# Floor and Ceil from a BST

## Introduction:

Binary Search Trees (BSTs) are a category of simple data structures which are utilized to provide fast searches, insertions and deletions. A common issue with BSTs is finding a minimum and maximum value which is infinitely connected to a specific certain key. The top line refers to the little value greater than or equal to the target value, and the bottom line denotes the square key of the maximum value that goes to a specified key. In this work we discuss the strengths of algorithmic treatment of these values, the complexities and characteristic of BSTs as well as peculiarities of tree path traversal.

## BST Traversal:

If one wants to comprehend this particular process of reaching fallaciously both floor and ceiling, then knowledge about tree traversal should be possessed. To view tree BST from different points of view, in-order, pre-order, and post-order traversals are used which allows one to see how the nodes are captured throughout the history.

• Start from the parent and continue all way through the tree hierarchy.
• Compare the key of the current node with the one stored in the key field.
• There would be if the keys are having the same keys
• Left sub-tree if not enough.
• Revert to the left sub-tree if there is some.
• Maintain the best candidates for floor and ceiling critical about the contrasts.
• Then rightly advance the floor when the key is to happen less than the current node's key.
• If the key is greater than current node's key, change the ceiling to the updated node.
• Repeat until the last step (the leaf ).

### Java Code Implementation:

Output:

Explanation:

The recursion approach permits to searching of the BST effectively and redefining instantaneously ceiling and floor values by comparison key. The termination conditions guarantee the appropriate values are reported when an elementary key equivalent in the BST.

### Search Operations:

The BSTs' advantage is that when a user makes a search operation in a database, even more, for a subset of values, BSTs provide a fast response. The property of the binary search guarantees the search method is logarithmic in terms of the time complexity and although the search method works effusively for large datasets

Sub-querying values with a specified range is a point where floor and ceiling values become most useful. These values determine the limits of the range that together set the base for optimizing queries.

The floor value in a magnitude is the largest value that is not exceeding the specified range and the ceiling value is the smallest value that is not lower than the specified range.

### Query Optimization:

Query optimization can be aided by discovering ceiling and floor values according to the binary search tree methodology that results in the narrowing of the search space parameters. Software accrued can locate potential discovery among existingrecords set flat the queries explicitly specifying a boundary.

### Range Queries:

The floor and ceiling numbers areof great importance when it comes to range searches since it is essential to know the elements that fall within the given range. This is true about spatial databases and the GIS domain.

## Conclusion:

It would appear that the process for identifying floor value in the Binary Search Trees, and, quite importantly the process of identification for the ceiling value, is indeed a path of interrogations, investigations, and comparisons. These algorithms are arraigned around a comparison of keys and rules of tree traversal and have many application use in a wide spectrum better use. It is not concerned with the optimization of memory allocation, enhancements of database questions, or money but in deciding computing and prudently gets the colours of the floor and ceiling value as its value.

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