average

 #include <stdio.h>

/*
algorithm explanation

use following formulas to calculate average value of n numbers(a1,a2,...,an):

1. average(n)=(a1 + a2 + ... + an)/n;

2. average(n)=a1/n + a2/n + ... + an/n;

                          ┌ 0 (n < 1)
                          │
3. average(n)=┤
                          │
                          └ average(n-1) + (an - average(n-1))/n (n>0)

   formula 3 equal to : average(n) = (average(n-1)*(n-1) + an)/n

here, formula 3 is the best one for computer to calculate average value.
*/

double avr_loop(double *a, int n)
{
 double avr=.0L;
 int i;

 for (i=0; i<n; i++)
 {
  avr+=(a[i]-avr)/(i+1);
 }

 return avr;
}

double avr_rcv(double *a, int n)
{
 static double avr=.0L;

 if (n==0)
  return a[0];

 avr = avr_rcv(a, n-1);
 return (avr + (a[n-1]-avr)/n);
}

/*
void main()
{
 double a[6]={.1L,.2L,.3L,.4L,.5L,.6L};

 printf("average: % lf,%lf", avr_loop(a,6),avr_rcv(a,6));
}*/