Binary Search Tree Remove Todays announcements: PA2 available soon - - PowerPoint PPT Presentation

Binary Search Tree Remove

Today’s announcements:

◮ PA2 available soon

Today’s Plan

◮ Average height of BST ◮ Remove

Warm up: Worst case time to perform find in a BST with n nodes: Worst case time to perform n inserts into an empty BST: Best case? Average case?

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Average depth in a BST

Choose a binary tree with n nodes,

• 1. equally likely from all n node binary trees:

Average depth is Θ(√n).

• 2. by inserting n items in random order into an empty BST:

Average depth is Θ(log n).

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Quicksort and inserting into an empty BST

Quicksort

• 1. Pick an array element as the pivot
• 2. Reorder the array so that all elements < pivot are to its left,

and all elements ≥ pivot are to its right.

• 3. Recursively sort each partition.

The first pivot is compared with every other element. The first element inserted into an empty BST is compared to every

• ther element.

Hmmm...

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Find node with minimum key in BST

Node *& findMin(Node *& root) { if( root == NULL || root->left == NULL ) return root; return findMin(root->left); }

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete

key

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete succ

key k2

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle toDelete succ

k2 k2

Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle succ

k2 k2

toDelete Remove a node from a Binary Search Tree

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void remove(KType key, Node *& root) { Node *& handle= pfind(key, root); if (handle == NULL) return; Node * toDelete = handle; if (handle->left == NULL) {// Leaf or only right child handle = handle->right; } else if (handle->right == NULL) { // Only left child handle = handle->left; } else { // Two children Node *& succ = findMin(handle->right); handle->key = succ->key; toDelete = succ; succ = succ->right; // succ has no left child } delete toDelete; }

handle succ

k2 k2

toDelete Remove a node from a Binary Search Tree

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