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Description
Problem
The Pane class acts simultaneously as the data model to represent actual panes and as splits which contain nothing but exactly 2 child panes and a split ratio / direction. In a sense Pane represents both a leaf and internal nodes in a binary tree simultaneously. Member functions of Pane iterating through that tree are complex and make changes difficult (#13306), as iteration happens almost exclusively via recursion, making retaining state cumbersome.
Proposal
Let's implement a binary heap class that works independently of Pane. This would allow us to use regular text-book algorithms for its implementation. Internal nodes of the heap would retain split ratios and directions and leaf nodes of the heap contain shared_ptr<Pane> references. Traversal/iteration would also be simplified. This separate heap would be cheap to clone, allowing us to implement things like UI state persistence (#13306) more easily.