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This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
The simple Sethi–Ullman algorithm works as follows (for a load/store architecture): . Traverse the abstract syntax tree in pre- or postorder . For every leaf node, if it is a non-constant left-child, assign a 1 (i.e. 1 register is needed to hold the variable/field/etc.), otherwise assign a 0 (it is a non-constant right child or constant leaf node (RHS of an operation – literals, values)).
The set of all nodes at a given depth is sometimes called a level of the tree. The root node is at depth zero. Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has height of 2. Sibling - Nodes that share the same parent ...
For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will). By contrast, a breadth-first (level-order) traversal ...
Permuting the vertices on each level of the Stern–Brocot tree by a bit-reversal permutation produces a different tree, the Calkin–Wilf tree, in which the children of each number a / b are the two numbers a / a + b and a + b / b . Like the Stern–Brocot tree, the Calkin–Wilf tree contains each positive rational ...
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A labeled tree with Prüfer sequence {4,4,4,5}. Consider the above algorithm run on the tree shown to the right. Initially, vertex 1 is the leaf with the smallest label, so it is removed first and 4 is put in the Prüfer sequence.
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