Trees

What is a tree? You know…  tall  green  leafy  possibly fruit  branches  roots  I’m sure you’ve seen them

In the context of C (and CS in general) Trees are a Data Structure (Like a linked list) They  Are upside-down  Have one root  Have branches  Have leaves  (No fruit)

A Tree (In general)

Nodes

Edges (Links (Pointers))

The Root

Leaves

Branches (A.K.A. Sub-Trees)

Parent / Children

Some info The root has no parent The leaves have no children The interior nodes have at least one child, and a parent

Types of trees Binary trees  Every node has (at most) two childen Trinary trees  Every node has (at most) three childen N-ary trees  Every node has as many children as it wants/needs

We care about binary trees

Binary search trees

Binary Trees typedef struct S_tree { int value; // For example struct S_tree *left, *right; } tree; Just like a linked list, but instead of one pointer, it has two! (left and right)

In Order Traversal Printing an entire binary search tree. void print_tree(tree *t) { if (t == NULL) return; print_tree(t->left); printf(“%d\n”,t->val); print_tree(t->right); } Recursion!

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 7

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 7 18

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree

Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree