Class Chart

object --+
         |
        Chart

Sudoku is a popular puzzle game of Japanese origin. It involves placing integer numbers in a chart according to a certain set of rules. The class Chart represents Sudoku game charts. Each chart consists of a number of cells. In addition to being arranged in rows and columns, the cells form equally-sized and -shaped groups called "regions". A typical Sudoku chart consists of 9 rows or nine columns each, arranged in 9 regions of 3 by 3 cells each. A simple diagram of such a Sudoku chart is shown below (# denotes a cell, lines mark region borders).:

   ###|###|###
   ###|###|###
   ###|###|###
   ---+---+---       
   ###|###|###
   ###|###|###
   ###|###|###
   ---+---+---       
   ###|###|###
   ###|###|###
   ###|###|###

Below, the term "chart size" is used to mean the width and height (which are equal) of a Sudoku chart. For instance, the chart size of the above chart is 9.

Placing numbers

During a game of Sudoku, the player places numbers in the cells forming the chart. A few simple rules govern the placement of numbers:

• only positive integer numbers ranging from 1 to chart size are used
• the same number can not appear more than once in any one row
• the same number can not appear more than once in any one column
• the same number can not appear more than once in any one region

The player must always follow these rules if they wish to form a valid solution to a Sudoku puzzle. Below, the diagram on the left shows a partial but valid Sudoku chart (# denotes an empty cell where no number has been placed yet). The diagram on the right is invalid in several ways (note the conflicting numbers marked in bold).:

   14#|86#|#23        ###|5##|9##
   3#5|#42|#71        6##|2##|48#
   #29|1#3|#85        #9#|#1#|B57#
   ---+---+---        ---+---+---
   2#8|#1#|3##        #B4#|6B4#|127
   6#4|53#|21#        #28|#7#|##B3
   713|2##|96#        #57|9##|B3##
   ---+---+---        ---+---+---
   #32|#54|1#6        ##3|8##|6##
   #8#|321|4##        #6#|##9|B548
   5#1|7#9|#32        ##4|##5|##9

Please see e.g. Wikipedia for a more detailed description of Sudoku charts and the rules of the game! Note that the Wikipedia page also contains some additional information on some more complex Sudoku variants which are not relevant for this class.

Chart and region sizes

This class supports charts of different sizes and regions of different shapes, given the following simplifying assumptions:

• all charts are square
• all regions are rectangular
• all regions are identical in size with each other
• all regions cover the entire chart and do not overlap with each other

Each chart's dimensions can be defined in terms of its region width and region height. The chart size (i.e., width * height of the whole square) is the product of region width and region height. For instance:

• A standard 9-by-9 sudoku chart (as illustrated above) has a region width and region height of 3 and its cells can contain numbers between 1 and 9.
• A chart with a region height of 2 and region width of 3 has a size of 2*3=6, meaning it has six rows and columns, and its cells can contain numbers between 1 and 6:

     ###|###
     ###|###
     ---+---    
     ###|###
     ###|###
     ---+---    
     ###|###
     ###|###
  

• A chart with a region height of 4 and region width of 2 has a size of 2*4=8, and its cells can contain numbers between 1 and 8:

     ##|##|##|##
     ##|##|##|##
     ##|##|##|##
     ##|##|##|##
     --+--+--+--
     ##|##|##|##
     ##|##|##|##
     ##|##|##|##
     ##|##|##|##
  

The class Chart supports placing numbers onto charts and is capable of determining whether such placements violate the basic Sudoku rules of "only one per row/column/region". The class does not support canceling number placements. Once a cell is filled, there's no way to go back.