positions_average.cpp

//Suppose you have 4 numbers: 0, 9, 6, 4 and 3 strings composed with them:
//s1 = "6900690040"
//s2 = "4690606946"
//s3 = "9990494604"

//Compare s1 and s2 to see how many positions they have in common: 0 at index 3, 6 at index 4, 4 at index 8 : 3 common positions out of ten.

//Compare s1 and s3 to see how many positions they have in common: 9 at index 1, 0 at index 3, 9 at index 5 : 3 common positions out of ten.

//Compare s2 and s3. We find 2 common positions out of ten.

//So for the 3 strings we have 8 common positions out of 30 ie 0.2666... or 26.666...%

//Given n substrings (n >= 2) in a string s our function pos_average will calculate the average percentage of positions that are the same between the (n * (n-1)) / 2 sets of substrings taken amongst the given n substrings. It can happen that some substrings are duplicate but since their ranks are not the same in s they are considered as different substrings.

//The function returns the percentage formatted as a float with 10 decimals but the result is tested at 1e.-9 (see function assertFuzzy in the tests).
//Example:

//Given string s = "444996, 699990, 666690, 096904, 600644, 640646, 606469, 409694, 666094, 606490" composing a set of n = 10 substrings (hence 45 combinations), pos_average returns 29.2592592593.

//In a set the n substrings will have the same length ( > 0 ).

#include <string>
#include <vector>
#include <cmath>

double posAverage(const std::string &s)
{
  int slen = s.find(',');
  int n = ((int)s.length() - slen) / (slen + 2) + 1;
  char t; int sum = 0; int total = 0; int tempsum = 0;
	for (int j = 0; j < slen; j++)
  {
    for (t='0'; t<='9'; t++)
    {
      for (int i = 0; i < n; i++)
      {
        if (s[i*(slen + 2) + j] == t)
          tempsum+=1;
      }
      if (tempsum > 1)
        sum += tempsum * (tempsum-1) / 2 ;
      tempsum = 0;
    }
  }
  
  total = n * (n - 1) / 2 * slen;
  
  return (double) sum/total * 100;
}