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Problem Statement for "DevuAndBeautifulSubstrings"

Problem Statement

Devu likes to play with binary strings: strings in which each character is either '0' or '1'.

Devu calls a binary string beautiful if it is nonempty and no two consecutive characters in the string are equal.. The beauty level of a binary string is the number of beautiful substrings it contains. For example, the beauty level of "0001" is 5. This string contains four beautiful substrings of length 1 and one beautiful substring of length 2.

You are given ints n and cnt. Return the number of binary strings of length n with beauty level equal to cnt.

Definition

Class:
DevuAndBeautifulSubstrings
Method:
countBeautifulSubstrings
Parameters:
int, int
Returns:
long
Method signature:
long countBeautifulSubstrings(int n, int cnt)
(be sure your method is public)

Constraints

  • n will be between 1 and 50, inclusive.
  • cnt will be between 0 and n * (n + 1) / 2, inclusive.

Examples

  1. 2

    2

    Returns: 2

    There are four binary strings of length 2: "00", "01", "10", and "11". Their beauty levels are 2, 3, 3, and 2, respectively. Hence, there are two binary strings of length 2 with beauty level 2.

  2. 2

    1

    Returns: 0

    There is no binary string of length 2 with beauty level 1.

  3. 3

    4

    Returns: 4

  4. 15

    35

    Returns: 642

  5. 40

    820

    Returns: 2

  6. 50

    94

    Returns: 32357325751902

  7. 1

    0

    Returns: 0

  8. 1

    1

    Returns: 2

  9. 2

    0

    Returns: 0

  10. 2

    1

    Returns: 0

  11. 2

    2

    Returns: 2

  12. 2

    3

    Returns: 2

  13. 3

    0

    Returns: 0

  14. 3

    1

    Returns: 0

  15. 3

    2

    Returns: 0

  16. 3

    3

    Returns: 2

  17. 3

    4

    Returns: 4

  18. 3

    5

    Returns: 0

  19. 3

    6

    Returns: 2

  20. 50

    114

    Returns: 11702340820662

  21. 50

    697

    Returns: 4080

  22. 50

    881

    Returns: 120

  23. 50

    1211

    Returns: 0

  24. 50

    844

    Returns: 48

  25. 50

    600

    Returns: 23424

  26. 50

    1249

    Returns: 0

  27. 50

    1121

    Returns: 0

  28. 50

    123

    Returns: 6112844691130

  29. 50

    790

    Returns: 48

  30. 49

    1047

    Returns: 0

  31. 49

    1072

    Returns: 0

  32. 49

    351

    Returns: 16468878

  33. 49

    987

    Returns: 0

  34. 49

    859

    Returns: 0

  35. 49

    494

    Returns: 413568

  36. 49

    767

    Returns: 108

  37. 49

    709

    Returns: 144

  38. 49

    1011

    Returns: 0

  39. 49

    882

    Returns: 12

  40. 44

    62

    Returns: 70552643202

  41. 47

    71

    Returns: 1517606097672

  42. 43

    85

    Returns: 235736203608

  43. 46

    155

    Returns: 17909350386

  44. 47

    140

    Returns: 125325724122

  45. 43

    91

    Returns: 168151379926

  46. 50

    68

    Returns: 1014068076524

  47. 43

    69

    Returns: 206737586850

  48. 42

    109

    Returns: 18006203328

  49. 46

    163

    Returns: 10269094988

  50. 44

    86

    Returns: 486259569590

  51. 47

    155

    Returns: 42511148992

  52. 46

    143

    Returns: 42132742866

  53. 44

    82

    Returns: 552904213284

  54. 49

    190

    Returns: 25111043444

  55. 45

    132

    Returns: 40069738172

  56. 47

    128

    Returns: 312711092862

  57. 50

    93

    Returns: 32910768777764

  58. 49

    187

    Returns: 29932241848

  59. 50

    146

    Returns: 1092802455310

  60. 48

    96

    Returns: 6798263258824

  61. 46

    119

    Returns: 264900322248

  62. 49

    77

    Returns: 8862853544598

  63. 49

    81

    Returns: 13269771945790

  64. 50

    113

    Returns: 12531251617894

  65. 48

    140

    Returns: 299217500616

  66. 47

    147

    Returns: 74998267002

  67. 49

    152

    Returns: 296890702074

  68. 46

    117

    Returns: 309608181790

  69. 47

    95

    Returns: 3275480162930

  70. 43

    126

    Returns: 11043317034

  71. 49

    197

    Returns: 16214631972

  72. 43

    85

    Returns: 235736203608

  73. 44

    122

    Returns: 36352306268

  74. 48

    118

    Returns: 1606517633804

  75. 46

    85

    Returns: 2181828009154

  76. 47

    108

    Returns: 1443815758118

  77. 40

    65

    Returns: 30839036520

  78. 42

    115

    Returns: 11035087484

  79. 50

    88

    Returns: 32710109848602

  80. 49

    82

    Returns: 14174298118770

  81. 50

    103

    Returns: 23082314773038

  82. 49

    96

    Returns: 14604429192108

  83. 49

    78

    Returns: 10037041082054

  84. 50

    95

    Returns: 31655612945468

  85. 17

    32

    Returns: 6450

  86. 26

    117

    Returns: 4620

  87. 22

    77

    Returns: 3516

  88. 36

    320

    Returns: 3108

  89. 24

    109

    Returns: 2064

  90. 21

    81

    Returns: 1104

  91. 25

    105

    Returns: 4338

  92. 24

    118

    Returns: 1196

  93. 40

    451

    Returns: 1764

  94. 31

    229

    Returns: 1312

  95. 44

    580

    Returns: 1200

  96. 35

    283

    Returns: 1896

  97. 41

    460

    Returns: 1140

  98. 14

    72

    Returns: 4

  99. 7

    12

    Returns: 6

  100. 32

    528

    Returns: 2

  101. 5

    15

    Returns: 2

  102. 45

    45

    Returns: 2

  103. 8

    23

    Returns: 6

  104. 7

    18

    Returns: 4

  105. 11

    47

    Returns: 6

  106. 17

    111

    Returns: 4

  107. 11

    66

    Returns: 2

  108. 39

    556

    Returns: 4

  109. 38

    633

    Returns: 8

  110. 6

    6

    Returns: 2

  111. 34

    502

    Returns: 4

  112. 5

    15

    Returns: 2

  113. 12

    46

    Returns: 4

  114. 19

    115

    Returns: 0

  115. 43

    20

    Returns: 0

  116. 38

    666

    Returns: 0

  117. 30

    438

    Returns: 0

  118. 13

    9

    Returns: 0

  119. 8

    0

    Returns: 0

  120. 50

    1010

    Returns: 0

  121. 46

    36

    Returns: 0

  122. 26

    290

    Returns: 0

  123. 29

    428

    Returns: 0

  124. 40

    606

    Returns: 0

  125. 32

    415

    Returns: 0

  126. 29

    414

    Returns: 0

  127. 11

    63

    Returns: 0

  128. 46

    41

    Returns: 0

  129. 46

    1051

    Returns: 0

  130. 22

    174

    Returns: 0

  131. 46

    1051

    Returns: 0

  132. 50

    1234

    Returns: 0

  133. 50

    1100

    Returns: 0

  134. 50

    150

    Returns: 817735475708


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