![]() ![]() #COMPLETE BINARY TREE FULL#A complete binary tree can be a full binary tree (when the deepest levels are completely full). The deepest level can have nodes that can have either one left child or can be completely full. So, the natural way to route a packet of data from an input terminal to an output in the complete binary tree is along the corresponding directed path. A very elegant sequential representation for such binary trees results from sequentially numbering the nodes, starting with nodes on level 1, then those on. A complete binary tree is a type of binary tree in which all the levels are completely filled (i.e, have two children), except the possibly the deepest level. Recall that there is a unique path between every pair of vertices in a tree. It is a full binary tree as all the nodes have either 0 or 2 children. A perfect binary tree is a tree where all the interior nodes have 2 children and all the leaf nodes are on the same level. Thus, you can imagine a data packet hopping through the network from an input terminal, through a sequence of switches joined by directed edges, to an output terminal. It is a complete binary tree as all the nodes are left filled. A switch receives packets on incoming edges and relays them forward along the outgoing edges. The circles represent switches, which direct packets through the network. In this diagram and many that follow, the squares represent terminals, sources and destinations for packets of data. The term packet refers to some roughly fixed-size quantity of data- 256 bytes or 4096 bytes or whatever. ![]() The kinds of communication networks we consider aim to transmit packets of data between computers, processors, telephones, or other devices. ![]() Here is an example with 4 inputs and 4 outputs. ![]()
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