AIFBS_BTreeNode.cpp

#include <iostream>
#include "AIFBS_BTreeNode.hpp"
namespace AIFBS {
	
	/**
	*	Implentations
	*	All Tree Node Base definations
	**/
	
	template <class T>
	AIFBS_BTreeNode<T>::AIFBS_BTreeNode(int t1, bool leaf1)
	{
		n = 0;
		
		t = t1;
		leaf = leaf1;
	
		keys = new T[2*t-1];
		C = new AIFBS_BTreeNode<T> *[2*t];
	}
	
	template <class T>
	void AIFBS_BTreeNode<T>::traverse()
	{
		int i;
		std::cout<<" "<<n<<": ";
		for (i = 0; i < n; i++)
		{
			if (leaf == false)
				C[i]->traverse();
			std::cout << " " << keys[i];
		}
	
		if (leaf == false)
			C[i]->traverse();
	}

	template <class T>
	AIFBS_BTreeNode<T> *AIFBS_BTreeNode<T>::search(T k)
	{
		// Find the first key greater than or equal to k
		int i = 0;
		while (i < n && k > keys[i])
			i++;
	
		// If the found key is equal to k, return this node
		if (keys[i] == k)
			return this;
	
		// If key is not found here and this is a leaf node
		if (leaf == true)
			return NULL;
	
		// Go to the appropriate child
		return C[i]->search(k);
	}

	template <class T>
	T *AIFBS_BTreeNode<T>::searchKeyRef(T k)
	{
		// Find the first key greater than or equal to k
		int i = 0;
		while (i < n && k > keys[i])
			i++;
	
		// If the found key is equal to k, return this node
		if (keys[i] == k)
			return &keys[i];
	
		// If key is not found here and this is a leaf node
		if (leaf == true)
			return NULL;
	
		// Go to the appropriate child
		return C[i]->searchKeyRef(k);
	}
	template <class T>
	void AIFBS_BTreeNode<T>::insertNonFull(T k)
	{
		// Initialize index as index of rightmost element
		int i = n-1;
	
		// If this is a leaf node
		if (leaf == true)
		{
			// The following loop does two things
			// a) Finds the location of new key to be inserted
			// b) Moves all greater keys to one place ahead
			while (i >= 0 && keys[i] > k)
			{
				keys[i+1] = keys[i];
				i--;
			}
	
			// Insert the new key at found location
			keys[i+1] = k;
			n = n+1;
		}
		else // If this node is not leaf
		{
			// Find the child which is going to have the new key
			while (i >= 0 && keys[i] > k)
				i--;
	
			// See if the found child is full
			if (C[i+1]->n == 2*t-1)
			{
				// If the child is full, then split it
				splitChild(i+1, C[i+1]);
	
				// After split, the middle key of C[i] goes up and
				// C[i] is splitted into two. See which of the two
				// is going to have the new key
				if (keys[i+1] < k)
					i++;
			}
			C[i+1]->insertNonFull(k);
		}
	}
	
	// A utility function to split the child y of this node
	// Note that y must be full when this function is called
	template <class T>
	void AIFBS_BTreeNode<T>::splitChild(int i, AIFBS_BTreeNode *y)
	{
		// Create a new node which is going to store (t-1) keys
		// of y
		AIFBS_BTreeNode<T> *z = new AIFBS_BTreeNode<T>(y->t, y->leaf);
		z->n = t - 1;
	
		// Copy the last (t-1) keys of y to z
		for (int j = 0; j < t-1; j++)
			z->keys[j] = y->keys[j+t];
	
		// Copy the last t children of y to z
		if (y->leaf == false)
		{
			for (int j = 0; j < t; j++)
				z->C[j] = y->C[j+t];
		}
	
		// Reduce the number of keys in y
		y->n = t - 1;
	
		// Since this node is going to have a new child,
		// create space of new child
		for (int j = n; j >= i+1; j--)
			C[j+1] = C[j];
	
		// Link the new child to this node
		C[i+1] = z;
	
		// A key of y will move to this node. Find location of
		// new key and move all greater keys one space ahead
		for (int j = n-1; j >= i; j--)
			keys[j+1] = keys[j];
	
		// Copy the middle key of y to this node
		keys[i] = y->keys[t-1];
	
		// Increment count of keys in this node
		n = n + 1;
	}
	
	
	//************************************************************//
	//						REMOVE ADDED						  //
	//************************************************************//
	
	// A utility function that returns the index of the first key that is
	// greater than or equal to k
	
	template <class T>
	int AIFBS_BTreeNode<T>::findKey(T k)
	{
		int idx=0;
		while (idx<n && keys[idx] < k)
			++idx;
		return idx;
	}
	
	// A function to remove the key k from the sub-tree rooted with this node
	template <class T>
	void AIFBS_BTreeNode<T>::remove(T k)
	{
		int idx = findKey(k);
	
		// The key to be removed is present in this node
		if (idx < n && keys[idx] == k)
		{
	
			// If the node is a leaf node - removeFromLeaf is called
			// Otherwise, removeFromNonLeaf function is called
			if (leaf)
				removeFromLeaf(idx);
			else
				removeFromNonLeaf(idx);
		}
		else
		{
	
			// If this node is a leaf node, then the key is not present in tree
			if (leaf)
			{
				std::cout << "The key "<< k <<" is does not exist in the tree\n";
				return;
			}
	
			// The key to be removed is present in the sub-tree rooted with this node
			// The flag indicates whether the key is present in the sub-tree rooted
			// with the last child of this node
			bool flag = ( (idx==n)? true : false );
	
			// If the child where the key is supposed to exist has less that t keys,
			// we fill that child
			if (C[idx]->n < t)
				fill(idx);
	
			// If the last child has been merged, it must have merged with the previous
			// child and so we recurse on the (idx-1)th child. Else, we recurse on the
			// (idx)th child which now has atleast t keys
			if (flag && idx > n)
				C[idx-1]->remove(k);
			else
				C[idx]->remove(k);
		}
		return;
	}	

	// A function to remove the idx-th key from this node - which is a leaf node
	template <class T>
	void AIFBS_BTreeNode<T>::removeFromLeaf (int idx)
	{
	
		// Move all the keys after the idx-th pos one place backward
		for (int i=idx+1; i<n; ++i)
			keys[i-1] = keys[i];
	
		// Reduce the count of keys
		n--;
	
		return;
	}
	
	// A function to remove the idx-th key from this node - which is a non-leaf node
	template <class T>
	void AIFBS_BTreeNode<T>::removeFromNonLeaf(int idx)
	{
	
		T k = keys[idx];
	
		// If the child that precedes k (C[idx]) has atleast t keys,
		// find the predecessor 'pred' of k in the subtree rooted at
		// C[idx]. Replace k by pred. Recursively delete pred
		// in C[idx]
		if (C[idx]->n >= t)
		{
			T pred = getPred(idx);
			keys[idx] = pred;
			C[idx]->remove(pred);
		}
	
		// If the child C[idx] has less that t keys, examine C[idx+1].
		// If C[idx+1] has atleast t keys, find the successor 'succ' of k in
		// the subtree rooted at C[idx+1]
		// Replace k by succ
		// Recursively delete succ in C[idx+1]
		else if (C[idx+1]->n >= t)
		{
			T succ = getSucc(idx);
			keys[idx] = succ;
			C[idx+1]->remove(succ);
		}
	
		// If both C[idx] and C[idx+1] has less that t keys,merge k and all of C[idx+1]
		// into C[idx]
		// Now C[idx] contains 2t-1 keys
		// Free C[idx+1] and recursively delete k from C[idx]
		else
		{
			merge(idx);
			C[idx]->remove(k);
		}
		return;
	}
	
	// A function to get predecessor of keys[idx]
	template <class T>
	T AIFBS_BTreeNode<T>::getPred(int idx)
	{
		// Keep moving to the right most node until we reach a leaf
		AIFBS_BTreeNode<T> *cur=C[idx];
		while (!cur->leaf)
			cur = cur->C[cur->n];
	
		// Return the last key of the leaf
		return cur->keys[cur->n-1];
	}
	
	template <class T>
	T AIFBS_BTreeNode<T>::getSucc(int idx)
	{
	
		// Keep moving the left most node starting from C[idx+1] until we reach a leaf
		AIFBS_BTreeNode<T> *cur = C[idx+1];
		while (!cur->leaf)
			cur = cur->C[0];
	
		// Return the first key of the leaf
		return cur->keys[0];
	}
	
	// A function to fill child C[idx] which has less than t-1 keys
	template <class T>
	void AIFBS_BTreeNode<T>::fill(int idx)
	{
	
		// If the previous child(C[idx-1]) has more than t-1 keys, borrow a key
		// from that child
		if (idx!=0 && C[idx-1]->n>=t)
			borrowFromPrev(idx);
	
		// If the next child(C[idx+1]) has more than t-1 keys, borrow a key
		// from that child
		else if (idx!=n && C[idx+1]->n>=t)
			borrowFromNext(idx);
	
		// Merge C[idx] with its sibling
		// If C[idx] is the last child, merge it with with its previous sibling
		// Otherwise merge it with its next sibling
		else
		{
			if (idx != n)
				merge(idx);
			else
				merge(idx-1);
		}
		return;
	}
	
	// A function to borrow a key from C[idx-1] and insert it
	// into C[idx]
	template <class T>
	void AIFBS_BTreeNode<T>::borrowFromPrev(int idx)
	{
	
		AIFBS_BTreeNode<T> *child=C[idx];
		AIFBS_BTreeNode<T> *sibling=C[idx-1];
	
		// The last key from C[idx-1] goes up to the parent and key[idx-1]
		// from parent is inserted as the first key in C[idx]. Thus, the loses
		// sibling one key and child gains one key
	
		// Moving all key in C[idx] one step ahead
		for (int i=child->n-1; i>=0; --i)
			child->keys[i+1] = child->keys[i];
	
		// If C[idx] is not a leaf, move all its child pointers one step ahead
		if (!child->leaf)
		{
			for(int i=child->n; i>=0; --i)
				child->C[i+1] = child->C[i];
		}
	
		// Setting child's first key equal to keys[idx-1] from the current node
		child->keys[0] = keys[idx-1];
	
		// Moving sibling's last child as C[idx]'s first child
		if (!leaf)
			child->C[0] = sibling->C[sibling->n];
	
		// Moving the key from the sibling to the parent
		// This reduces the number of keys in the sibling
		keys[idx-1] = sibling->keys[sibling->n-1];
	
		child->n += 1;
		sibling->n -= 1;
	
		return;
	}
	
	// A function to borrow a key from the C[idx+1] and place
	// it in C[idx]
	template <class T>
	void AIFBS_BTreeNode<T>::borrowFromNext(int idx)
	{
	
		AIFBS_BTreeNode<T> *child=C[idx];
		AIFBS_BTreeNode<T> *sibling=C[idx+1];
	
		// keys[idx] is inserted as the last key in C[idx]
		child->keys[(child->n)] = keys[idx];
	
		// Sibling's first child is inserted as the last child
		// into C[idx]
		if (!(child->leaf))
			child->C[(child->n)+1] = sibling->C[0];
	
		//The first key from sibling is inserted into keys[idx]
		keys[idx] = sibling->keys[0];
	
		// Moving all keys in sibling one step behind
		for (int i=1; i<sibling->n; ++i)
			sibling->keys[i-1] = sibling->keys[i];
	
		// Moving the child pointers one step behind
		if (!sibling->leaf)
		{
			for(int i=1; i<=sibling->n; ++i)
				sibling->C[i-1] = sibling->C[i];
		}
	
		// Increasing and decreasing the key count of C[idx] and C[idx+1]
		// respectively
		child->n += 1;
		sibling->n -= 1;
	
		return;
	}
	
	// A function to merge C[idx] with C[idx+1]
	// C[idx+1] is freed after merging
	template <class T>
	void AIFBS_BTreeNode<T>::merge(int idx)
	{
		AIFBS_BTreeNode<T> *child = C[idx];
		AIFBS_BTreeNode<T> *sibling = C[idx+1];
	
		// Pulling a key from the current node and inserting it into (t-1)th
		// position of C[idx]
		child->keys[t-1] = keys[idx];
	
		// Copying the keys from C[idx+1] to C[idx] at the end
		for (int i=0; i<sibling->n; ++i)
			child->keys[i+t] = sibling->keys[i];
	
		// Copying the child pointers from C[idx+1] to C[idx]
		if (!child->leaf)
		{
			for(int i=0; i<=sibling->n; ++i)
				child->C[i+t] = sibling->C[i];
		}
	
		// Moving all keys after idx in the current node one step before -
		// to fill the gap created by moving keys[idx] to C[idx]
		for (int i=idx+1; i<n; ++i)
			keys[i-1] = keys[i];
	
		// Moving the child pointers after (idx+1) in the current node one
		// step before
		for (int i=idx+2; i<=n; ++i)
			C[i-1] = C[i];
	
		// Updating the key count of child and the current node
		child->n += sibling->n+1;
		n--;
	
		// Freeing the memory occupied by sibling
		delete(sibling);
		return;
	}
	
}