <<"=";
cout << setprecision(15) << calc(s,&endss) << endl;
}
} else {
strncpy(s,argv[1],MAXLEN-1);s[MAXLEN-1]=0;
if (argc>=3) {
pcs=atoi(argv[2]);
if (pcs<0||15<pcs) pcs=15;
printf("%.*lf\n",pcs,calc(s,&endss));
} else {
printf("%.15lg\n",calc(s,&endss));
}
}
*/
return 0;
}
//123+4+5+67-89=110
//123+4-5-6-7-8+9=110
//123-4+5-6-7+8-9=110
//123-4-5+6+7-8-9=110
//12+34+56+7-8+9=110
//12+3+45+67-8-9=110
//12-3+4-5+6+7+89=110
//1+234-56-78+9=110
//1+2+34+5+67-8+9=110
//1-2+3+45-6+78-9=110
enum class ops
{
plus,
minus,
multiplies,
divides,
power,
root,
concat//10*a+b
};
int level(ops op)
{
switch (op)
{
case ops::plus:
case ops::minus:
return 0;
case ops::concat:
return 1;
default:
return 0;
}
}
struct operation
{
ops op;
int lv;
operation(ops t = ops::plus)
:op(t), lv(level(t))
{}
int operator()(int a, int b)
{
switch (op)
{
case ops::plus:
return a+b;
case ops::minus:
return a-b;
case ops::concat:
return 10*a+b;
default:
return 0;
}
}
operator const char*()
{
switch (op)
{
case ops::plus:
return "+";
case ops::minus:
return "-";
default:
return "";
}
}
};
int calculate(vector<int> nums, vector<operation> opers)
{
for (int lv = 9; lv >= 0; lv--)
{
auto itn = nums.begin();
auto ito = opers.begin();
for(; ito != opers.end();)
{
if (ito->lv == lv)
{
//calculate here, remove a number and a operator,
//then replace the other number with the answer
int ans = (*ito)(itn[0], itn[1]);
nums.erase(itn);
*itn = ans;
opers.erase(ito);
}
else
{
++itn;
++ito;
}
}
}
return nums[0];
}
int main()
{
ops op[] = {ops::plus, ops::minus, ops::concat};
vector<int> nums{1,2,3,4,5,6,7,8,9};
int ans=110;
vector<operation> opers;
for (int i=0; i<6561; i++)
{
int t=i;
for (int j=0; j<8; j++)
{
opers.push_back(op[t%3]);
t/=3;
}
if (calculate(nums, opers) == 110)
{
for (int j=0; j<8; j++)
{
cout<<j+1<<opers[j];
}
cout<<9<<"=110"<<endl;
}
opers.clear();
}
return 0 ;
}