BST Numbers, Memory, Removal & Tree Maps. BST Numbers n = number values contained h = height

BST Numbers, Memory, Removal & Tree Maps

BST Numbers

Ideal binary tree:• Leaf nodes dominate :

max number leaves =

• Height directly related to n:n = 2(h+1) – 1

• Height = Height related to log of tree size

n = number values containedh = height

BST Numbers

Ideal binary tree:• Leaf nodes dominate :

max number leaves =

• Height directly related to n:n = 2(h+1) – 1

• Height = Height related to log of tree sizeAlgorithm that descends one path doing constant work at each node is O(logn)

n = number values containedh = height

BST Memory

• BST manages memory…– Destructor– Copy/Assignment

BST DeleteDestructor

deleteSubtree at root

deleteSubtree(node)deleteSubtree on childrendelete node

BST CopyBSTNode* copySubtree(BSTNode* currentNode)

If currentNode is nullptrreturn nullptr

BSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST CopyBSTNode* copySubtree(BSTNode* currentNode)

If currentNode is nullptrreturn nullptr

BSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BSTNode* copySubtree(BSTNode* currentNode)If currentNode is nullptr

return nullptrBSTNode* newNode = new BSTNode(currentNode->value)newNode->left = copySubtree(currentNode->left) newNode->right= copySubtree(currentNode->right)return newNode

BST Copy

BST Memory

• Duplicate

• Copy Constror Assignment Operator

BST Removal

• Case 1: No children

BST Removal

• Case 1: No children

• Prune from parent and delete

BST Removal

• Case 2: One child

BST Removal

• Case 2: One child

• Hook parent to the one child

BST Removal

• Case 3: Two Children

BST Removal

• Case 3: Two Children

• Identify replacement (smallest on right)

BST Removal

• Case 3: Two Children

• Move value to node being replaced

• Case 3: Two Children

• Remove smallest on right

BST Removal

• Recursive Remove:

How It Works

• SmallestValue( startNode )– Return value of leftmost

child of startNode

Helpers

• RemoveSmallestNode( startNode )– Return pointer to

subtree with leftmostnode removed

Helpers