This is the order in which a binary search tree should be traversed for ordered output, i.e.:
  • everything to the left is smaller than parent
  • everything to the right is larger than parent
This ordering makes sense for binary trees and not k-ary trees in general because if there are more than two nodes it is not clear what the top node should go in the middle of.
This is unlike pre-order depth-first search and post-order depth-first search which generalize obviously to general trees.
This is a bit harder than iterative pre-order: now we have to check if there is a left or right element or not:
  • (START) push current
  • if there is left:
    • move left
  • else:
    • (ELSE) pop
    • visit
    • if there is right
      • move right
      • GOTO START
    • else:
      • GOTO ELSE
The control flow can be slightly simplified if we allow NULLs:

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