A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 5.1 Definitions and Properties 155AABB(a)(b)AABEMPTYEMPTYB(c)(d)Figure 5.2 Two different binary trees. (a) A binary tree whose root has a nonemptyleft child. (b) A binary tree whose root has a non-empty right child. (c) Thebinary tree of (a) with the missing right child made explicit. (d) The binary treeof (b) with the missing left child made explicit.(a)(b)Figure 5.3 Examples of full and complete binary trees. (a) This tree is full (butnot complete). (b) This tree is complete (but not full).Figure 5.3 illustrates the differences between full and complete binary trees. 1There is no particular relationship between these two tree shapes; that is, the tree ofFigure 5.3(a) is full but not complete while the tree of Figure 5.3(b) is complete butnot full. The heap data structure (Section 5.5) is an example of a complete binarytree. The Huffman coding tree (Section 5.6) is an example of a full binary tree.1 While these definitions for full and complete binary tree are the ones most commonly used, theyare not universal. Some textbooks even reverse these definitions! Because the common meaningof the words “full” and “complete” are quite similar, there is little that you can do to distinguishbetween them other than to memorize the definitions. Here is a memory aid that you might finduseful: “Complete” is a wider word than “full,” and complete binary trees tend to be wider than fullbinary trees because each level of a complete binary tree is as wide as possible.