BINARY TREE
- 1. BINARY TREE 1 A SEMINAR ON BY=Mubeen Momin Abdul Qadeer (co-3g) Roll no = 5
- 2. Binary Trees • According to the definition of trees, a node can have any number of children. • A binary tree is restricted to only having 0, 1, or 2 children. • A complete binary tree is one where all the levels are full with exception to the last level and it is filled from left to right. • A full binary tree is one where if a node has a child, then it has two children.
- 3. BINARY TREES Every node in a binary tree can have at most two children. The two children of each node are called the left child and right child corresponding to their positions. A node can have only a left child or only a right child or it can have no children at all. Left child is always less that its parent, while right child is greater than its parent.
- 4. TERMINOLOGY Each node has to be reachable from the roots through a unique sequence of arcs called a path. The number of arcs in a path is called the length of the path. The level of a node is the length of the path from the root to the node plus 1. The height of a non-empty tree is the maximum level of a node in the tree.
- 5. Picture of a binary tree5 a b c d e g h i l f j k The root is drawn at the top
- 6. Tree traversals A binary tree is defined recursively: it consists of a root, a left subtree, and a right subtree To traverse (or walk) the binary tree is to visit each node in the binary tree exactly once Tree traversals are naturally recursive Since a binary tree has three “parts,” there are six possible ways to traverse the binary tree: root, left, right left, root, right left, right, root root, right, left right, root, left right, left, root 6
- 7. Tree Traversals using “flags” • The order in which the nodes are visited during a tree traversal can be easily determined by imagining there is a “flag” attached to each node, as follows • To traverse the tree, collect the flags 7 preorder inorder postorder A B C D E F G A B C D E F G A B C D E F G A B D E C F G D B E A F C G D E B F G C A
- 8. SORTED BINARY TREES A binary tree is sorted if every node in the tree is larger than (or equal to) its left descendants, and smaller than (or equal to) its right descendants Equal nodes can go either on the left or the right (but it has to be consistent) 8 10 8 15 4 12 20 17