TreeThinking.txt

                                ** Visualizing Binary Trees in ASCII **

                  1                                                                         Let's try something different. The left child goes to the right.
                 / \
                2   3     <--- No room for 3.left                                                     1 2 4 7
               / \   \                                                                                3 9
              4   5   6                                                                                 5        <-- The oddness is here because we had to skip a row.
             /         \                                                                              6                 But there is no ambiguity!
            7           8 <--- Width totally determined by leaves!                                    8

            
                                                                                            This is a variant, where the right child goes to the right, left goes down (skipping occupied rows)

                                                                                                      1 3 6 8
                 1                                                                                    2 5
               /   \   <-- widen this                                                                 4
              2     3       <-- and this                                                              7
             / \   / \                                                                                  9       <-- This is the oddness here...again 5 and 9 want to collide!
            4   5 9   6    <--- and 5.right and 9.left can still collide!
           /           \                                                                    If we keep track of the count of nodes, and the count of left and right, then we can
          7             8                                                                       allocate a static int[left_count][right_count] array for this representation. Alternatively we can use
                                                                                                dynamic structure. The static structure may waste space depending on the shape.


                                                                                                    There is a question: why is 5 the first child of 2 and not the second child of 3?
                                                                                                    That is because it would have been on a new row!

                                                                                                     1 3 6 8
                                                                                                     2
                                                                                                     4
                                                                                                     7
       1      An alternative visualization of a tree, where children are indented.                     9
        2     Avoids ALL collisions but still makes siblings seem far apart                            5
         4
          7                                                                                      Okay but what if 2 has first children?
         5                                                                                               1 3 6 8
        3                                                                                                2 a b
         9                                                                                               4
         6                                                                                               7
          8                                                                                                9     <-- is this a branch of 3 or a?
                                                                                                             5   <-- is this a branch of b or 6?        We can tell in a sequence, but not in a snapshot

                                                                                                                      One option is to use the space to point to the parent.
                                                                                                          1 3 6 8
                                                                                                          2 a b
                                                                                                          4
                                                                                                          7
                                                                                                            a 9        <-- 9 follows a, not 3.
                                                                                                              6 5      <-- 5 follows 6, not b.




                                                                                                ...Just realized I did it wrong. each branch should duplicate the parent in that column.
                                                                                                Otherwise the parent is ambiguous.

                                                                                                1 2 3 4                 1234
                                                                                                1 5 6                   156
                                                                                                  2 7 8                 1278
                                                                                                  5 9 a                 159a
                                                                                                    7 b c d             127bcd
                                                                                                  5 e f                 15ef
                                                                                                        c g             127bcg