// Random Number Generation & Useful subfunctions
// Written by Microsoft Visual C++


double myu(double a, double b) // Uniform Distribution
{
  double y;
  if(a>b) {
	printf("\nThe first parameter should be less than the second!");
	exit(1);
  }
  y = (double)rand()/(RAND_MAX);
  return (a+(b-a)*y); 
}

double myexp(double beta) // Exponential Distribution
{
  double u;
  do {
     u = myu(0,1);
  }  while(u<=0||u>=1);
  return (-1*beta*log(u));
}

double myn(double mu, double sigma2) // Normal Distribution
{
  double mu1, mu2, z;
  do {
    mu1 = myu(0,1);
    mu2 = myu(0,1);
  } while (mu1<=0||mu1>=1);
  z = sqrt(-2*log(mu1))*sin(2*3.14159*mu2);
  return (mu+sqrt(sigma2)*z);
}

double mylogn(double mu, double sigma2) // Lognormal Distribution
{
  double z;
  z = myn(mu,sigma2);
  return (exp(z));
}

double myt(double a,double b,double m) // Triangular Distribution
{
 double c,u,y;
 if(a>=m||m>=b) {
	printf("\nThe first parameter should be the smallest!");
	printf("\nAnd the second one should be the largest!\n");
	exit(1);
   }
 c=(m-a)/(b-a);
 u=myu(0,1);
 if(u<c)
   y=sqrt(c*u);
 else
   y=1-sqrt((1-c)*(1-u));
 return(a+(b-a)*y);
}

double randomoptimistic(double *p, int samplenumber, double alpha)
{       
  int i, j;
  double w;
  for(i=1; i<=samplenumber; i++)
    for(j=i+1; j<=samplenumber; j++) 
      if(*(p+i) < *(p+j)) {
         w = *(p+j);
	     *(p+j) = *(p+i);
	     *(p+i) = w;
      }
  return *(p+(int)(alpha*samplenumber));
}

double randompessimistic(double *p, int samplenumber, double alpha)
{
  int i, j;
  double w;
  for(i=1; i<=samplenumber; i++)
    for(j=i+1; j<=samplenumber; j++) 
      if(*(p+i) > *(p+j)) {
         w = *(p+j);
	     *(p+j) = *(p+i);
	     *(p+i) = w;
      }
  return *(p+(int)(alpha*samplenumber));
}



double triangle(double x, double a, double b, double c)
{
  if(a<x&&x<b) return (x-a)/(b-a);
  if(b<=x&&x<c) return (x-c)/(b-c);
  return 0;
}

double trapezoidal(double x, double a, double b, double c, double d)
{
  if(a<x&&x<b) return (x-a)/(b-a);
  if(b<=x&&x<=c) return 1;
  if(c<x&&x<d) return (x-d)/(c-d);
  return 0;
}

double fuzzyoptimistic(double x[], double mu[], int samplenumber, double alpha)
 {
   double v1, v2, xx, min=9999, max=-9999;
   int    i;
   
   for(i=1; i<=samplenumber; i++) {
       if(x[i]<min) min=x[i];
	   if(x[i]>max) max=x[i];
   }
	
   do {
       	xx=(min+max)/2;
        v1=0;
		v2=0;
		for(i=1; i<=samplenumber; i++)  {
  	       if((x[i]>=xx)&&(mu[i]>v1)) 
	         v1=mu[i];
	       if((x[i]<xx)&&(mu[i]>v2))
             v2=mu[i];
		}
        v1=(v1+1-v2)/2;
        if(v1>=alpha) min=xx;
    	else max=xx;
   }while((max-min)>0.001);
 
   return (max+min)/2;
}

 double fuzzypessimistic(double x[], double mu[], int samplenumber, double alpha)
 {
   double v1, v2, xx, min=9999, max=-9999;
   int    i;
  
   for(i=1; i<=samplenumber; i++){
     
	   if(x[i]<min) min=x[i];
	   if(x[i]>max) max=x[i];
   }
   
   do {
       	xx=(min+max)/2;
        
		v1=0;
		v2=0;

		for(i=1; i<=samplenumber; i++)  {
   
	       if((x[i]<=xx)&&(mu[i]>v1)) 
	         v1=mu[i];

	       if((x[i]>xx)&&(mu[i]>v2))
             v2=mu[i];
		}

        v1=(v1+1-v2)/2;

        if(v1>=alpha) max=xx;
        
		else min=xx;
   }while((max-min)>0.001);
 
   return (max+min)/2;
}


double fuzzymean(double x[], double mu[], int samplenumber, int integralnumber=2000)
{
	int i,k;
	double Expect=0, left=9999, right=-9999, b1,b2,r;
	
	for(i=1;i<=samplenumber;i++) {
	  if(left>x[i]) left=x[i];
	  if(right<x[i]) right=x[i];
	}
	for(k=1; k<=integralnumber; k++) {
	  r=myu(left,right);
	  b1=0;
	  b2=0;
	  if(r>=0) {
		for(i=1; i<=samplenumber; i++) {
		  if(x[i]>=r&&b1<mu[i]) b1 = mu[i];
		  if(x[i]<r&&b2<mu[i]) b2 = mu[i];
		}		
		Expect = Expect+(b1+1-b2)/2.0;
	  }
	  else {
		for(i=1; i<=samplenumber; i++) {
		  if(x[i]<=r&&b1<mu[i]) b1 = mu[i];
		  if(x[i]>r&&b2<mu[i]) b2 = mu[i];
		}		
		Expect = Expect-(b1+1-b2)/2.0;
	  }
	}
	return Expect*(right-left)/integralnumber+((left>0)?left:0)+((right<0)?right:0);
}













//////////////////////////////////////////
/////////////////////////////////////////
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void sortminmax(double *p,int min,int max)
{
  int i,j;
  double w;
  for(i=min; i<max; i++)
    for(j=i+1; j<=max; j++)
       if(*(p+i) > *(p+j)) {
	      w = *(p+i);
	      *(p+i) = *(p+j);
	      *(p+j) = w;
       }
}

void sortmaxmin(double *p,int min,int max)
{
  int i, j;
  double w;
  for(i=min; i<max; i++)
    for(j=i+1; j<=max; j++)
      if(*(p+i) < *(p+j)) {
         w = *(p+i);
	     *(p+i) = *(p+j);
	     *(p+j) = w;
      }
}

double findmaxn(double *p,int min,int max,int n)
{
  int i, j;
  double w;
  for(i=min; i<=n; i++)
    for(j=i+1; j<=max; j++) 
      if(*(p+i) < *(p+j)) {
         w = *(p+j);
	     *(p+j) = *(p+i);
	     *(p+i) = w;
      }
  return *(p+n);
}

double findminn(double *p,int min,int max,int n)
{
  int i, j;
  double w;
  for(i=min; i<=n; i++)
    for(j=i+1; j<=max; j++) 
      if(*(p+i) > *(p+j)) {
         w = *(p+j);
	     *(p+j) = *(p+i);
	     *(p+i) = w;
      }
  return *(p+n);
}

double expect(double f[], double mu[], int m1, int m2=2000)
{
	int i,k;
	double Expect=0, left=9999, right=-9999, b1,b2,r;
	
	for(i=1;i<=m1;i++) {
	  if(left>f[i]) left=f[i];
	  if(right<f[i]) right=f[i];
	}
	for(k=1; k<=m2; k++) {
	  r=myu(left,right);
	  b1=0;
	  b2=0;
	  if(r>=0) {
		for(i=1; i<=m1; i++) {
		  if(f[i]>=r&&b1<mu[i]) b1 = mu[i];
		  if(f[i]<r&&b2<mu[i]) b2 = mu[i];
		}		
		Expect = Expect+(b1+1-b2)/2.0;
	  }
	  else {
		for(i=1; i<=m1; i++) {
		  if(f[i]<=r&&b1<mu[i]) b1 = mu[i];
		  if(f[i]>r&&b2<mu[i]) b2 = mu[i];
		}		
		Expect = Expect-(b1+1-b2)/2.0;
	  }
	}
	return Expect*(right-left)/m2+((left>0)?left:0)+((right<0)?right:0);
}


int mybe(double p) // Bernoulli Distribution
{
  if(p>1||p<0) {
	 printf("\nParameter is out of bound!\n");
	 exit(1);
  }
  if(myu(0,1)<=p) return 1;
  else return 0;
}


int mybn(int n, double p)
{
 int i, y=0;
 for(i=1; i<=n; i++)
	y=y+mybe(p);
 return y;
}


double myc(double alpha, double beta)
{
  double u;
  do {
	 u = myu(0,1);
  } while (u<=0);
  return (alpha-beta/tan(3.14159*u));
}


double myemp(double *a,int n) // Empirical Distribution
{
 int i,m;
 double mu;
 for(i=1;i<n;i++)
   {
	if(a[i-1]>a[i])
	  {
	   printf("\nThe observations should be ordered from small to large!\n");
	   exit(1);
	  }
   }
 mu=myu(0,1);
 m=(int)((n-1)*mu+1);
 return (a[m-1]+((n-1)*mu-m+1)*(a[m]-a[m-1]));
}


double mychi(int k)
{
  int i;
  double z,y=0;
  if(k<1)
	{
	 printf("\nThe parameter should be a integer larger than zero!\n");
	 exit(1);
	}
  for(i=1;i<=k;i++)
	{
	 z=myn(0,1);
	 y=y+z*z;
	}
  return y;
}


double myf(int k1, int k2)
{
  double y1, y2;
  y1 = mychi(k1);
  for(;;){
  y2 = mychi(k2);
  if(y2!=0) break;
  }
  return((y1/k1)/(y2/k2));
}


double mys(int k)
{
  double y, z;
  z = myn(0,1);
  y = mychi(k);
  return (z/sqrt(y/k));
}

double myer(int k,double beta)
{
 int i;
 double y;
 y=0;
 if(k<=0)
   {
	printf("\nThe first parameter should be a integer larger than zero!\n");
	exit(1);
   }
 for(i=1;i<=k;i++)
   y=y+myexp(beta);
 return y;
}


double myg(double alpha, double beta)
{
  double x, v;
  x = 0;
  if(alpha<=0||beta<=0)
	{
	 printf("\nParameter should all larger than zero!\n");
	 exit(1);
	}
  mark:
  v = myexp(1);
  x = x + v;
  if(alpha == 1) {
	 x = beta*x;
	 return x;
  }
  alpha = alpha -1;
  goto mark;
}


double myb(int alpha, int beta)
{
  double y1, y2;
  y1 = myg(alpha,1);
  y2 = myg(beta,1);
  return (y1/(y1+y2));
}


double myw(double alpha, double beta)
{
  double v;
  if(alpha<=0||beta<=0)
	{
	 printf("\nParameter should all larger than zero!\n");
	 exit(1);
	}
  v = myexp(1);
  return (beta*pow(v,(1/alpha)));
}


int myge(double p)
{
 int x;
 double r;
 if(p>=1||p<=0)
	{
	 printf("\nParameter is out of bound!\n");
	 exit(1);
	}
 do {
	r=myu(0,1);
 } while (r<=0||r>=1);
 x= (int)(log(r)/log(1-p));
 return x;
}


int mynb(int k,double p)
{
 int i,y;
 if(k<=0)
   {
	printf("\nThe first parameter should be a integer larger than zero!\n");
	exit(1);
   }
 y=0;
 for(i=1;i<=k;i++)
   y=y+myge(p);
 return y;
}


double myl(double a,double b) 
{
  double mu;
   do {
    mu = myu(0,1);
    } while (mu<=0||mu>=1);
  return(a-b*log(1/mu-1));
}

int myp(double lamd) // Poisson Distribution
{
 int x;
 double b,u;
 if(lamd<=0)
   {
	printf("\nThe parameter should be larger than zero!\n");
	exit(1);
   }
 x=0;
 b=1;
 do
   {
	u=myu(0,1);
	b=b*u;
	x=x+1;
   }while(b>=exp(-lamd));
 return(x-1);
}

double mynormal(double x, double c, double w)
{
	return(exp(-(x-c)*(x-c)/(w*w)));
}

double randommean(double x[], int samplenumber)
{
	int i;
	double Expect=0;
	
	for(i=1;i<=samplenumber;i++) 
		Expect=Expect+x[i];

	return Expect/samplenumber;
}