< Algorithm Implementation | Trees
Wikipedia has related information at B+ tree |
This video gives you a quick view of insertion and deletion process in b+ tree. Mar 20, 2013 C Program To Perform Insertion, Deletion And Traversal In Red Black Tree C Program To Perform Insertion, Deletion and Traversal in AVL Tree C Program To Perform Insertion, Deletion and Traversal In B-Tree C Program To Implement Priority Queue Using Binary Heaps Construct Binary Search Tree From In-order and Pre-order Traversal Outputs.
Here is the source code of the Java Program to Perform Sorting Using B-Tree. The Java program is successfully compiled and run on a Windows system. The program output is also shown below. Import java.util.Random; BSTNodes left, right; int data; left = null; right = null. Mar 04, 2017 B-Tree Insertion and Deletion. B-Tree Insertion and Deletion. Skip navigation Sign in. Insertion in B Tree of Order 4| Data Structures| Balanced Tree (in HINDI).
In computer science, a B+ tree is a type of tree data structure. It represents sorted data in a way that allows for efficient insertion and removal of elements. It is a dynamic, multilevel index with maximum and minimum bounds on the number of keys in each node.
A B+ tree is a variation on a B-tree. In a B+ tree, in contrast to a B tree, all data are saved in the leaves. Internal nodes contain only keys and tree pointers. All leaves are at the same lowest level. Leaf nodes are also linked together as a linked list to make range queries easy.
The maximum number of keys in a record is called the order of the B+ tree.
Hibbeler mechanics of materials solutions. The minimum number of keys per record is 1/2 of the maximum number of keys. For example, if the order of a B+ tree is n, each node (except for the root) must have between n/2 and n keys.
The number of keys that may be indexed using a B+ tree is a function of the order of the tree and its height.
For a n-order B+ tree with a height of h:
- maximum number of keys is
- minimum number of keys is
The B+ tree was first described in the paper 'Rudolf Bayer, Edward M. McCreight: Organization and Maintenance of Large Ordered Indices. Acta Informatica 1: 173-189 (1972)'.
Sample implementation in C++[edit]
CAREFUL: THE FOLLOWING CODE EXAMPLES DO NOT IMPLEMENT A PROPER B+-TREE. While they are very similar to a B+-Tree, they do not fulfill the B+-Tree criteria (as the authors admit in some comments).
This code snippet has been tested under Linux on a 32-bit x86 computer. Deletion of keys has not been implemented yet. It can be done quite easily in a lazy way with an amortized cost of O(log n), by rebuilding the tree from scratch every time that there are as many deleted keys as non-deleted keys. The rebuilding can be done in O(n) time, so its amortized cost is only O(1). This approach, however, would not be appropriate for real time systems.
The implementation uses the Boost library to have compile-time assertions and efficient memory allocation. The latter could be done with the
new operator
instead, resulting in some performance penalty.Violate the B+Tree definition during inner node split[edit]
After convert it into Java code, I realize the following code doing split insertInner() violate the B+ Tree definitionFor example, what if N = 4, so after you split, we end up with 3 nodes, root node with 1 key, original node with 1 key, and the sibling node with 3 keys. So it (original node) violates the B+ Tree rules at least half full in the inner node. Look like we still need the canonical algorithm to make it right. Not shortcut here. So this algorithm is not strict B+ Tree, but it works. Anyway, I convert above C++ code to Java code shown below.
It doesn't really work because generic arrays cannot be created by casting from a newly created array of a concrete ancestor like Object.
ie. T[] a = new T[10] won't work. see the field declarations of LNode.
Sample Implementation In Java[edit]
Retrieved from 'https://en.wikibooks.org/w/index.php?title=Algorithm_Implementation/Trees/B%2B_tree&oldid=3482460'
#include
int n; /* n < M No. of keys in node will always less than order of B
int keys[M-1]; /*array of keys*/
struct node *p[M]; /* (n+1 pointers will be in use) */
enum KeyStatus { Duplicate,SearchFailure,Success,InsertIt,LessKeys };
void insert(int key);
void DelNode(int x);
enum KeyStatus ins(struct node *r, int x, int* y, struct node** u);
enum KeyStatus del(struct node *r, int x);
int main()
int key;
printf(“Creation of B tree for node %dn”,M);
{
Program Of Insertion And Deletion In B Tree
printf(“2.Deleten”);
printf(“4.Displayn”);
printf(“Enter your choice : “);
{
printf(“Enter the key : “);
insert(key);
case 2:
scanf(“%d”,&key);
break;
printf(“Enter the key : “);
search(key);
case 4:
display(root,0);
case 5:
default:
break;
}/*End of while*/
}/*End of main()*/
void insert(int key)
struct node *newnode;
enum KeyStatus value;
if (value Duplicate)
if (value InsertIt)
struct node *uproot = root;
root->n = 1;
root->p[0] = uproot;
}/*End of if */
enum KeyStatus ins(struct node *ptr, int key, int *upKey,struct node
{
int pos, i, n,splitPos;
enum KeyStatus value;
{
*upKey = key;
}
pos = searchPos(key, ptr->keys, n);
return Duplicate;
if (value != InsertIt)
/*If keys in node is less than M-1 where M is order of B tree*/
{
/*Shifting the key and pointer right for inserting the new key*/
{
ptr->p[i+1] = ptr->p[i];
/*Key is inserted at exact location*/
ptr->p[pos+1] = newPtr;
++ptr->n; /*incrementing the number of keys in node*/
}/*End of if */
/*If keys in nodes are maximum and position of node to be inserted is
if (pos M – 1)
lastKey = newKey;
}
else /*If keys in node are maximum and position of node to be inserted
{
lastPtr = ptr->p[M-1];
{
ptr->p[i+1] = ptr->p[i];
ptr->keys[pos] = newKey;
}
(*upKey) = ptr->keys[splitPos];
(*newnode)=malloc(sizeof(struct node));/*Right node after split*/
ptr->n = splitPos; /*No. of keys for left splitted node*/
(*newnode)->n = M-1-splitPos;/*No. of keys for right splitted node*/
{
if(i < (*newnode)->n – 1)
(*newnode)->keys[i] = ptr->keys[i + splitPos + 1];
(*newnode)->keys[i] = lastKey;
(*newnode)->p[(*newnode)->n] = lastPtr;
}/*End of ins()*/
void display(struct node *ptr, int blanks)
if (ptr)
int i;
printf(” “);
printf(“%d “,ptr->keys[i]);
for (i=0; i <= ptr->n; i++)
}/*End of if*/
{
struct node *ptr = root;
while (ptr)
n = ptr->n;
printf(” %d”,ptr->keys[i]);
pos = searchPos(key, ptr->keys, n);
{
printf(“Key %d found in position %d of last dispalyed
return;
ptr = ptr->p[pos];
printf(“Key %d is not availablen”,key);
{
while (pos < n && key > key_arr[pos])
return pos;
{
enum KeyStatus value;
switch (value)
case SearchFailure:
break;
uproot = root;
free(uproot);
}/*End of switch*/
{
int *key_arr;
struct node **p,*lptr,*rptr;
if (ptr NULL)
/*Assigns values of node*/
key_arr = ptr->keys;
min = (M – 1)/2;/*Minimum number of keys*/
pos = searchPos(key, key_arr, n);
{
return SearchFailure;
for (i=pos+1; i < n; i++)
key_arr[i-1] = key_arr[i];
}
return –ptr->n >= (ptrroot ? 1 : min) ? Success : LessKeys;
{
int nkey;
{
qp1 = qp->p[nkey];
![Program Of Insertion And Deletion In B Tree Program Of Insertion And Deletion In B Tree](https://opendsa-server.cs.vt.edu/ODSA/Books/CS3/html/_images/BPins.png)
break;
}/*End of while*/
qp->keys[nkey – 1] = key;
value = del(p[pos], key);
return value;
if (pos > 0 && p[pos-1]->n > min)
pivot = pos – 1; /*pivot for left and right node*/
rptr = p[pos];
rptr->p[rptr->n + 1] = rptr->p[rptr->n];
{
rptr->p[i] = rptr->p[i-1];
rptr->n++;
rptr->p[0] = lptr->p[lptr->n];
return Success;
if (posn > min)
pivot = pos; /*pivot for left and right node*/
rptr = p[pivot+1];
lptr->keys[lptr->n] = key_arr[pivot];
key_arr[pivot] = rptr->keys[0];
rptr->n–;
{
rptr->p[i] = rptr->p[i+1];
rptr->p[rptr->n] = rptr->p[rptr->n + 1];
}/*End of if */
if(pos n)
else
rptr = p[pivot+1];
lptr->keys[lptr->n] = key_arr[pivot];
for (i=0; i < rptr->n; i++)
lptr->keys[lptr->n + 1 + i] = rptr->keys[i];
C++ Program For Insertion And Deletion In B Tree
}
free(rptr); /*Remove right node*/
{
p[i] = p[i+1];
return –ptr->n >= (ptr root ? 1 : min) ? Success : LessKeys;
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