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Also, define how initialization of nodes works, by adding an init()
method that is called after creating a node.

Initialization now happens after the full tree structure has been
created, and recursively processes all nodes in the tree. Subtrees that
are added later use the same pattern; InnerNode now has helper methods
for this.

BUG=616090

Review-Url: https://codereview.chromium.org/2513453004
Cr-Commit-Position: refs/heads/master@{#438135}