B-tree: minimum

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General Information

Algorithmic Problem:

Type of algorithm: loop

Auxiliary data: A pointer p of type "pointer to a B-tree node".

Abstract View

Invariant: Before and after each iteration:

  1. p points to some node N of the B-tree.

Variant: p is redirected from the current node N to the first child of the current node.

Break condition:

  1. p points to a leaf of the B-tree.

Description of the algorithm

To get the minimum of a B-Tree, you have to go to the leftest child while it exists.

Pseudocode

Minimum(x)
1 while leaf(x) = false
2        x = c_0(x)
3 return key_0(x)