Tree Representation in Memory

Internal

• Trees

Overview

Rooted trees can be implemented in several ways:

• Use linked data structures
• Use an array and a heap structure

Representing Rooted Trees as Linked Data Structures

Each tree node is represented by an object that has a key attribute and pointers to other nodes, which vary depending on the tree type:

Binary Trees

A binary tree node has three pointers:

• p, which points to the parent node. Only the root has a NULL parent.
• left and right, which point to the left and the right child. If the node has no left child, left is NULL. If the node has no right child, right is NULL.

public class N {
  public N p; // parent, may be null for root
  public N l; // left child
  public N r; // right child
  public String k; // key

  public N(String k) {
    this.k = k;
  }
}

https://github.com/ovidiuf/playground/blob/master/algorithms/trees/binary-tree/src/main/java/playground/bt/N.java

Trees whose Nodes have an Arbitrary Number of Children

One option to represent trees whose nodes have an arbitrary number of children is to extend the scheme used for representing binary tree to any class of trees in which the number of children in each node is at most some constant k: we replace the left and right attributes by child0, child1, ... childk-1. However, this is not ideal: we cannot represent an unbounded number of children, and also when the number of children k is bounded by some large constant, but most nodes have a small number of children, we waste a lot of memory.

Another scheme to represent an arbitrary number of children is left-child, right-sibling representation. Instead of having a pointer to each of its children, each node has only three pointers:

• parent
• left-child points to the leftmost child
• right-sibling points to the node's sibling immediately to the right.

Representing Rooted Trees in an Array

Trees can be represented in memory by using an array where each element of the array contains a pointer to a tree node. The data structure that represents a tree in an array is called a heap.

Binary Heap

A data structure that represents a binary tree using an array is called a binary heap.

Heaps