Binary Search Tree and Heap in Prolog
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- The document discusses building a sorted tree dictionary to efficiently store and lookup horse winnings from a database. - It shows an implementation of a sorted tree as a binary search tree to store horse names and winnings, allowing lookups in O(log n) time rather than O(n) for a linear search. - An extension discusses representing the sorted tree as a heap, where each node is greater than or equal to its children, and defines a heap1 predicate to check if a tree satisfies the heap property.
Binary Search Tree and Heap in Prolog
- 1. Sorted Tree Dictionary Logic Programming - Fall 12 Benjamin GUILLET
- 2. What's the matter? ● We want to build a index (dictionary) of performances of horses ● Let's build a database! winnings(abaris, 582). winnings(careful,17). winnings(jingling_silver, 300). winnings(maloja, 356). ● It's slow! O(n)
- 3. Solution ● Create a Sorted Tree Dictionary ● Basically: a Binary Search Tree (BST). ● Search: O(log n)
- 4. Implementation: w(H, W, L, G). w(massinga, 858, , ). w(braemar,385, , _). w(panorama, 158, , _). w(adela, 588, _, _). w(nettleweed, 579, _, _ ). w(massinga, 858, w(braemar,385, w(adela, 588,_,_), _), w(panorama, 158, w(nettleweed, 579,_,_), _) ).
- 5. Implementation: lookup lookup(H, w(H, G, _, _), G1) :- !, G1=G. lookup(H, w(H1, _, Before, _), G) :- H @< H1, lookup(H, Before, G). lookup(H, w(H1, _, _, After), G) :- H @> H1, lookup(H,After,G).
- 6. Experiment (1) lookup(massinga, X, 858), lookup(braemar, X, 385), lookup(nettleweed, X, 579), lookup(panorama, X, 158). w(massinga,858, w(braemar,385,_,_), w(nettleweed,579,_, w(panorama,158,_,_) ) w(massinga, 858, , ). ). w(nettleweed, 579, , _ ). w(braemar,385, _, _). w(panorama, 158, _, _).
- 7. Experiment (2) lookup(adela, X, 588), lookup(braemar, X, 385), lookup(nettleweed, X, 579), lookup(massinga, X, 858). X = w(adela,588,_,w(braemar,385,_,w(nettleweed,579,w(massinga,858,_,_), _))) ? w(adela,588,_, w(braemar,385,_, w(adela, 588, _, ). w(nettleweed,579, w(massinga,858,_,_), _) w(braemar,385, _, ). ) ) w(nettleweed, 579, , _ ). w(massinga, 858, _, _).
- 8. Extension: Is it a heap?! heap: ● Shape property: almost complete binary tree ● Heap property: each node is greater than or equal to each of its children
- 9. Extension (2) | ?- heap1(node(5, node(3, empty, empty), node(4, empty, empty))). 1. The empty tree is a binary heap. 2. For node(K, L, R), it is a heap if: a. L and R are heaps. b. If L and/or R are not empty, then their key is less than or equal to K. c. If L has depth d, then R has depth d or d - 1.
- 10. Extension (3) heap1(H) :- heap1(H, _). heap1(empty, 0). heap1(node(K, L, R), H) :- heap1(L, LH), heap1(R, RH), (L = node(LK, _, _) *-> K @>= LK; true), (R = node(RK, _, _) *-> K @>= RK; true), (LH is RH; LH is RH + 1), H is LH + 1.
- 11. Extension (4) |?- heap1(node(5, node(4, node(6,empty,empty), empty), node(3,empty,empty))).
- 12. Thank you!