Statistics

Problem Statement for "Mixture"

Problem Statement

You are trying to create a very precise mixture of a number of different chemicals. The exact amounts of the chemicals are given as a int[], desiredMixture, where desiredMixture[i] indicates how much of chemical i is required. You will be given a String[], availableMixtures, each element of which represents a mixture of chemicals that may be purchased (the chemical components for the mixture might not be available in pure form). Each element of availableMixtures will be formatted as a single-space separated list of integers, where the ith integer in availableMixtures[j] indicates how much chemical i is present in mixture j. Additionally, there will be one extra, final integer in each element of availableMixtures indicating the price of that mixture. You need not purchase the available mixtures in integral amounts. Hence if an element of availableMixtures were "3 5 9", you could purchase a mixture with 3 units of chemical 0 and 5 units of chemical 1 for a price of 9, and you could also purchase a mixture with 1.5 units of chemical 0 and 2.5 units of chemical 1 for a price of 4.5.

Your task is to determine the lowest price that the desired mixture can be achieved for. If it is impossible to achieve the desired mixture, return -1.

Definition

Class:
Mixture
Method:
mix
Parameters:
int[], String[]
Returns:
double
Method signature:
double mix(int[] mixture, String[] availableMixtures)
(be sure your method is public)

Constraints

  • mixture will contain between 1 and 10 elements, inclusive.
  • Each element of mixture will be between 1 and 10, inclusive.
  • availableMixtures will contain between 1 and 10 elements, inclusive.
  • Each element of availableMixtures will be formatted as N+1 single-space separated integers, where N is the number of elements in mixtures.
  • Each integer in availableMixtures will be between 0 and 10, inclusive, with no extra leading zeros.

Examples

  1. {1,2,3}

    {"1 0 0 1","0 1 0 2","0 0 1 3"}

    Returns: 14.0

    Here, there are three chemicals, and each one is available in only its pure form. Given the prices of the three chemicals and the desired quantities, the total cost is 1*1+2*2+3*3=14.

  2. {1,2,3}

    {"1 0 0 1","0 1 0 2","0 0 1 3","2 2 2 4"}

    Returns: 10.0

    Here, it is cheaper if we buy some of the mixture of all three chemicals.

  3. {1,1,1,1,1,1,1,1,1,1}

    {"10 9 9 9 9 9 9 9 9 10 0", "0 10 9 9 9 9 9 9 9 0 0", "0 0 10 9 9 9 9 9 9 0 0", "0 0 0 10 9 9 9 9 9 0 0", "0 0 0 0 10 9 9 9 9 0 0", "0 0 0 0 0 10 9 9 9 0 0", "0 0 0 0 0 0 10 9 9 0 0", "0 0 0 0 0 0 0 10 9 0 0", "0 0 0 0 0 0 0 0 10 1 0", "0 0 0 0 0 0 0 0 0 10 1"}

    Returns: -1.0

    This mixture is impossible. It can almost be achieved, but the closest you can get is to have the right amount of the first 9 chemicals, but just a little bit too much of the last one.

  4. {7,7,8,10}

    {"9 0 4 8 4", "8 8 9 0 1", "0 10 3 10 7", "10 2 2 0 1", "8 9 10 2 6", "1 2 5 8 8", "4 7 8 9 6", "2 10 6 8 10", "6 3 9 7 1", "3 6 9 9 1"}

    Returns: 3.5855425945563804

    The following table shows which mixtures to purchase to achieve the desired mixture as cheaply as possible: i | amount ---+-------- 0 | 202 / 943 2 | 239 / 943 3 | 595 / 1886 9 | 1808 / 2829

  5. {1}

    {"1 1","2 2","3 1","2 1"}

    Returns: 0.3333333333333333

  6. {6,6,8,6,4,6,5}

    {"6 4 1 5 4 6 2 2","9 9 9 1 2 0 1 9","10 4 3 0 0 2 2 10","7 9 6 0 9 9 8 5","6 7 8 2 7 8 4 0","3 2 7 7 1 7 10 1","9 4 5 9 3 10 2 8","7 3 8 2 10 1 2 3","10 4 3 3 8 7 2 1","3 6 9 10 5 8 8 5"}

    Returns: 5.173512399691586

  7. {4,8,3,3,5,6,10}

    {"4 8 8 5 9 8 2 10","8 8 7 6 8 0 5 6","7 10 2 6 8 10 9 7","0 10 1 1 8 7 9 3","9 9 0 2 3 3 9 6","10 1 7 8 2 10 5 9","7 4 6 5 0 10 10 0","1 9 5 2 5 0 9 5","0 10 3 10 5 0 8 6","3 1 0 0 4 4 6 6"}

    Returns: 4.283320277379531

  8. {10,7,8,10,10,7,5}

    {"5 9 2 9 2 0 2 6","8 6 6 8 6 9 2 10","1 6 10 9 2 7 7 2","0 1 0 1 1 4 0 9","10 10 8 2 3 5 10 6","4 4 2 6 3 2 4 0","5 4 3 4 7 6 10 0","7 1 6 3 9 4 1 10","2 4 2 7 0 2 5 2","10 5 0 8 8 3 8 8"}

    Returns: 10.853957265921384

  9. {8,10,6,10,7,5,10}

    {"4 5 4 7 10 10 3 5","6 4 8 1 1 8 0 4","2 4 7 7 10 5 6 1","9 8 1 9 8 3 2 10","1 3 3 7 0 0 10 2","2 1 0 6 10 9 10 0","10 7 1 4 7 5 10 8","2 4 9 8 6 1 2 1","4 8 2 2 2 5 3 5","3 10 5 7 1 9 5 5"}

    Returns: 7.957057635769299

  10. {8,8,7,10,7,10,7}

    {"10 0 5 5 2 3 4 6","6 1 3 4 0 7 7 3","6 9 9 5 5 2 10 8","7 7 10 6 2 9 6 0","1 4 1 1 8 10 7 3","10 0 8 3 7 8 1 10","7 5 0 9 8 7 7 8","3 8 6 8 5 1 10 7","3 10 8 8 5 9 3 5","5 2 10 10 7 8 9 5"}

    Returns: 6.951635249280288

  11. {10,5,10,5,6,10,8}

    {"4 1 1 3 4 2 3 10","3 2 10 0 6 1 4 1","3 2 1 3 0 10 10 3","3 8 3 10 2 10 7 1","5 5 0 6 6 4 6 3","7 6 0 2 6 10 1 2","8 4 7 3 4 10 2 9","1 4 0 2 6 0 4 4","6 1 9 2 0 1 2 7","5 4 5 9 0 1 1 4"}

    Returns: 10.591768511633525

  12. {7,6,9,10,10,4,6}

    {"2 8 1 6 10 5 5 0","1 7 4 3 6 5 7 8","10 4 6 0 1 2 2 6","3 0 9 8 6 4 8 8","5 1 5 4 1 1 8 2","10 3 1 2 5 10 10 1","4 1 10 1 7 4 9 3","0 5 2 1 6 6 8 2","1 10 9 10 0 9 4 7","5 2 5 7 7 0 2 3"}

    Returns: 5.161066116975455

  13. {3,3,5,8,5,4,5}

    {"4 1 5 2 4 3 3 2","0 6 8 10 0 1 6 10","4 9 2 1 5 7 7 1","8 5 9 10 0 4 8 4","1 4 7 10 6 1 5 6","9 5 5 10 4 6 2 3","0 2 0 8 3 1 3 7","8 0 1 10 10 8 4 0","5 1 9 9 8 6 6 0","10 3 10 0 7 1 8 2"}

    Returns: 3.631869936500985

  14. {8,4,6,8,6,4,6}

    {"4 3 0 6 2 5 10 6","6 0 9 1 6 3 4 0","3 3 6 0 2 1 1 1","3 7 6 3 2 7 2 7","3 0 3 4 7 4 8 3","8 2 4 5 9 7 6 8","3 1 8 5 7 8 4 8","7 3 3 8 0 0 5 2","9 2 3 10 9 9 1 9","9 5 4 10 10 7 1 4"}

    Returns: 3.7257518624558834

  15. {5,6,5,9,3,6,8}

    {"4 9 2 5 1 10 2 4","0 10 0 7 6 6 9 7","0 9 1 10 8 1 8 10","7 6 1 5 1 3 7 9","4 6 1 8 8 1 10 10","0 0 7 6 0 5 2 6","5 6 1 10 9 3 6 3","1 1 6 0 9 2 10 7","4 9 1 7 8 8 5 2","5 7 8 8 4 6 9 5"}

    Returns: 10.839380539907527

  16. {8,10,6,9,6,4,8}

    {"5 2 7 9 8 1 2 7","3 0 10 8 0 3 4 4","8 8 3 4 1 4 2 6","8 0 5 10 4 0 8 8","10 1 1 3 7 2 1 8","2 6 1 8 3 4 7 8","4 9 1 8 4 1 8 4","3 6 8 3 9 7 8 9","6 7 3 8 4 0 6 3","0 2 4 6 1 3 1 6"}

    Returns: 7.823322980941565

  17. {7,8,9,10,4,10,5}

    {"5 5 6 6 0 7 2 7","7 1 10 6 9 8 6 0","0 8 1 10 6 7 0 4","9 8 0 4 6 9 4 4","4 6 9 0 6 0 10 3","8 8 4 5 8 7 0 8","7 6 4 6 2 7 10 1","2 4 6 3 5 9 3 5","10 1 10 10 7 1 8 1","10 10 6 5 6 5 4 1"}

    Returns: 8.319746481403076

  18. {7,7,4,8,7,7,6}

    {"9 7 6 2 2 6 10 6","4 3 1 8 8 7 0 5","4 4 7 5 6 1 3 2","8 1 1 2 7 9 10 5","10 3 2 2 0 4 7 8","0 3 3 7 10 3 4 7","0 5 1 8 1 3 10 7","7 3 7 2 2 1 3 8","6 7 10 6 9 1 1 1","3 10 2 3 3 4 6 2"}

    Returns: 6.928795922640846

  19. {8,7,4,4,4,5,3}

    {"10 10 1 0 4 5 0 0","0 8 10 0 5 10 1 6","6 9 8 7 7 2 3 1","9 7 7 1 10 7 8 8","1 0 9 8 4 3 0 4","2 7 4 10 5 6 3 5","8 3 2 3 2 2 6 3","1 3 7 1 0 9 2 3","1 5 8 4 4 3 8 8","0 3 0 1 5 7 3 2"}

    Returns: 2.666549113817997

  20. {4,6,5,7,7,10,8}

    {"4 2 3 9 6 9 5 9","6 5 0 1 0 5 1 5","2 0 0 4 1 8 8 4","2 3 0 0 7 7 2 6","0 9 2 8 10 6 4 8","0 1 1 0 0 4 7 8","5 10 1 8 0 0 4 1","5 8 0 4 5 6 8 6","5 4 10 0 5 9 6 8","9 2 6 3 3 5 1 1"}

    Returns: 10.046185666378841

  21. {8,5,7,7,10,8,7}

    {"7 2 0 6 5 8 1 0","3 2 8 3 3 8 7 10","0 3 5 7 10 6 9 9","3 2 8 0 10 1 8 6","9 9 1 10 2 4 0 9","8 5 6 5 10 6 3 2","5 6 0 8 4 7 7 5","0 8 10 10 5 1 7 0","6 3 10 6 1 4 4 2","4 7 8 3 5 8 9 8"}

    Returns: 4.1582005740123735

  22. {9,7,8,6,9,6,10}

    {"9 3 0 3 10 2 7 4","7 3 3 10 7 1 4 4","10 9 7 3 7 2 7 0","4 7 2 2 2 5 5 6","0 0 4 1 7 9 9 4","5 2 2 1 8 5 2 0","3 10 9 4 8 8 8 1","10 8 7 0 3 2 8 9","3 1 8 6 0 9 5 7","4 0 3 8 8 1 0 4"}

    Returns: 6.200169014575328

  23. {7,5,2,2,2,6,7}

    {"9 2 0 9 1 8 8 6","10 8 3 7 4 0 7 6","7 2 2 9 2 10 2 3","10 8 10 10 0 3 3 3","1 10 1 6 8 4 7 0","10 5 2 1 0 9 10 1","4 4 8 2 0 7 0 10","9 7 5 3 1 8 10 7","9 5 4 0 10 3 1 3","0 4 1 5 3 4 8 9"}

    Returns: 1.2891999603752162

  24. {6,6,5,5,7,4,5}

    {"7 9 4 5 6 10 1 8","10 7 2 9 7 6 6 6","6 9 4 7 0 4 10 4","2 3 3 4 7 1 6 3","2 0 10 8 0 8 6 4","7 10 4 5 8 5 2 3","8 8 9 4 1 0 8 9","9 7 8 0 1 7 7 0","8 3 5 4 6 2 1 6","4 4 2 6 6 8 9 1"}

    Returns: 3.792137724276822

  25. {5,9,8,7,9,8,7}

    {"1 5 6 1 9 2 8 0","2 7 10 7 3 3 4 3","9 4 6 5 2 9 6 4","5 8 2 0 8 1 1 9","9 5 9 5 3 7 9 2","1 1 2 5 1 6 0 9","0 5 3 8 10 5 0 8","8 7 1 1 0 4 5 8","1 5 7 2 0 6 7 9","10 7 6 8 9 4 1 9"}

    Returns: 9.904872087508924

  26. {6,9,8,7,8,8,8,8}

    {"1 10 9 7 9 6 9 9 2","6 8 9 5 7 5 8 6 4","4 10 5 9 0 3 9 5 7","9 2 0 8 3 6 9 6 2","9 7 4 0 1 9 1 4 4","3 3 1 2 0 4 9 7 7","8 2 2 5 9 8 3 2 0","3 0 1 2 0 10 3 7 6","7 6 6 10 6 5 4 2 4","9 0 4 8 4 1 3 4 2"}

    Returns: 3.2867029787581328

  27. {6,7,9,10,10,9,7,10}

    {"5 7 0 7 1 4 9 10 9","9 10 1 3 7 10 5 7 7","7 3 7 2 9 10 1 8 10","4 5 2 9 5 3 8 7 6","0 4 6 10 8 7 2 1 0","2 2 7 6 9 2 1 5 7","1 1 10 10 0 5 8 8 5","1 8 3 3 8 0 4 2 9","3 1 5 10 2 10 1 4 1","10 0 4 1 10 8 10 10 8"}

    Returns: 10.489921734948188

  28. {6,8,8,8,9,5,7,8}

    {"3 9 1 8 6 1 2 9 5","8 1 0 10 6 0 4 4 8","0 9 5 6 1 7 5 9 4","2 5 6 9 10 3 10 5 5","7 5 8 4 8 1 8 8 4","7 3 1 7 7 9 7 8 9","5 6 9 1 9 6 0 3 5","6 0 4 1 6 7 3 5 7","1 7 0 8 10 4 0 9 10","8 5 2 10 0 1 5 4 3"}

    Returns: 6.555450296750259

  29. {8,7,7,10,7,8,7,7}

    {"8 9 9 8 4 5 9 4 6","10 0 0 7 1 8 2 7 3","0 3 0 5 0 3 5 5 7","1 9 8 10 5 9 0 2 5","2 7 6 10 7 1 6 0 1","7 7 2 3 4 10 4 0 8","9 1 9 2 10 1 7 6 9","8 4 9 10 0 2 0 0 4","6 8 2 3 0 5 8 7 6","2 6 5 1 6 5 2 0 7"}

    Returns: 9.10955568375407

  30. {9,5,10,8,8,9,7,10}

    {"7 8 2 3 9 1 10 8 5","7 4 9 8 8 1 0 10 9","3 2 6 0 1 1 4 1 8","8 3 7 9 0 8 5 1 8","2 8 10 4 6 3 7 10 7","10 6 2 4 2 9 1 8 10","5 0 1 1 9 4 1 0 10","1 1 4 7 2 6 7 8 1","3 2 8 0 5 5 7 6 2","10 1 6 0 3 2 6 10 0"}

    Returns: 11.039557621133785

  31. {8,5,8,5,9,10,6,9}

    {"6 5 5 1 8 5 10 1 8","2 1 2 3 3 9 0 8 10","6 7 4 4 7 10 7 3 0","2 0 10 1 2 4 1 10 0","8 10 5 5 9 7 7 6 0","10 5 1 10 7 10 0 9 6","9 2 2 7 7 9 9 5 2","5 2 10 4 7 1 1 6 8","1 5 10 4 8 8 1 5 10","6 2 8 2 5 1 1 3 0"}

    Returns: 8.854244907120767

  32. {6,9,4,10,8,6,8,9}

    {"6 7 10 2 9 0 2 2 0","7 0 0 8 9 3 3 2 0","2 5 5 7 1 4 1 10 0","2 8 1 9 8 5 9 5 3","3 7 7 7 3 4 10 2 8","4 8 8 5 6 6 4 1 9","7 7 0 6 6 4 7 8 6","10 2 4 0 3 7 0 1 5","4 5 8 0 9 6 5 2 1","7 1 3 6 4 10 0 9 1"}

    Returns: 4.339266377415257

  33. {2,5,9,4,10,4,9,4}

    {"10 1 2 3 10 10 2 6 7","0 1 9 3 8 0 7 1 10","10 10 10 8 1 5 8 8 3","6 2 2 6 6 8 1 9 0","4 6 4 0 5 2 8 7 10","0 1 5 0 8 1 10 8 2","5 8 8 8 4 7 9 6 10","0 10 3 7 9 9 4 1 5","1 10 5 6 7 9 3 4 10","6 1 6 1 6 9 4 2 7"}

    Returns: 11.186928621722409

  34. {2,5,9,4}

    {"0 1 9 3 10" ,"0 1 5 0 2" ,"5 8 8 8 10" ,"0 10 3 7 5"}

    Returns: 7.183431952662722

  35. {4,9,7,5,8,6,7,7,5,8}

    {"8 0 0 0 0 0 0 0 0 0 10","0 7 0 0 0 0 0 3 0 0 5","8 0 3 0 0 0 3 0 0 0 4","4 2 0 7 0 0 0 6 0 6 10","0 0 5 0 6 0 0 0 0 0 7","0 0 0 0 0 4 0 0 0 8 4","0 1 0 0 0 0 5 0 0 0 4","0 0 0 0 0 0 0 6 0 0 3","0 2 0 0 0 9 0 0 8 0 9","0 0 0 0 0 0 0 0 0 1 7"}

    Returns: 53.172619047619044

  36. {5,9,2,5,8,2,9,5,2,7}

    {"3 0 0 0 0 0 0 1 0 0 1","0 10 0 0 0 0 0 0 0 0 4","0 0 7 8 0 10 0 0 0 0 9","0 0 0 4 0 0 0 0 0 0 1","2 0 0 0 4 0 0 0 0 0 3","0 0 0 0 0 10 8 0 0 0 5","0 0 0 1 0 0 7 0 0 0 1","0 0 0 0 0 0 0 4 0 0 5","0 0 10 0 7 0 0 0 10 0 1","0 0 0 0 0 0 0 0 0 9 9"}

    Returns: 24.901190476190475

  37. {8,9,3,9,8,8,5,7,4,4}

    {"9 0 0 0 10 0 0 3 0 0 2","0 7 0 0 0 0 0 0 0 0 9","4 10 8 0 0 5 0 0 0 0 6","0 0 0 7 0 0 0 0 0 0 9","0 0 0 0 10 0 0 0 0 0 5","0 0 0 0 0 5 2 0 0 3 10","0 0 0 0 0 0 8 0 0 0 10","0 0 0 0 0 0 0 4 0 0 3","0 0 0 0 1 0 0 0 10 0 1","0 0 0 0 0 0 0 0 5 1 5"}

    Returns: 43.211011904761904

  38. {8,2,2,10,5,6,7,10,10,7}

    {"8 0 0 7 0 0 0 0 10 0 10","0 3 0 0 0 0 4 0 0 0 7","6 0 9 0 0 0 0 0 0 0 5","0 9 0 10 0 0 0 0 1 6 9","0 0 0 0 5 0 0 0 0 0 9","0 1 0 10 0 6 0 0 0 0 1","0 1 0 2 6 0 9 0 1 8 10","0 0 0 0 0 0 0 7 0 0 1","0 0 6 0 0 0 0 0 8 0 9","0 0 0 0 0 6 0 0 0 1 8"}

    Returns: 28.481304910008937

  39. {6,6,6,6,10,4,4,6,2,7}

    {"4 0 0 0 6 10 0 0 0 0 2","0 3 0 0 0 0 0 0 0 0 10","0 0 3 0 0 0 0 0 0 0 8","0 0 0 1 0 0 0 0 0 0 10","10 0 0 0 10 0 0 0 0 10 9","0 4 0 5 0 2 4 0 0 0 1","0 3 0 0 0 0 2 7 0 0 9","0 0 0 0 8 5 0 10 0 0 7","0 0 0 0 0 0 0 0 9 0 1","0 4 0 0 7 0 0 0 0 7 7"}

    Returns: 52.58938149972633

  40. {7,8,2,3,2,4,5,9,3,3}

    {"4 0 0 2 0 0 0 3 0 0 4","0 6 0 0 1 0 0 0 0 0 6","0 0 5 0 0 0 0 0 7 0 6","0 0 0 8 1 0 0 0 0 0 7","0 0 0 0 4 0 5 0 0 0 5","0 0 1 0 4 4 0 0 0 0 10","2 0 0 0 0 0 2 0 0 0 9","0 8 0 0 0 5 0 9 0 0 8","0 0 2 0 0 5 0 0 5 8 1","0 0 0 0 0 0 0 4 0 10 10"}

    Returns: 34.848877006918634

  41. {5,6,2,2,3,5,6,5,9,3}

    {"7 0 6 0 0 0 0 0 4 0 3","0 2 1 0 6 0 0 0 8 0 9","0 0 10 0 0 0 0 0 0 0 4","0 0 0 8 0 3 0 3 8 0 4","0 0 0 0 10 0 6 0 0 0 5","0 10 0 0 0 8 0 0 0 0 1","5 0 0 0 0 0 10 0 0 0 3","0 0 0 0 0 0 0 8 0 0 5","4 0 0 0 0 0 5 0 5 4 2","0 0 0 8 0 0 0 7 0 6 10"}

    Returns: 10.4653304973822

  42. {3,9,3,8,2,8,8,9,8,6}

    {"1 9 0 0 0 0 0 0 0 6 2","0 3 0 0 0 0 9 0 0 0 1","0 0 5 0 7 3 10 9 0 0 6","0 2 0 5 0 0 0 0 0 0 7","10 0 0 0 4 0 0 0 0 0 7","0 0 0 0 0 1 0 0 8 0 4","6 0 0 0 0 8 4 6 0 0 7","0 0 0 0 0 3 0 6 0 0 4","0 0 5 2 0 9 0 5 10 0 5","0 0 0 6 0 0 0 0 0 10 3"}

    Returns: 20.484996399059963

  43. {7,9,3,2,3,4,8,8,3,9}

    {"6 1 2 0 0 0 0 0 0 0 1","0 4 0 0 0 0 5 0 0 0 5","0 0 9 0 0 0 0 1 0 0 8","0 0 0 3 0 4 0 0 0 0 6","0 0 0 0 10 3 1 0 9 0 10","0 0 0 0 0 3 0 0 0 2 6","0 0 4 0 7 0 5 0 0 0 8","2 0 0 0 0 0 2 7 0 0 4","0 0 0 0 0 0 0 0 4 0 1","0 5 0 0 0 0 0 0 0 9 6"}

    Returns: 25.308238051529187

  44. {6,2,2,8,2,3,1,5,6,3}

    {"7 0 0 7 0 0 0 5 5 0 10","0 10 6 0 0 0 0 2 0 0 8","0 0 10 0 8 0 0 0 0 0 4","0 0 0 8 1 9 0 0 6 0 5","0 3 0 0 1 0 0 0 0 0 7","0 0 0 0 6 4 0 0 0 0 8","0 0 0 0 0 0 1 0 0 0 9","0 0 0 0 0 0 0 7 0 0 8","0 0 0 0 0 0 0 0 1 2 9","6 0 2 4 0 0 0 0 0 7 8"}

    Returns: 32.055920002129014

  45. {2,6,6,7,10,2,10,9,3,3}

    {"10 0 0 0 0 0 0 6 0 0 4","0 7 6 0 0 0 0 0 0 0 2","0 0 3 10 10 0 0 0 0 0 5","0 0 0 2 0 0 0 0 0 0 5","0 0 0 0 9 2 5 1 0 0 2","0 0 0 6 0 7 0 0 0 0 7","0 0 5 10 0 7 1 0 0 1 9","0 0 1 0 0 0 0 6 0 3 9","0 0 0 0 2 0 9 5 5 0 3","0 0 0 0 0 0 0 0 0 7 2"}

    Returns: 28.432384532760473

  46. {8,5,8,5,6,4,9,9,8,4}

    {"6 0 0 0 0 0 0 0 0 0 2","0 9 0 10 0 0 7 0 0 2 9","0 8 7 0 4 0 0 0 0 0 7","0 0 8 3 0 0 0 0 1 0 1","0 0 0 3 4 0 0 0 0 0 8","0 0 0 0 0 2 0 0 0 0 9","0 0 0 0 1 0 5 0 0 0 4","0 0 0 2 0 0 0 6 0 0 1","0 0 0 0 0 0 0 3 6 0 3","3 0 6 0 0 0 0 3 9 5 1"}

    Returns: 38.123957176617985

  47. {3,7,2,10,4,4,5,7,9,2}

    {"5 8 0 0 2 0 5 0 0 0 8","0 10 0 0 10 0 0 0 0 0 5","0 0 2 0 0 0 0 0 0 0 2","0 0 0 8 0 2 4 2 0 0 2","0 0 0 2 1 8 0 0 0 0 1","0 0 0 0 10 7 5 9 0 0 5","0 0 0 0 0 0 2 3 8 0 1","0 0 0 8 0 0 0 5 0 0 9","0 0 0 0 0 0 0 0 6 0 2","0 0 0 0 0 0 0 0 0 2 7"}

    Returns: 26.38108108108108

  48. {2,8,7,10,1,5,9,9,4,9}

    {"5 0 0 1 0 0 5 4 0 10 8","0 5 0 0 0 0 0 2 0 0 3","0 0 2 0 0 0 0 0 0 0 6","3 7 0 1 0 7 0 0 0 0 8","0 0 0 4 4 0 3 0 0 0 6","0 0 1 0 0 4 0 0 0 5 6","0 0 0 0 0 0 1 0 0 0 2","0 0 0 0 0 0 0 1 0 0 4","0 0 0 7 0 0 0 0 1 0 4","0 0 5 0 0 0 0 0 8 10 3"}

    Returns: 70.80620437956205

  49. {7,9,9,2,10,8,7,1,4,10}

    {"10 0 0 0 0 0 6 0 0 0 1","0 10 0 0 0 0 0 0 0 0 10","0 0 7 0 0 6 0 0 0 0 8","0 0 0 7 0 0 0 0 0 0 5","0 0 0 0 10 0 0 0 0 3 5","0 0 1 0 0 7 1 0 0 0 5","0 4 0 0 0 0 4 0 5 0 1","0 0 0 0 1 0 2 10 0 0 5","0 0 0 4 0 0 0 5 9 0 10","0 0 1 0 0 0 0 0 0 10 1"}

    Returns: 25.855488551257068

  50. {8,9,3,2,6,10,6,5,5,5}

    {"3 8 0 0 2 8 0 0 0 0 8","0 3 6 8 4 1 2 0 0 1 10","6 0 10 0 0 0 0 0 0 0 5","0 0 0 7 0 6 10 0 0 0 10","4 0 0 0 7 0 1 0 0 0 4","7 0 0 0 0 2 0 0 0 0 5","0 0 0 0 0 0 10 0 0 0 4","0 0 0 0 0 0 5 7 7 0 8","1 0 0 0 0 0 0 0 7 0 4","0 0 0 0 0 0 0 0 0 8 8"}

    Returns: 26.103779853319125

  51. {5,8,10,7,5,3,4,4,10,5}

    {"9 0 0 0 7 0 0 0 0 0 6","0 4 0 1 0 2 5 0 0 10 5","0 3 6 0 7 0 0 0 0 0 7","0 0 7 9 0 0 0 4 0 7 2","0 0 0 0 5 0 0 8 0 0 8","0 0 0 0 0 4 7 0 0 0 2","0 0 0 9 0 0 1 2 2 0 7","0 6 5 0 0 0 0 1 0 0 7","0 0 0 0 0 0 0 0 7 0 5","0 0 0 0 0 5 0 0 2 4 1"}

    Returns: 24.092866548483464

  52. {7,8,4,5,6,5,7,4,2,8}

    {"10 2 9 0 0 7 0 0 0 0 10","0 4 0 0 0 0 0 0 0 0 1","0 0 10 0 0 0 0 4 10 0 1","6 0 0 8 0 7 0 0 6 7 9","0 0 0 0 6 0 10 0 0 0 1","0 1 0 0 0 1 0 0 0 7 8","0 0 0 0 5 0 8 0 8 0 2","9 0 0 0 0 0 5 9 2 0 10","0 0 1 9 0 0 0 0 1 0 10","0 8 0 0 7 0 0 6 0 1 8"}

    Returns: 23.171089733800887

  53. {5,8,10,7,5,3,4,4,10,5}

    {"10 2 9 0 0 7 0 0 0 0 10","0 4 0 0 0 0 0 0 0 0 1","0 0 10 0 0 0 0 4 10 0 1","6 0 0 8 0 7 0 0 6 7 9","0 0 0 0 6 0 10 0 0 0 1","0 1 0 0 0 1 0 0 0 7 8","0 0 0 0 5 0 8 0 8 0 2","9 0 0 0 0 0 5 9 2 0 10","0 0 1 9 0 0 0 0 1 0 10","0 8 0 0 7 0 0 6 0 1 8"}

    Returns: -1.0

  54. {1,1,1,1,1,1,1,1,1,1}

    {"0 0 0 0 0 0 0 0 8 0 10","0 4 0 0 0 0 0 0 0 0 1","0 0 10 0 0 0 0 4 10 0 1","6 0 0 8 0 7 0 0 6 7 9","0 0 0 0 6 0 10 0 0 0 1","0 1 0 0 0 1 0 0 0 7 8","0 0 0 0 5 0 8 0 8 0 2","0 0 0 0 0 0 2 2 0 2 10","0 0 0 9 9 9 0 0 1 0 10","1 1 1 0 0 0 0 0 0 0 8"}

    Returns: 15.222222222222221

  55. { 7, 7, 8, 10 }

    { "9 0 4 8 4", "8 8 9 0 1", "0 10 3 10 7", "10 2 2 0 1", "8 9 10 2 6", "1 2 5 8 8", "4 7 8 9 6", "2 10 6 8 10", "6 3 9 7 1", "3 6 9 9 1" }

    Returns: 3.5855425945563804

  56. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    {"10 9 9 9 9 9 9 9 9 10 0", "0 10 9 9 9 9 9 9 9 0 0", "0 0 10 9 9 9 9 9 9 0 0", "0 0 0 10 9 9 9 9 9 0 0", "0 0 0 0 10 9 9 9 9 0 0", "0 0 0 0 0 10 9 9 9 0 0", "0 0 0 0 0 0 10 9 9 0 0", "0 0 0 0 0 0 0 10 9 0 0", "0 0 0 0 0 0 0 0 10 1 0", "0 0 0 0 0 0 0 0 0 10 1" }

    Returns: -1.0

  57. {1, 2, 3 }

    {"1 0 0 1", "0 1 0 2", "0 0 1 3" }

    Returns: 14.0

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