What are sibling nodes in a binary tree?

Sibling nodes in a binary tree are nodes that share the same parent node.

In a binary tree, each node can have at most two children, referred to as the left child and the right child. If two nodes have the same parent, they are considered sibling nodes. For example, in a binary tree with a root node A, and two child nodes B and C, B and C are sibling nodes because they share the same parent, A.

The concept of sibling nodes is important in understanding the structure and traversal of binary trees. In a binary tree, nodes are organised in levels, starting with the root node at level 0. All nodes at the same level are not necessarily siblings, as they may not share the same parent. For instance, in a binary tree with root A, children B and C, and grandchildren D, E, F and G (where D and E are children of B, and F and G are children of C), D and E are siblings, F and G are siblings, but D and F are not siblings, despite being at the same level.

The sibling relationship is also significant in certain operations on binary trees. For example, in tree rotations used in balancing operations of self-balancing binary search trees, sibling nodes play a crucial role. In a right rotation, the left child of a node becomes the node's parent, and the node becomes the right child of its former left child. The right child of the node becomes the left child of its former sibling.

In conclusion, understanding the concept of sibling nodes is fundamental in studying binary trees. It helps in comprehending the tree's structure, traversal methods, and various operations performed on the tree.