Statistics

Problem Statement

	S = { a1 * a2 * a3 : ai in Ri }

Definition

Class:

ProductSet

Method:

howMany

Parameters:

int[], int[]

Returns:

int

Method signature:

int howMany(int[] lows, int[] highs)

(be sure your method is public)

Constraints

• lows and highs will each contain exactly 3 elements.
• Each element of highs will be between 0 and 100, inclusive.
• Element i of lows will be between 0 and highs[i], inclusive.

Examples

1. {1,1,1}

   {2,2,2}

   Returns: 4

   The possible distinct products are 1, 2, 4, and 8. All of the products are listed below: 1*1*1 = 1 1*1*2 = 2 1*2*1 = 2 1*2*2 = 4 2*1*1 = 2 2*1*2 = 4 2*2*1 = 4 2*2*2 = 8

2. {0,1,1}

   {2,2,2}

   Returns: 5

   Now the possible products are 0, 1, 2, 4, and 8.

3. {0,0,0}

   {100,100,100}

   Returns: 46912

   Note that the maximum possible product is 100*100*100 = 1 million. Marking off all possible products, we see there are only 46912 distinct values.

4. {100,100,1}

   {100,100,1}

   Returns: 1

5. {0,0,0}

   {100,100,0}

   Returns: 1

6. {1,1,0}

   {1,1,92}

   Returns: 93

7. {6,3,91}

   {55,29,93}

   Returns: 1824

8. {27,100,20}

   {34,100,35}

   Returns: 98

9. {53,4,4}

   {87,53,89}

   Returns: 26911

10. {8,0,15}

    {17,5,82}

    Returns: 1362

11. {39,0,44}

    {79,41,52}

    Returns: 7984

12. {19,98,78}

    {57,99,93}

    Returns: 1104

13. {6,66,12}

    {6,67,12}

    Returns: 2

14. {76,19,40}

    {79,36,69}

    Returns: 1523

15. {6,89,51}

    {19,90,99}

    Returns: 1002

16. {72,25,85}

    {97,67,99}

    Returns: 9258

17. {42,3,60}

    {54,29,95}

    Returns: 7276

18. {90,11,98}

    {100,45,99}

    Returns: 691

19. {9,95,32}

    {89,95,56}

    Returns: 1285

20. {48,36,99}

    {67,99,99}

    Returns: 946

21. {17,34,14}

    {35,63,18}

    Returns: 1524

22. {93,58,100}

    {100,61,100}

    Returns: 32

23. {76,46,92}

    {90,75,93}

    Returns: 837

24. {83,3,53}

    {99,96,54}

    Returns: 2741

25. {2,2,25}

    {78,74,29}

    Returns: 7700

26. {36,89,93}

    {73,95,100}

    Returns: 1847

27. {4,41,32}

    {71,99,42}

    Returns: 16362

28. {36,46,49}

    {56,58,87}

    Returns: 5359

29. {66,27,46}

    {67,31,94}

    Returns: 439

30. {91,29,87}

    {98,60,97}

    Returns: 1909

31. {56,56,40}

    {67,61,61}

    Returns: 1026

32. {91,56,13}

    {99,60,87}

    Returns: 3067

33. {38,97,37}

    {39,98,61}

    Returns: 98

34. {92,78,74}

    {95,80,99}

    Returns: 282

35. {50,92,67}

    {63,95,97}

    Returns: 1485

36. {70,70,25}

    {89,84,87}

    Returns: 8117

37. {81,73,74}

    {100,98,77}

    Returns: 1320

38. {99,7,59}

    {100,59,70}

    Returns: 1154

39. {45,91,97}

    {51,94,98}

    Returns: 54

40. {16,41,96}

    {100,76,100}

    Returns: 8414

41. {12,2,93}

    {82,56,100}

    Returns: 11898

42. {20,24,68}

    {75,84,98}

    Returns: 26648

43. {22,65,83}

    {51,87,99}

    Returns: 7399

44. {52,92,32}

    {100,99,84}

    Returns: 10737

45. {53,42,30}

    {76,78,52}

    Returns: 7813

46. {21,21,40}

    {70,77,62}

    Returns: 13828