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11-7 notes - 11-7 Notes Algorithms and Data Structures...

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11-7 Notes Algorithms and Data Structures Every node of a B-tree must contain at least t-1 keys and at most 2t-1 keys (except root may have as few as one key) M / \ DH QTX / | \ / | | \ BC FG JKL NP RS UW YZ Find out how are we going to implement insertion and deletion in a B-Tree that is guaranteed? Insertion o Key: how do we (1) not create new levels at a level below current leaves, (2) insert if a leaf is already full? o Idea: node splitting T = 3 (full = 5 keys) Leaf: PQRST Parent: NW Split leaf at R New Leaves: PQ && ST new Parent: NRW Redistribute any sub-leaves o Code SPLIT(x) //x is full K k t (x) Create node x L from k 1 (x)…k t-1 (x) Create x R from k t+1 (x)…k 2t-1 (x) Move k into parent of x Add pointers to x L , x R on either side of k o Problems: What if the parent is full? Make sure it never happens What if x is root? create a new root What is the parent? Always go down, never up o Idea: do recursive DoINsert(x,k) o * Invariant: when we call DoInsert(x,k),
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