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【C】一次方程求解
作者:ktprime / 发布于2012/7/23/ 582
支持分数，百分数，小数等形式输入，没有输入“=” 当计算器使用，特别适合低年级的”笨小孩“使用，采用分数计算可能造成结果溢出。支持形式： x - = 2 -2x 100% + 0.5 3/2x = 1.1 + 2/2
<div>/************************************************************
一次方程/计算器
copyright (C) 2009 by Huang Yuanbing
version 2.00
mail to: bailuzhou@163.com
free use for non-commercial purposes

some bug for input large number
*************************************************************/

//# include <cctype>
//# include <cstdio>
//# include <cstdlib>
//# include <memory.h>
# include <limits.h>

# include <deque>
# include <limits>
# include <cctype>
# include <cstdio>
# include <memory>
# include <cstring>
# include <cmath>
# include <cstdlib>
using namespace std;

# define X  'x'
# define MAXC 256
# define ISOPER(c) (c == '+' || c == '-' || c == '*' || c == '/')

#if _WIN32
typedef __int64 int64;
#else
typedef long long int64;
#endif

typedef int64 stype;

bool showLog = false;
bool showDot = false;
bool isLinear = true;

stype gcd(stype a, stype b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}


/*
analzye the expression is valid or not
and replaceChar some char with mathematical symbol
*/

class Analyzer
{
private :
bool validCharSet[MAXC];
int charNums[MAXC];
char inputExpr[MAXC * 2];
char convertExpr[MAXC * 2];
bool isValid;

void initCharSet( )
{
const char* validChar = "xy0123456789+-*/()[]{} 	.%=";
memset(validCharSet, false, sizeof(validCharSet));
memset(charNums, 0, sizeof(charNums));
memset(convertExpr, 0, sizeof(convertExpr));
for (int i = 0; validChar[i]; i++)
validCharSet[validChar[i]] = true;
}

public :

char* getExp( )
{
return convertExpr;
}

bool isEquation( )
{
return charNums['='] == 1 && convertExpr[0] != '=';
}

Analyzer(const char* epstr)
{
isValid = true;
initCharSet( );
if (epstr) {
int leng = strlen(epstr);
if (leng > MAXC) {
printf("Warn: too many chars\n");
leng = MAXC - 1;
}

for (int i = 0; i < leng; i++) {
char c = epstr[i];
if (!validCharSet[c]) {
isValid = false;
printf("Error: invalid char %c\n", c);
break;
} else {
inputExpr[i] = c;
charNums[c] ++;
}
}
if (isValid)
inputExpr[leng] = '\0';
}
}

void removeSpace( )
{
/* 		if (!strchr(convertExpr, ' ') &&
!strchr(convertExpr, '\t')) {
return;
} */

char lastc = convertExpr[0];
int nchars = isspace(lastc) ? 0 : 1;

for (int i = 1; convertExpr[i]; i++) {
char currc = convertExpr[i];
if (!isspace(currc))
convertExpr[nchars++] = currc;
lastc = currc;
}

if (nchars == 0) {
isValid = false;
} else {
convertExpr[nchars] = '\0';
}

if (showLog) {
printf("in removeSpace line %d \n", __LINE__);
puts(convertExpr);
}
}

void replaceSpace( )
{
if (!strchr(inputExpr, ' ') &&
!strchr(inputExpr, '\t')) {
return;
}

char lastc = inputExpr[0];
int nchars = isspace(lastc) ? 0 : 1;

//remove continous space and keep only one
for (int i = 1; inputExpr[i]; i++) {
char currc = inputExpr[i];
if (!isspace(currc) || !isspace(lastc))
inputExpr[nchars++] = currc;
lastc = currc;
}

//remove tail space
while (nchars > 0 && isspace(inputExpr[nchars - 1]))
nchars--;

if (nchars == 0 || inputExpr[0] == '\0') {
isValid = false;
} else {
inputExpr[nchars] = '\0';
//bug fix 2 2
lastc = inputExpr[0];
for (int i = 0; i < inputExpr[i]; i++) {
char currc = inputExpr[i];
if (isspace(currc) && isdigit(lastc) && isdigit(inputExpr[i + 1])) {
isValid = false;
puts("Error: two number is splited by space");
break;
}
lastc = currc;
}
}

if (showLog) {
printf("in replaceSpace line %d \n", __LINE__);
puts(inputExpr);
}
}

void replaceBracket( )
{
if (showLog) {
printf("in replaceBracket line %d \n", __LINE__);
puts(inputExpr);
}
if (charNums['('] != charNums[')']) {
puts("Error: bracket '(' not equal to ')' ");
isValid = false;
} else if (charNums['='] > 1) {
puts("Error: too many =");
isValid = false;
} else if (inputExpr[0] == '=') {
puts("Error: start with = ");
isValid = false;
}
//remove empty and table
int brackets = 0, nchars = 0;
for (int i = 0; i < inputExpr[i]; i++) {
char c = inputExpr[i];
if (!isspace(c))
convertExpr[nchars++] = c;
if (c == '(')
brackets ++;
else if (c == ')') {
brackets--;
if (brackets < 0) {
isValid = false;
puts("Error: too many ) before (");
break;
}
}
}

if (nchars == 0) {
puts("Warn: only empty space");
isValid = false;
}

replaceChar('[', '(');
replaceChar(']', ')');
replaceChar('{', '(');
replaceChar('}', ')');
convertExpr[nchars] = 0;
}

void replaceChar(char s, char d)
{
char *ps = strchr(convertExpr, s);
while (ps) {
*ps	= d;
ps = strchr(convertExpr, s);
}
}


//0.2 + 1.112%  1/2.5 1/2.5/2  16.9(2x+1)
//replaceChar x.y with (x + y/10), ex 1.2 --> (12/10)
void replaceDot( )
{
if (showLog) {
printf("in replaceDot line %d \n", __LINE__);
puts(convertExpr);
}

char* pd = strchr(convertExpr,'.');
while (pd) {
if (isdigit(pd[-1]) && isdigit(pd[1])) {

stype n1 = 0, n2 = 0, m1 = 1;
char* pe = pd + 1;
for (; isdigit(*pe); pe++) {
n1 = n1 * 10 + *pe - '0';
m1 *= 10;
}

char* ps = pd - 1;
while (isdigit (*ps))
ps--;

for (char* pc = ps + 1; pc < pd; pc++)
n2 = n2 * 10 + *pc - '0';

n1 = m1 * n2 + n1;
char pn[100] = {0};
if (*pe != '(')
sprintf(pn, "(%I64d/%I64d)", n1, m1);
else
sprintf(pn, "(%I64d/%I64d)*", n1, m1);
// ps pd    pe
//x + 2.1 - x = 0
int leng = strlen(pn) + 0;
memmove(ps + leng + 1, pe, strlen(pe) + 3);
memcpy(ps + 1, pn, leng);
} else {
isValid = false;
puts("Error: not number near .");
break;
}
pd = strchr(pd + 1 ,'.');
}
}

//3.1% , x%, 20%  1/25%, (20+1)%
//replaceChar x% with (x/100), ex 20% --> (20 / 100)
void replacePercent( )
{
if (showLog) {
printf("in replacePercent line %d \n", __LINE__);
puts(convertExpr);
}

char* pp = strchr(convertExpr,'%');

while (pp) {
if ( isdigit(pp[-1]) ) {
char* ps = pp - 1;
char* pe = pp + 1;
while (isdigit(*ps))
ps--;
char pn[MAXC] = {0};
stype dn = atoi(ps + 1);
sprintf(pn, "(%I64d/100)", dn);
int leng = strlen(pn);
memmove(ps + leng + 1, pe, strlen(pe) + 3);
memcpy(ps + 1, pn, leng);
} else if (pp[-1] == X || pp[-1] == ')') {
char* ps = pp - 1;
char* pe = pp + 1;
char pn[MAXC] = {0};
if (pp[-1] == ')') {
while (*ps != '(')
ps--;
}
pp[0] = 0;
sprintf(pn, "(%s/100)", ps);
int leng = strlen(pn);
memmove(ps + leng, pe, strlen(pe) + 3);
memcpy(ps, pn, leng);
} else {
isValid = false;
puts("Error: invalid operator before %");
break;
}

pp = strchr(pp + 3,'%');
}
}

//the unitary  (operator x with be replaced with (0 operator x)
// (-2) --> (0 - 2)
bool addStarZero( )
{
if (showLog) {
printf("in addStarZero line %d \n", __LINE__);
puts(convertExpr);
}

char buf[MAXC + MAXC] = {0};
char* pc = buf;

for (int i = 0; convertExpr[i]; i++) {
char c = convertExpr[i];
//bug fix : x = 2(x+1) or x = 2x-1
if (isdigit(pc[-1]) && (c == X || c == '('))
*pc++ = '*';
//bug fix : 2(x) (2+3)x x(2+1)
else if (c == X && pc[-1] == ')')
*pc++ = '*';
//bug fix : x = -1 or x = -(-x) or -x = 2
else if ((c == '+' || c == '-') &&
(pc[-1] == '(' || pc[-1] == '=' || 0 == buf[0])) {
*pc++ = '0';
}
*pc++ = c;
}

strcpy(convertExpr, buf);

return true;
}

int getComplexty(char c)
{
int complexty = -12345678;

if (c == '(')
complexty = 2;
else if (c == ')')
complexty = -2;
else if (isdigit(c) || c == X)
complexty = 1;
else if (ISOPER(c))
complexty = -1;
else if (c == '=')
complexty = 0;
return complexty;
}

//digit, X, oper, ( )
bool checkComplexty( )
{
if (showLog) {
printf("in checkComplexty line %d \n", __LINE__);
puts(convertExpr);
}

char lastc = convertExpr[0];
int complx = getComplexty(lastc);

for (int i = 1; convertExpr[i] && isValid; i++) {
char currc = convertExpr[i];
bool currd = isdigit(currc), lastd = isdigit(lastc);
bool curro = ISOPER(currc), lasto = ISOPER(lastc);

if ((curro || currc == '=') && convertExpr[i + 1] == 0) {
printf("Error: wrong %c in last\n", currc);
isValid = false;
} else if (lastc == '(') {
if (curro || currc == ')') {
printf("Error: wrong %c before %c\n", lastc, currc);
isValid = false;
}/* else if (isspace(currc) && ')' == convertExpr[i + 1]) {
isValid = false;
puts("Error: ()");
}*/
} else if (lastc == ')') {
if (currd || currc == '(') {
printf("Error: wrong %c before %c\n", lastc, currc);
isValid = false;
}
} else if (lastc == X) {
if (currc == X || currd || currc == '(') {
printf("Error: wrong %c before %c\n", lastc, currc);
isValid = false;
}
} else if (lastd) {
if (currc == X ) {
printf("Error: wrong %c before %c\n", lastc, currc);
isValid = false;
}/* else if (isspace(currc) && isdigit(convertExpr[i + 1])) {
isValid = false;
puts("Error: two digit split by space");
}*/
} else if (lasto || lastc == '=') {
if (lastc == '=' && (complx < 0 || complx > 1)) {
puts("Error: complexty failed before = ");
isValid = false;
}
if (curro || currc == ')' || currc == '=') {
printf("Error: wrong %c before %c\n", lastc, currc);
isValid = false;
}
} else {
printf("invlaid input %c or not precommand\n", currc);
}

if (!(currd && lastd)) {
complx += getComplexty(currc);
if (complx < 0) {
isValid = false;
printf("Error: not invlaid express for complexty = %d\n", complx);
}
}
lastc = currc;
}

return isValid;
}

bool getState( )
{
replaceSpace( );
if (isValid)
replaceBracket();
if (isValid)
replaceDot();
if (isValid)
replacePercent();
if (isValid)
addStarZero();
if (isValid)
checkComplexty();

return isValid;
}
};

/**
class Fraction: numerator / denominator
and Fraction can support arithmetic + - / *
*/
class Fraction
{
private:
stype numerator;
stype denominator;

public:

Fraction( )
{
numerator = 0;
denominator = 1;
}

Fraction(stype n, stype m = 1)
{
numerator = n;
denominator = m;
if (m == 0) {
puts("the denominator can not be 0");
exit(2);
} else if (m < 0) {
n = -n;
m = -m;
}
if (m > 1)
Reduction();
}

Fraction& operator = (stype m)
{
numerator = m;
denominator = 1;
return *this;
}

void setReverse( )
{
numerator = -numerator;
}

bool operator == (stype mn) const
{
return numerator == mn * denominator;
}

bool operator != (stype mn) const
{
return numerator != mn * denominator;
}

bool operator > (stype mn) const
{
return numerator > mn * denominator;
}

// numerator/denominator + r.numerator/r.denominator
Fraction& operator += (const Fraction &r)
{
//overflow
stype factor = gcd(denominator, r.denominator);
if (factor > 1) {
numerator = r.numerator * (denominator / factor) +
(r.denominator / factor) * numerator;
denominator *= r.denominator / factor;
} else {
numerator = r.numerator * denominator + r.denominator * numerator;
denominator *= r.denominator;
}
Reduction();
return *this;
}

Fraction operator + (const Fraction &r)
{
Fraction tmp = *this;
return tmp += r;
}

// numerator/denominator - r.numerator/r.denominator
Fraction& operator -= (const Fraction &r)
{
stype factor = gcd(denominator, r.denominator);
if (factor > 1) {
numerator = -r.numerator * (denominator / factor) +
(r.denominator / factor) * numerator;
denominator *= r.denominator / factor;
} else {
numerator = -r.numerator * denominator + r.denominator * numerator;
denominator *= r.denominator;
}
Reduction();
return *this;
}

Fraction operator - (const Fraction &r)
{
Fraction tmp = *this;
return tmp -= r;
}

Fraction& operator *= (const Fraction &r)
{
stype factor1 = gcd(denominator, r.numerator);

stype factor2 = gcd(numerator, r.denominator);

if (factor1 == 0 || factor2 == 0) {
*this = 0;
} else {
denominator /= factor1;
numerator /= factor2;
denominator *= r.denominator / factor2;
numerator *= r.numerator / factor1;
Reduction();
}
return *this;
}

Fraction operator * (const Fraction &r)
{
Fraction tmp = *this;
return tmp *= r;
}

Fraction& operator /= (const Fraction &r)
{
if (r != 0) {
stype factor1 = gcd(denominator, r.denominator);
stype factor2 = gcd(numerator, r.numerator);

if (factor1 == 0 || factor2 == 0) {
*this = 0;
} else {
denominator /= factor1;
numerator *= r.denominator / factor1;

numerator /= factor2;
denominator *= r.numerator / factor2;
Reduction();
}
} else {
printf("%I64d / %I64d\n", r.denominator, r.numerator);
puts("devide 0!!!");
exit(1);
}

return *this;
}

Fraction operator / (const Fraction &r) const
{
Fraction tmp = *this;
return tmp /= r;
}

void Reduction( )
{
stype factor = gcd(denominator, numerator);
if (factor != 1) {
denominator /= factor;
numerator /= factor;
}
if (denominator < 0) {
denominator = -denominator;
numerator = -numerator;
}
}

void print(bool newline = true) const
{
if (denominator == 1)
printf("%I64d", (int64)numerator);
else {
if (!showDot)
printf("%I64d/%I64d", (int64)numerator, (int64)denominator);
else
printf("%.3lf", 1.0*numerator / denominator);
}
if (newline)
putchar('\n');
}
};

/**
class Axb save the linear express ax + b
a and b all are Fraction
and Axb can support arithmetic + - / *
*/
class Axb
{
private :
Fraction a, b;

public :

Axb(stype m, stype n)
{
a = m;
b = n;
}

Axb& operator += (const Axb &r)
{
a += r.a;
b += r.b;
return *this;
}

Axb operator + (const Axb &r)
{
Axb tmp = *this;
return tmp += r;
}

Axb& operator -= (const Axb &r)
{
a -= r.a;
b -= r.b;
return *this;
}

Axb operator - (const Axb &r)
{
Axb tmp = *this;
return tmp -= r;
}
//r must be number with a = 0
Axb& operator *= (const Axb &r)
{
if (a != 0 && r.a != 0) {
printf("Warn : not linear equation for ");
print(false);
printf(" * ");
r.print(true);
isLinear = false;
} else if (r.a == 0) {
a *= r.b;
b *= r.b;
} else {
a = b * r.a;
b *= r.b;
}

return *this;
}

Axb operator * (const Axb &r)
{
Axb tmp = *this;
return tmp *= r;
}
//r must be number with a = 0 and b != 0
Axb& operator /= (const Axb &r)
{
if (r.a != 0) {
printf("Warn : not linear equation for ");
print(false);
printf(" / ");
r.print(true);
isLinear = false;
} else {
a /= r.b;
b /= r.b;
}
return *this;
}

Axb operator / (const Axb &r)
{
Axb tmp = *this;
return tmp /= r;
}

void solveEquation( )
{
if (a == 0) {
if (b != 0)
puts("方程没有解");
else
puts("方程无穷多解");
} else {
Fraction x = b / a;
printf("x = ");
x.setReverse( );
x.print(true);
}
}

void print(bool newline = false) const
{
if (a != 0) {
if (a != 1 && a != -1)
a.print(false);
else if (a == -1)
putchar('-');
putchar(X);
if (b > 0) {
putchar('+');
b.print(false);
} else if (b != 0)
b.print(false);
} else {
b.print(false);
}
if (newline) {
putchar('\n');
}
}
};

struct Oper
{
enum OP
{
OADDSUB = 1,
OMULDIV = 2,
OLEFTBR = 3,
OREFTBR = 0
};

char Operator;
int priority;

Oper(char O)
{
Operator = O;
if (Operator == '+' || Operator == '-')
priority = OADDSUB;
else if (Operator == '*' || Operator == '/')
priority = OMULDIV;
else if (Operator == '(')
priority = OLEFTBR;
else if (Operator == ')')
priority = OREFTBR;
}
};

/**
calculate the input express
use two stack to simulate
*/
class Calculator
{
private :
char expre[MAXC + MAXC];
deque <Axb> daxb;
deque <Oper> dope;

public :

Calculator(char* pexpre)
{
if (showLog) {
printf("Calculator : ");
puts(pexpre);
}
memcpy(expre, pexpre, strlen(pexpre) + 1);
removeEqual();
}

bool removeEqual( )
{
char* pe = strchr(expre, '=');
/**if (pe == expre) {
puts("Warn  : with only = ");
return false;
}*/
if (pe) {
int leng = strlen(pe);
memmove(pe + 2, pe + 1, leng + 2);
pe[0] = '-';
pe[1] = '(';
pe[leng + 1] = ')';
pe[leng + 2] = 0;
}
if (showLog) {
printf("Calculator removeEqual : ");
puts(expre);
}
return true;
}

bool adjustQueue( )
{
if (daxb.size() >= 2 && dope.size() < 1) {
puts("stack wrong");
return false;
}

if (daxb.size() < 2 || dope.size() < 1)
return false;

Axb a = daxb.back();
daxb.pop_back();
Axb b = daxb.back();
daxb.pop_back();
char oper = dope.back().Operator;

if (showLog) {
printf("a = ");
a.print();
printf(" %c b = ", oper);
b.print(true);
}

if (oper == '*')
daxb.push_back(a * b);
else if (oper == '/')
daxb.push_back(b / a);
else if (oper == '+')
daxb.push_back(a + b);
else if (oper == '-')
daxb.push_back(b - a);

if (showLog) {
printf("new = ");
daxb.back().print(true);
}
dope.pop_back();

return true;
}

stype atoint64(char* &exp)
{
stype num = 0;
while (isdigit(*exp)) {
if (num > LONG_LONG_MAX / 10 || num < LONG_LONG_MIN / 10) {
puts("Warn: atoint64 number overflow");
break;
}
num = 10 * num + *exp++ - '0';
}
exp--;
return num;
}

Axb expval( )
{
char* exp = expre;
if (showLog){
puts(exp);
}

while (*exp) {
char c = *exp;
if (isdigit(c) || c == X) {
if (c != X)
daxb.push_back(Axb(0, atoint64(exp)));
else
daxb.push_back(Axb(1, 0));
if (daxb.size() >= 2 && dope.back().priority == dope.back().OMULDIV)
adjustQueue();
} else if (ISOPER(c)) {
dope.push_back(Oper(c));
if (daxb.size() >= 2 &&
dope[dope.size() - 2].priority != dope.back().OLEFTBR &&
dope.back().priority <= dope[dope.size() - 2].priority) {
dope.pop_back();
adjustQueue();
dope.push_back(Oper(c));
}
} else if (c == '(' || c == ')') {
if (c == ')') {
while (dope.back().Operator != '(')
adjustQueue();
dope.pop_back();
} else
dope.push_back(Oper(c));
while (dope.size() > 0 && dope.back().priority == dope.back().OMULDIV)
adjustQueue();
}
exp++;
}

//	if (dint.size() == 1)
//		adjustQueue();

while (daxb.size() >= 2)
adjustQueue();
return daxb[0];
}
};

static void printInfo( )
{
puts("---------------------------------------------------------------");
puts("1.求解带x的一元一次线性方程: 2x/3 = (x - 2) * 3.5 - 10");
puts("2.四则运算计算器: (1.2 + 2.8)/3.1 - 25% * 6");
puts("3.输入 dot 显示小数结果");
puts("4.输入 log 显示计算过程");
puts("Copyright by Huang Yuanbing 2009 - 2010");

#ifdef _MSC_VER
printf("Compiled by MS/vc++ %d", _MSC_VER);
#else
printf("Compiled by GNU/g++ %d.%d.%d",
__GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__);
#endif

#if _M_AMD64 || __x86_64__
printf(" on Windows 64 bit");
#endif
printf(" on %s %s\n", __TIME__, __DATE__);
puts("---------------------------------------------------------------\n");
}

void unitTest()
{
Axb a(1, 1);
int m, n;
while (scanf ("%d %d", &m, &n) == 2) {
Axb t(m, n);
t.print();

a += t;
a.print();

a -= t;
a.print();

a /= Axb(0,m);
a.print();

a *= Axb(0,m);
a.print();
}
}

int main( )
{
printInfo( );

int ncase = 1;
char caxb[MAXC] = {0};
while ( gets(caxb) ) {

if (strcmp(caxb, "log") == 0) {
if (showLog)
puts("disable log");
else
puts("enable log");
showLog = !showLog;
continue;
} else if (strcmp(caxb, "dot") == 0) {
if (showDot)
puts("display format a.b");
else
puts("display format a/b");
showDot = !showDot;
continue;
} else if (strcmp(caxb, "exit") == 0) {
return 0;
}

isLinear = true;
Analyzer a(caxb);
if ( a.getState() ) {
printf("case %d result : ", ncase++);
Calculator c(a.getExp());
Axb ab = c.expval();
if (!isLinear) {
//				puts("not linear equation");
} else if ( !a.isEquation() )
ab.print();
else
ab.solveEquation();
}

putchar('\n');
putchar('\n');
memset(caxb, 0, sizeof(caxb));
}

return 0;
}

// x / 0.5
</div>
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