Addition trees are binary trees where only the leaves can store arbitrary numbers (float’s in our case). Values associated to internal nodes get computed according to a fixed rule: the sum of the values associated to the subtrees (thus, in some applications, it may not be necessary to actually store the value). Note that there are no empty addition trees.
Addition trees are the main combinatorial structure behind Huffman codes (see https://jutge.org/problems/P62266 for more). They are also a very close relative of the Product Trees of https://jutge.org/problems/P30012.
We describe addition trees in preorder as indicated below. Write a program that reads such a description and prints the preorder, inorder and postorder traversals of the tree read. (The pdf version of the statement of https://jutge.org/problems/P62266 graphically depicts one of the public test trees below.)
Addition trees are described here in preorder as follows: for leaves, the corresponding float is given, whereas for internal nodes only the character ’+’ is written. All these tokens are space-separated and might come distributed arbitrarily along several lines.
Three sequences of floats, as obtained by preorder, inorder, and postorder of the tree described by the input. Print each float with 4 decimal places.
Author: José Luis Balcázar
Generation: 2026-01-25T17:15:45.696Z
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