Succinct (0-1) Encoding of Binary Tree

Succinct encoding is an approach to encode a Binary Tree to the lowest possible space and maintain the structural information. The number of structurally different binary trees on n nodes is nth Catalan's Number. Catalan numbers are a sequence of natural numbers that occur in various problems like counting the possible Binary Search trees with n values, counting the number of binary trees with n+1 leaves etc. Some Catalan numbers for n = 0, 1, 2, 3 ... are 1, 1, 2, 5 ...
They can be found using ...