StudyDSA

Preorder Tree Traversal

Preorder traversal is a method of exploring a tree where we visit each node before its children. The traversal follows a root-left-right sequence, meaning we process the current node, then recursively traverse the left subtree, and finally the right subtree.

1. Visit Current Node

Start by processing the current node. This typically involves printing its value, adding it to a result list, or performing some operation specific to your task. In the initial call, this will be the root of the tree.

2. Traverse Left Subtree

After processing the current node, recursively apply the preorder traversal to the left subtree. This step ensures that we explore the entire left side of each node before moving to the right.

3. Traverse Right Subtree

Once the left subtree is fully explored, recursively apply the preorder traversal to the right subtree. This completes the exploration of the current node and its descendants.

Preorder traversal is particularly useful for creating a copy of the tree, serializing a tree structure, or evaluating prefix expressions. Its time complexity is O(n), visiting each node once, and space complexity is O(h) in the worst case, where h is the tree's height, due to the recursive call stack.

Inorder Tree Traversal

Inorder traversal is a method of exploring a tree where we visit each node between its left and right children. The traversal follows a left-root-right sequence, meaning we first recursively traverse the left subtree, then process the current node, and finally traverse the right subtree.

1. Traverse Left Subtree

Start by recursively applying the inorder traversal to the left subtree. This ensures that we explore the entire left side of the current node before processing it.

2. Visit Current Node

After the left subtree is fully explored, process the current node. This typically involves printing its value, adding it to a result list, or performing some operation specific to your task. In the initial call, this will be the root of the tree after its left subtree is processed.

3. Traverse Right Subtree

Finally, recursively apply the inorder traversal to the right subtree. This completes the exploration of the current node and its descendants.

Inorder traversal is particularly useful for binary search trees, as it visits nodes in ascending order. It's also used for creating postfix expressions from expression trees. Like preorder traversal, its time complexity is O(n), visiting each node once, and space complexity is O(h) in the worst case, where h is the tree's height, due to the recursive call stack.

Postorder Tree Traversal

Postorder traversal is a method of exploring a tree where we visit each node after its children. The traversal follows a left-right-root sequence, meaning we first recursively traverse the left subtree, then the right subtree, and finally process the current node.

1. Traverse Left Subtree

Start by recursively applying the postorder traversal to the left subtree. This ensures that we explore the entire left side of the current node before moving to the right.

2. Traverse Right Subtree

After the left subtree is fully explored, recursively apply the postorder traversal to the right subtree. This step completes the exploration of all descendants before processing the current node.

3. Visit Current Node

Finally, process the current node. This typically involves printing its value, adding it to a result list, or performing some operation specific to your task. In the initial call, the root of the tree will be the last node processed.

Postorder traversal is particularly useful for operations that require processing child nodes before their parents, such as deleting a tree or evaluating postfix expressions. Like other traversal methods, its time complexity is O(n), visiting each node once, and space complexity is O(h) in the worst case, where h is the tree's height, due to the recursive call stack.

Level Order Tree Traversal

Level order traversal, also known as breadth-first search (BFS) for trees, is a method of exploring a tree where we visit nodes level by level, from left to right. Unlike the previous traversals, level order traversal is typically implemented iteratively using a queue rather than recursively.

1. Initialize Queue

Start by creating a queue and adding the root node. The queue will be used to keep track of nodes at each level.

2. Process Current Level

While the queue is not empty, dequeue a node, process it (e.g., print its value or add it to the result list), and enqueue its children (first left, then right) if they exist.

3. Move to Next Level

After processing all nodes at the current level (i.e., when all nodes from the previous level have been dequeued), the queue will contain all nodes of the next level. Repeat step 2 for this new level.

Level order traversal is useful for tasks that require processing nodes based on their distance from the root, such as finding the minimum depth of a tree or serializing a tree. Its time complexity is O(n), visiting each node once, and its space complexity is O(w), where w is the maximum width of the tree, as the queue will contain at most all nodes at the widest level.