/*********************************************
* This program allows user performing combi- *
* natory analysis, such as Factorial N,      *
* Combination C(n,p) and Permutation A(n,p). *
* ------------------------------------------ *
* Ref.: "Mathématiques en Turbo-Pascal By    *
*        M. Ducamp and A. Reverchon (2),     *
*        Eyrolles, Paris, 1988" [BIBLI 05].  *
* ------------------------------------------ *
* Sample runs:                               *
*                                            *
* COMBINATORY ANALYSIS                       *
*                                            *
*   1:  Factorial n!                         *
*   2:  Combination C n,p                    *
*   3:  Permutation A n,p                    *
*   0:  Quit                                 *
*                                            *
*   Your choice (0 to 3): 1                  *
*                                            *
*   N = 100                                  *
*   N! = 9.3248476268  10^ 157               *
*                                            *
*   Your choice (0 to 3): 2                  *
*                                            *
*   N = 7                                    *
*   P = 3                                    *
*   Cnp =           35                       *
*                                            *
*   Your choice (0 to 3): 3                  *
*                                            *
*   N = 10                                   *
*   P = 6                                    *
*   Anp =       151200                       *
*                                            *
*             C++ Release 1.1 By J-P Moreau  *
*                   (www.jpmoreau.fr)        *
* ------------------------------------------ *
* Release 1.1: bug corrected in function     *
*              Cnp().                        *
*********************************************/
#include <stdio.h>
#include <math.h>

#define  MAXREAL  1E40
#define  PI       3.1415926535 

int  n,p,choice; float r1,r2,s;


  //Factorial n!
  float Factorial(int n, float *mantissa, float *exponent) {
    int i; float fa;
    fa=1;
    if (n<25) {
      for (i=1; i<=n; i++) fa=fa*i;
      return fa;
    }
    else {
      fa=(float) ((log(2*PI*n)/2 + n*log(n)-n)/log(10));
      *exponent=(float) int(fa); 
      *mantissa=(float) exp((fa-int(fa))*log(10));
      return 0;
    }
  }

  //Combination Cn,p
  float Cnp(int n,int p) {
    int i,u; float r,x;
    if (p>n) return 0;
    r=1;
    if (p>n-p) u=n-p; else u=p;
    for (i=0; i<u; i++) {
      x=(float) (n-i)/(u-i);
      if (r>MAXREAL/x) return 0;
      r=r*x;
    }
    return r;
  }

  //Permutation An,p
  float Anp(int n,int p) {
    int i; float r;
    if (p>n) return 0;
    r=1;
    for (i=n-p+1; i<=n; i++) {
      if (r>MAXREAL/i) return 0;
      r=r*i;
    }
    return r;
  }


void main()  {
  choice=1;    
  do {
    printf("\n COMBINATORY ANALYSIS\n\n");
    printf("  1:  Factorial n!\n");
    printf("  2:  Combination C n,p\n");
    printf("  3:  Permutation A n,p\n");
    printf("  0:  Quit\n\n");
    printf("  Your choice (0 to 3): "); scanf("%d",&choice);
    printf("\n");
    if (choice<0) choice=0;
    if (choice>3) choice=3;
    switch(choice) {
      case 0: goto e100;  //quit
      case 1: {           //Factorial n
                printf("  N = "); scanf("%d",&n);
                s=Factorial(n,&r1,&r2);
                printf("  N! = ");
                if (s>0) printf("%12.0f\n",s);
                else printf("%12.0f   10^%4.0f\n",r1,r2);
		break;
			  }
      case 2: {           //Combination n,p
                printf("  N = "); scanf("%d",&n);
                printf("  P = "); scanf("%d",&p);
                s=Cnp(n,p);
                printf("  Cnp = ");
                if (s>0) printf("%12.0f\n",s);
                else printf("  Quantity impossible to evaluate\n");
		break;
			  }
      case 3: {           //Permutation n,p
                printf("  N = "); scanf("%d",&n);
                printf("  P = "); scanf("%d",&p);
                s=Anp(n,p);
                printf("  Anp = ");
                if (s>0) printf("%12.0f\n",s);
                else printf("  Quantity impossible to evaluate\n");
			  }
	} //end switch
  } while (choice!=0);
e100:;//quit
}

// end of file combi.cpp