Download - K: 5
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
Is the treap a heap?
P: 9
P:2P: 6
P: 4
For every node v, the search key in v is greater than or equal to those in the children of v
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
Not a complete tree! NO!
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
Is the treap a Binary Search Tree?
K: 5
K:1 K: 8
K: 7BST? Yes!
K: 5
K:1 K: 8
K: 7
All keys smaller than the root are stored in the left subtree
All keys larger than the root are sorted in the right subtree
(K, P)(5,9)(7,4)(8,6)(1,2)
K: 5
P: 9K:1P:2 P: 6
K: 8K: 7
P: 4
(K, P)(5,9)(7,4)(8,6)(1,2)
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
K: 5
P: 9
K:1P:2
P: 6
K: 8
K: 7
P: 4
Assume no duplicate key / priority, only one treap is possible
(2,5) (5,2) (3,1) (4,7) (9,4) (8,3)
K:2P:5
K:5P:2
K:3P:1
K:4P:7
K:9P:4
K:8P:3
K:2P:5
K:5P:2
K:3P:1
K:4P:7
K:9P:4
K:8P:3
Arrange from left to right,
Smallest key Biggest key
K:2P:5
K:5P:2
K:3P:1
K:4P:7
K:9P:4
K:8P:3
Without destroying left to right arrangement,Shift the “nodes” up and down
Biggest priority
Smallest priority
K:2P:5
K:5P:2K:3
P:1
K:4P:7
K:9P:4
K:8P:3
K:2P:5
K:5P:2
K:3P:1
K:4P:7
K:9P:4
K:8P:3
