Sample tree: size, height and diameter
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nodes                         : 9
leaves                        : 4
height, counted in nodes      : 4
height, counted in edges      : 3
height via level order (BFS)  : 4
diameter, counted in nodes    : 7
diameter, counted in edges    : 6
one longest path              : [7, 5, 2, 1, 3, 6, 8]
height of the subtree at node : {1=4, 2=3, 3=3, 4=1, 5=2, 6=2, 7=1, 8=1, 9=1}
node visits, naive O(n^2) way : 26
node visits, one-pass way     : 9