treap

Efficient implementation of the implicit treap data structure.

What does this package provide?

This package implements a tree-like data structure called implicit treap. This data structure implements interface similar to random-access arrays, but with fast (logarithmic time complexity) insert/delete/split/merge/take/drop/rotate operations. In addition, treap allows you to specify and measure values of any monoids on a segment, like a sum of elements or minimal element on some contiguous part of the array.

When to use this package?

Use this package when you want the following operations to be fast:

1. Access elements by index.
2. Insert elements by index.
3. Delete elements by index.
4. Calculate monoidal operation (like sum, product, min, etc.) of all elements between two indices.
5. Call slicing operations like take or drop or split.

Below you can find the table of time complexity for all operations (where n is the size of the treap):

| Operation | Time complexity | Description | |-----------|-----------------|--------------------------------------| | size | O(1) | Get number of elements in the treap | | at | O(log n) | Access by index | | insert | O(log n) | Insert by index | | delete | O(log n) | Delete by index | | query | O(log n) | Measure monoid on the segment | | splitAt | O(log n) | Split treap by index into two treaps | | merge | O(log n) | Merge two treaps into a single one | | take | O(log n) | Take first i elements of the treap | | drop | O(log n) | Drop first i elements of the treap | | rotate | O(log n) | Put first i elements to the end |

The package also comes with nice pretty-printing!

ghci> t = fromList [1..5] :: RTreap (Sum Int) Int
ghci> prettyPrint t
   5,15:2
      ╱╲
     ╱  ╲
    ╱    ╲
   ╱      ╲
1,1:1   3,12:4
          ╱╲
         ╱  ╲
        ╱    ╲
      1,3:3 1,5:5

Alternatives

If you don't need to calculate monoidal operations, you may alternatively use Seq from the containers package as it provides more extended interface but doesn't allow to measure monoidal values on segments.

Acknowledgement

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