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revised: 01/13/2008, 07/04/2017

Part DD — 2D Arrays

Puzzles D01 ... D10

These puzzles involve 2D arrays. The dimensions of an array are given as row followed by column. A 3x5 array has 3 rows and 5 columns. Conceptually a 3x5 array looks like this:

If an array has R rows, the rows are indexed 0 ... R-1. And if it has C columns, the columns are indexed 0 ... C-1. Of course, row and column numbers are not stored as part of the array in main memory. Arrays are stored in main memory in row-major order, which means that the elements of a row are stored in sequence in memory. The elements of the array are stored in a contiguous block of memory, as follows (assume that memory addresses increase to the right):

Because of this, code that accesses every element of a 2D array should be written so that elements are accessed in sequence through memory:

  for ( r=0; r<Number_Of_Rows; r++ )
  {
    for ( c=0; c<Number_Of_Columns; c++ )
    {  
       ... do something with element[r][c] ...
    }
  }