Statistics

Problem Statement for "Subrectangle"

Problem Statement

Limak had an empty grid, divided into square cells. He chose some non-empty rectangle (with sides parallel to sides of the grid) and marked all cells inside the rectangle.


A grid with H rows and W columns can be encoded into a string of length H*W as follows: examine the cells of the grid in row major order, and write down '#' for each marked cell and '.' for each empty cell. In other words, write down the first (topmost) row from the left to the right, then the second row from the left to the right, and so on.


Limak wanted to write down a string representing his grid. Unfortunately, he is easily distracted and thus he missed some cells (maybe zero or all of them). In other words, he got a subsequence of the string representing his grid.


You are given a String S that Limak got. What is the minimum possible number of cells he missed?


You may choose any positive dimensions for the grid. All missed cells count: both empty and marked ones.

Definition

Class:
Subrectangle
Method:
minMissed
Parameters:
String
Returns:
int
Method signature:
int minMissed(String S)
(be sure your method is public)

Notes

  • It can be proved that for any valid input string S there is some valid grid such that S is a subsequence of the string that encodes the grid.

Constraints

  • S will contain between 0 and 300 characters, inclusive.
  • Each character in S will be either '.' or '#'.

Examples

  1. "..###.##"

    Returns: 2

    It's possible that Limak's grid looked like this: ..### ..### This grid is represented by the string "..###..###". Limak missed 2 cells in this case: ..###.(.)##(#). Here, we denote missed cells by putting them in brackets. It's the minimum possible number of missed cells, so the answer is 2.

  2. "#.##.#.#.."

    Returns: 2

    The following grid is represented by the string #.#(.)#.#.#.(#). #. #. #. #. #. #. The second-to-last character could also be a dot (meaning that the last row in the grid is empty).

  3. "####"

    Returns: 0

    It's possible that Limak had a grid of size 1x4 or 2x2 or 4x1 and he marked the whole grid. The grid would be then represented by the given string "####".

  4. ""

    Returns: 1

  5. "........................................"

    Returns: 1

  6. "###...###"

    Returns: 3

  7. ".#.###.##...#.####.###...###.##"

    Returns: 15

  8. ".................................................##..##...##.............................."

    Returns: 5

  9. "."

    Returns: 1

  10. "#"

    Returns: 0

  11. ".."

    Returns: 1

  12. "#."

    Returns: 0

  13. ".#"

    Returns: 0

  14. "##"

    Returns: 0

  15. "..."

    Returns: 1

  16. "#.."

    Returns: 0

  17. ".#."

    Returns: 0

  18. "##."

    Returns: 0

  19. "..#"

    Returns: 0

  20. "#.#"

    Returns: 1

  21. ".##"

    Returns: 0

  22. "###"

    Returns: 0

  23. "###."

    Returns: 0

  24. ".#..#"

    Returns: 1

  25. "..#.##"

    Returns: 2

  26. "......#"

    Returns: 0

  27. "....####"

    Returns: 0

  28. "##..#..##"

    Returns: 3

  29. ".###.#..#."

    Returns: 4

  30. ".##...#..##"

    Returns: 4

  31. "..##...#...."

    Returns: 3

  32. ".##..#.....##"

    Returns: 7

  33. ".##.#.#..#...."

    Returns: 2

  34. "#.#.##..#.#.#.#"

    Returns: 3

  35. "######.##.##########.##"

    Returns: 7

  36. ".####..###.#####.###..##"

    Returns: 11

  37. ".#...#............#.....#"

    Returns: 7

  38. "####################################"

    Returns: 0

  39. ".................##.....#............"

    Returns: 3

  40. "#####.##########.########.###.####.########.###"

    Returns: 13

  41. ".#...#....#..#.#.##...#...###.......##..##..#..#.##...##....."

    Returns: 29

  42. "#.......#.#..##...#..#..##.##.#.....###.##.#......#.#.#.#.##....#."

    Returns: 30

  43. ".#....#######.######...#.###...#####.#.#.#.#...#......#.....###.#.##..#"

    Returns: 39

  44. "##.##.######..################..######.#####....####.###.######.##.#.##.##..##.##.##..#.#.##"

    Returns: 37

  45. "###########.#..##.###.###############.#.####.#######...#######...#######.######..####..##...#####.."

    Returns: 57

  46. "...........#.......##...#.##.....#.#..........#.#.....#..#.................##...#...##.....##.#.........."

    Returns: 47

  47. "...##...#..#...#..####..#......##......#...#.....#..#.#..#.###.##..####......##.###..##..##..###....##...##"

    Returns: 58

  48. ".#.#.#....##..#......##.....#.#.#.#.#..#..###........##.......##........#...##.###......#........#.#.......#"

    Returns: 54

  49. "#.#............##....#.......#.##.....#....##....#.#.......#.......#........#..#...##.#........##...#..#..#.##...##"

    Returns: 56

  50. "#.######..#########..#..##.##.#.#########....###.###.########.##.....####.#.##.############.####.####.######.##########"

    Returns: 58

  51. "...##.####..#.###.##...####.#...#.....###....#....#####...#..##.######.....#.#..##....##..##.#.####.#.##.##.###....##...##."

    Returns: 67

  52. "..........##...#...................#.#.......#...##....#...#..#.......##..#....#.#...#...............#...#..#.#......#.#..##."

    Returns: 51

  53. ".#.##..###.##..#.###...###.#.####.#.######....##..#####.#.#.#..##.##.#.#.##.###.#.#....#.################.##.#.#.##.###.###..##..#..###.#"

    Returns: 65

  54. "..............#..#.....#.#....#.....#...##....###...#...#.........#.....#.....#.....#..........#........#.#..#.............#.......#.#....#..#"

    Returns: 56

  55. "#####..#..##..####.#.#######.#..#####.###...#.####.###.###....#.##.#..#...#########...##.######.#...##..#....######.##....#.#..###.##.##..##...#####"

    Returns: 86

  56. "....#..#..##.......##........#.#....#...#.###.#....#...##.......#.#...#.#.#.##....###..#...#..##.#...#............##....#.....####.....#.#...#......#......#..#..#."

    Returns: 77

  57. "####..#..########.#########..########..##.#########.#.#########..#.##.....#..#.#..###.##.###.#.#.######..###.##########..#.#.######.#######.#.#.#####.##############..##."

    Returns: 89

  58. "##.###..##..#####.#.#..#.#.##.#####.##.#####....##.##...##................##.#....##.....#.##....#.####..#....###.#.#.##.......#...####.##..#..##...#...#...#.....####.#..#.."

    Returns: 97

  59. "###.##.######...#..###.##.###..#...###..#######.####..#####.##.##.###.#.##....#######..#..###.#.#####.##..#.##...#..###.##......##.#######.###########..##########.####.#.####"

    Returns: 102

  60. ".####..##.....#.#..##..##.#..........#..#.....##...#.###.......##.#...##.#....#..#.#..#.#.#.#.#...#..###....##..##...##.....##.##..##.#...#...#.....####.#...##...##..#####.##....###"

    Returns: 97

  61. ".#........#...#.............#........#..........................#..........#.....#.........##...#..............#.................#......#..#.##................#......#..........#....."

    Returns: 65

  62. "..#....#..####..#..#.#.#.###...#..#..#.#......#....#.....##.#.##.#....#.#.......#....#...#....##.###...##...#.#.#.###.....###..##....#....####.###...#......#..#..#.##..#.....##.##.####"

    Returns: 96

  63. "##########################################################################################################################################################################################"

    Returns: 0

  64. "#######..######.#######.##..#.###.#....##.#######.#..############.########.##.##.##.######.######.#################..##.#.#..#####.####..####.#.####..###.###.#.###.#..#..###.###.#.#######"

    Returns: 92

  65. "..#.#.#..#.#..##.##.#######...##.#######..################..########..########....#.#.#.##..##.####......#..##.#.#.##.####.##.###....#.#.##.###..###..###.###..####.######.##....#.###.#.###"

    Returns: 106

  66. "###...##.####.##.#.##.....#.###.####..##..##.#####....#...#..#.#..#.#......#..#.##.#..#.##.##.#..###.#.###..#.##.##...#..#.##.##.######.#.####.#.#..###.....#.#.#......##.#.##.#..#.##...#..#.#."

    Returns: 84

  67. "..............................#..........................................#..........................#............................................................................................."

    Returns: 14

  68. ".....#........#................#..#.#.......#.........#.....#.#...#......#..##...#.....#.............###.#.............#...#...................#.............#..........##....#..........#.#...#...#.."

    Returns: 82

  69. ".####.##..##.#.##.#..##..#...#..#####.#...#..###...#.#..#.#..##..###.#...##.##..#.......###..#...#.##.#..#.##.##....##..##..#.##..#.##..#..##.###....##.....#.#.#.#########.#...#######..#..#.....#..####"

    Returns: 99

  70. "###########...######.########.##.###########.###..#...##.##.#.#.#.#######.###.##.##.#.#.##########.###.###.##.##.###.##.###..#####..######.###..###########################.##.###..#.##.#.####.##.###.####.##"

    Returns: 91

  71. "###.#.######.#############.###.#######.#########.###.######.##.########.####.###.#####.#.####.###.#############.#####..##.#################.###.#########..############.#######.#########..##########.#########"

    Returns: 73

  72. "..#...#......#.......#.#......#........#.#..........#..#......#.#............#.....##..#.#.###..#....##..#.......##...#......#...##....###.#..##.....####...#..............#...##.##..###....#......#.##.#...#.."

    Returns: 101

  73. "######.######.#######################.##.##..#.#######.###.#########.########.###.################.#.############.##.####################.######.###.#######.######.############..################.##.######.##.###"

    Returns: 69

  74. "#..#....#..##.#..#.......##....##.##.#...##.........#...######.......##.##.##.##..###.##.....##.........##..#.##.#..#...##..#...##..######......#.#.###..#####.###..##.........#.##........###.#.###.#..####.#..##..."

    Returns: 123

  75. ".....#.......#............................................................#............#............#...........................................................................................................#............"

    Returns: 26

  76. "#.####.##.##.########.################################.#..######.####.####.############################.#############.#######################.####.###.##.###.#####.###.##...##############.#####..###.####.###########.#####.#.#"

    Returns: 90

  77. "###.##..#..#.#############.#..#.######.##..#####.##.#.#.###.#######..######.######.#########.##.###..#.###.########.####..#.###########..#.##.############...#####.#.#.###..##..#.#####..#.########.#####..##.#.####.#.##..#######."

    Returns: 112

  78. "....###.##.##.#.#####.#.#.##.###.#.###.###.#..##.##.#..#####.#...##..#.#..#.#####...#..###..#.###.##..###..###..##.#.####......#..#.###.#####.#...#..####...###.##########.#.##.#..#..#.#..##..##.##..####.#....##.##..##.#..#.#.####"

    Returns: 107

  79. "..........................................#..........................##..........................#.............................................................................#.......#..............................................."

    Returns: 29

  80. "#####.#####.#####.###.###.######.#..#.##############.############################.#####.#####.#.#.############.######..#####.######.##.######.#################################.#######.##################.###################.#############"

    Returns: 84

  81. "####.####.###.#.#.###.######.###...#.#####.#.#.###..###.#.#.##.###.##.####.###.####.#.....#######.###.##...#..#####.#.####..#..##...##.#.#####.#####..###.######.#.#.####.##.###.#####.######.##..#..#..#...###.####.##.####.####..#.#.#.######..##"

    Returns: 123

  82. "###.#########.#####.#.##.#.#######.#.#.#.##.#####.#####..##...####.###.######.#######.#######.#.####.###.#.###.#..#.#.#####.###....##.#..##..#.##.######.####.####.###.#.#.##..#..####.##...##..#..##.##.#########.....#.#######.###..#.##############"

    Returns: 126

  83. ".......#....#..#.##.#....#..........#..#.#........#.......#....#.......#......#.#......................#....#.#..#..#....##.............#......................#.............#.#.##.....#.......##................#......#......#...#..#...................."

    Returns: 93

  84. ".........................................................#.....#.............#.#......................................................#....#.......................................#...............................................#......##................."

    Returns: 48

  85. "#########################################################################################.###############################.#####################..####################.################################################################################.#######"

    Returns: 50

  86. "######..###.################################.###########..######.#####.####.#########..#.###########.############.###########.##.##.#######################.######.#######################.#######..######.#####.######.##.##.#.###.####.###########..#############"

    Returns: 97

  87. "########.##########.#######.##########.##.######.#######################################.##.#######.##.####.#####.##################.#####################.####.#..##################.######.####.##..#####.################.#####.################.####.############"

    Returns: 89

  88. "####.#.##.##....###....#...#.#.##...#..##.##..###...##.######.####.#.#######..##.###.##.##..####....####.#.#..#..#####.#########.##.#.#..###########.#.####.####..#######.########.##..#...#..#########.##.#.####################.###.#.#.#..#####.....#####..########.#"

    Returns: 150

  89. "######.######.###########.##########.##########.#.####.############..##.##########.##########..##################..#.#################.###########.####.#########..######.#############.####################.#####.##########.######.##########.##.##.###########.####.###"

    Returns: 105

  90. ".........#.#.#...........#.......#....#.......#.........#...#...#......#..#.#...#......#.........##....#.#.......#..........###.....####.#..#.....#.......#.....###.................###..#.#.........#.........#..#...#......##...##....#........#.#...#....#.##..........#"

    Returns: 129

  91. "#.##..#.##.##.....#.#.#.#...#.####.#.######.#.##.##.###.......#..#.####...##....#..#.##..###.#.####.##.#.#...#####.##.#....#.#......##..#..##..##......#####..#.###.##..##..##.#.....#.#.##.#.#...##..####.#....##..#....#....######..#####..#..##.##.####..##.#..##.#..#.#.##.#"

    Returns: 132

  92. "...#.#....##.##......#......#.#.#..#.####.#..#..#...##..##......###...#....##.#..#.#.##..#####.##..###...#...#....#...#.#.###.#.......##.#......#....#..##..#..#...#.#.#...#.##..##...##..#.....##...#.#.....##.#.#....##...#...##.....#...........#.##.#....#...##....##...##.#...#......#"

    Returns: 147

  93. ".#.####.##.#.#.#####....###.#.########.#.##..##...##.##.#####.##.##.##.#..##..#..#..###########....##.#.#####..#.###..###.#...##.###.##.#####.#####.####..#.#...#######.###.###.#..##.##.##..###..##..##.##.#..####.##.####.#...#...#######.##.##...##..##...##.#####..#.###.##########.#.#.#.#"

    Returns: 149

  94. ".##.#.....######.##.####..#.###.....##.###.####.##.#..#.##########.##.#.####.#.####.##...###.###.#...#...#.#.##..#.###...##.####...##.#.##.##...#..##.##.#####.##...##..#.#.##.#..##########...#.##..#.####..#####.#######.##.###..###.#.###......#####.#.####.####.#####.#....#####.####...####"

    Returns: 156

  95. "#.####..##.#...##..##.#......#....#.##..##.#....##.......#.....###....#..#.#.....#.#.##...##.####.....##.#.#..#.##..#.#....#......#.###..#..#.##.###.....#...##.#...#..#.###.....#...##.........#...#.#.#.###.#.#.#.....#.##....#..#..#.#.##..#..#....#...#.....###.....##.##.#.#.###...##.......#...#"

    Returns: 150

  96. ".#.##...#..###.#.##...#...#..#.####..#.#..####.#.##.#....##..##...#..#.#######.....##.#.#....#....#.##..#..#.#.#..#.##.#.###.#..#...#.#...#....##.####.####..##.#.#...##.##.#...####.##.#...##.###.###...#.#.##..#....#######.....#.##.#..###.#####.####.#..#..##...##.##.#..#...#..####.##..#.##.###.#.#."

    Returns: 136

  97. "#..#####..#.#.###.....#......#######.###.#....#.####...#....###..#.##.....####..#.#####.#...##....#.###.#.###.##.##.#.#.##..##..###...##...#.#####..##...##.#...#.#.#.#....###...#.##..#.##.....#.##...#......#..##..#....#.###.##...##..##.##.##.###...##.###.#..##....#####....#.####.###..###.##..#.#..#"

    Returns: 155

  98. "########.#..#...###.##.#.#.##..#...#.#..#.##.#.#..##..#..#.....##...#......#..#.##.##..###.##..#..###.#...#.....##.###.#..#.#..###..#...#.#......#.#.#.##....#..##....###....##.###..#...##....#....#..##..#.####.....#.##.#..##.#...###.##.###.######.#####.....#.#.#....#####.##.#....#...#.#.####.###.#.#"

    Returns: 146

  99. "..###..###......#...###....#..#.###....#..#...##.#.#...#...######.#..##.##.#.####.#.###.#..##..##.###..###.##.##.#..##.#.#..#...##.#.#.#...##...#.######.#.##...##..##.##.##.#.###.###...#.##.....#.#.#..##...#..#..#.#...###.#..#.#####..##..#...#...##....#..####...###.#.....#..##.###.#..##..#####.###.#"

    Returns: 142

  100. "...#...##.##.#.#.##.##.#.##.##....####.###.###..##.##.##.###.....###.#...#..#....#.#.###.###.###....#.###.##.##......#.#.#.....#####.###.#######.##..#..###.#######..#.##..##.#.#.######......#.##....##.#.#####....##.##.###..###...#...#.#.###..##.#..##.#.#.#..#.#....#.#.##.#.##.#.##.###.#.##..#.###..."

    Returns: 138

  101. "..#..#..#.###.##..#.....#.##.##..#.#....#...#.#....####.#.....###.....##.##.#...#..##...#..............#.....#...#..####....##...#........#.#............#..#..#.####.#..#..#.##..#..#....#..##...#.#....###..##...#...##.#..#....#..#.#.....##.####..#.#...#...#....#..#..##...#.#........###..##.#.#.##..#"

    Returns: 153

  102. "#...##.##########.#######.######.#.##...#..############.###.##.#.#.###.##..#####..#.#...########.######.#.##.#.#.###..#..##.##..###.##.####.##.#.#.####..#.#.###.#.####.##.#..#.####.#..####.#..#.####..#.##.###..#.####.#.####..#####.##..###.####...#########.###.#.#.#########..####.##.##.########.####."

    Returns: 138

  103. "....#........##....#.......#................................#.........................#........#...#......#................#.......#.......#.........#..........................................#.................#........#.....#...#...#.......##..........#..................#..#.#.......#..#..........."

    Returns: 95

  104. "############.###.######################.######.###.##############.################.###############.##########.###################...#######.##############.############.#.##.##########.#########.######.#######.###.#######.#.################.#.######.#####.#.###.##.#######.##.######..#################"

    Returns: 112

  105. ".......................#.............#.....................................#.#.........................................................#...........................#.................................................................................................................................#......"

    Returns: 52

  106. "######################################################.##################################################################################################################################################################################.#.##########.###.#################################################"

    Returns: 52

  107. "#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#."

    Returns: 0

  108. ".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#"

    Returns: 0

  109. "#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#"

    Returns: 1

  110. "###.###..####.#.#.#.#.#..##.###...###.#...#.#.#.#.#.#.#.#.#.#.....#.#####.#.#.#..##.#.#.#...#.#.......#.#.#...#...#..##.###...#.#.#.#.#.#.#.#.#.#.#...#.#.#.#.#...#.#.###.#...####.####.....#.#..##.#.##..#.#.#...#.#...#.#.#.###.....#.#.#.#.#.#.#.......#.#.#.#.#.###.#.#.#.###.###.#.#...#.#.###.#.#....#"

    Returns: 98

  111. ".#.#.#.##........###...##..#.#.#.###.#...#.#.#####.##..#.#...#..#..###.#.#.#..#.#.##.#.#...#####.#..#.....##...#.#.#.#.#.#....####.#.....#.###.#.#.#.#.###.#.#.....#.###.#.#.#.#.#.#.#.#.###.#.#.#...#.#.#.#.....#.#.#...#.#.#.#...###.#.##..#.#.#####.#.#.#.###.#.#.#.#.#.#.##.##.#.#...#.####..###.###.#."

    Returns: 101

  112. "....................................................................................................######################################################################################################################################################.................................................."

    Returns: 0

  113. "............................................................................................................................................................................................................................................................................................................"

    Returns: 1

  114. "############################################################################################################################################################################################################################################################################################################"

    Returns: 0

  115. ".......######################################################################################################################################################.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..."

    Returns: 134

  116. "..#############################################################################################.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.................................................................................................#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..."

    Returns: 188

  117. "######################################################################################################################################################..##..##..##..##..##..##..##..##..##..##...................................................................................................."

    Returns: 88

  118. "...######..................................................................................................................................................................................................................................................................................................."

    Returns: 0

  119. ".......................................................................................................................................#####################......#####################......#####################......#####################......#####################......#####################......"

    Returns: 0

  120. "....................................................................................................................................................................................................................................................................###########################............."

    Returns: 0

  121. "#####.....####.#..#..#..#..#....#...#.####.##...##...##..##...####...##.#.....##...##.##.###..###....##..#.##.#.###.#..#....#.##.#.##.#..#..#.#..#.#...#.#.#.#...#...##..#.#...#.##...##.###.#....#.###.####.##.........#.####.##..##...#..#.#########...##..###.#..#.###.##.#....#...#....##.##.#.###..#..."

    Returns: 144

  122. "#..#.#..######..###...###.##.##.#.###.#.########.##..####.##..######..#####..#..#####.##.###.##.###...#.#..###.###.#.###.########.##..#.#.....##.##.###.#######.###.##..#..##.#...###..###.#####.########.#######.#.##.###.######.#.#.###.#.###..#####.####.###.#####..##..#.###.####.#####.######.#.#######"

    Returns: 156

  123. "#.#.....#...........#.#.#.#.#.#.#...#...#.....#.....#.....#.#...#...#...#.#.#...#.#...#.#...#.#.#...#.....#.#.#.#.#.#.....#...................#...#.......#.#...#.#.............#.....#...#.#.......#.#.#.#.#.......#...#...#.#.......#.#.#.#.......#...#.#.#...#.......#.......#.#.#.#.#.#.#.#.#.#.#...#..."

    Returns: 144

  124. "##.##.##...."

    Returns: 0

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