Analytics This website uses Google Analytics to collect anonymous information such as the number of visitors to the site, and the most popular pages. How to make it: An extension of a multiway search tree of order m is a B-tree of order m.
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However, they also have the same problems that binary search trees had - they can become unbalanced, which means that the construction of the tree becomes of vital importance. An extension of a multiway search tree of order m is a B-tree of order m. These restrictions make B-trees always at least half full, have few levels, and remain perfectly balanced. The nodes in a B-tree are usually implemented as a class that contains an array of m-l cells for keys, an array of m pointers to other nodes, and whatever other information is required in order to facilitate tree maintenance.
An algorithm for finding a key in B-tree is simple. Start at the root and determine which pointer to follow based on a comparison between the search value and key fields in the root node. Follow the appropriate pointer to a child node. Examine the key fields in the child node and continue to follow the appropriate pointers until the search value is found or a leaf node is reached that doesn't contain the desired search value. The condition that all leaves must be on the same level forces a characteristic behavior of B-trees, namely that B-trees are not allowed to grow at the their leaves; instead they are forced to grow at the root.
When inserting into a B-tree, a value is inserted directly into a leaf. This leads to three common situations that can occur:. This is the easiest of the cases to solve because the value is simply inserted into the correct sorted position in the leaf node. In this case, the leaf node where the value should be inserted is split in two, resulting in a new leaf node.
Half of the keys will be moved from the full leaf to the new leaf. The new leaf is then incorporated into the B-tree. The new leaf is incorporated by moving the middle value to the parent and a pointer to the new leaf is also added to the parent. This process is continues up the tree until all of the values have "found" a location. The new node needs to be incorporated into the tree - this is accomplished by taking the middle value and inserting it in the parent:.
The upward movement of values from case 2 means that it's possible that a value could move up to the root of the B-tree. If the root is full, the same basic process from case 2 will be applied and a new root will be created.
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