nodes in -ary tree can be derived we can also store complete -ary tree in an arraysimilar to the approach shown in section sequential tree implementations next we consider fundamentally different approach to implementing trees the goal is to store series of node values with the minimum information needed to reconstruct the tree structure this approachknown as sequential tree implementationhas the advantage of saving space because no pointers are stored it has the disadvantage that accessing any node in the tree requires sequentially processing all nodes that appear before it in the node list in other wordsnode access must start at the beginning of the node listprocessing nodes sequentially in whatever order they are stored until the desired node is reached thusone primary virtue of the other implementations discussed in this section is lostefficient access (typically th(log ntimeto arbitrary nodes in the tree sequential tree implementations are ideal for archiving trees on disk for later use because they save spaceand the tree structure can be reconstructed as needed for later processing sequential tree implementations can also be used to serialize tree structure serialization is the process of storing an object as series of bytestypically so that the data structure can be transmitted between computers this capability is important when using data structures in distributed processing environment sequential tree implementation stores the node values as they would be enumerated by preorder traversalalong with sufficient information to describe the tree' shape if the tree has restricted formfor example if it is full binary treethen less information about structure typically needs to be stored general treebecause it has the most flexible shapetends to require the most additional shape information there are many possible sequential tree implementation schemes we will begin by describing methods appropriate to binary treesthen generalize to an implementation appropriate to general tree structure because every node of binary tree is either leaf or has two (possibly emptychildrenwe can take advantage of this fact to implicitly represent the tree' structure the most straightforward sequential tree implementation lists every node value as it would be enumerated by preorder traversal unfortunatelythe node values alone do not provide enough information to recover the shape of the tree in particularas we read the series of node valueswe do not know when leaf node has been reached howeverwe can treat all non-empty nodes as internal nodes with two (possibly emptychildren only null values will be interpreted as leaf nodesand these can be listed explicitly such an augmented node list provides enough information to recover the tree structure