Succinct Encoding of Binary Tree - GeeksforGeeks

Succinct Encoding of Binary Tree - GeeksforGeeks

Succinct Encoding of Binary Tree

A succinct encoding of Binary Tree takes close to minimum possible space. The number of structurally different binary trees on n nodes is n'th Catalan number. For large n, this is about 4ⁿ; thus we need at least about log₂ 4 ⁿ = 2n bits to encode it. A succinct binary tree therefore would occupy 2n+o(n) bits.

One simple representation which meets this bound is to visit the nodes of the tree in preorder, outputting "1" for an internal node and "0" for a leaf. If the tree contains data, we can simply simultaneously store it in a consecutive array in preorder.

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