Discussion Section Assignment 7

Leftist Tree Tournament winner, Loser Tree Binary Search Tree

Hadi Hajimiri ([email protected])

 s-value: The distance to the nearest leaf The right descendant of each node has the

lower s-value In min (max) leftist tree the root contains

the minimum (maximum) item To delete a minimum item (in min leftist

tree), we remove the root and the left and right sub-trees are then merged (melded)

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Two ways:1. Merge each node one at a time into one HBLT

O(nlogn)2. Use a queue to store each node and resulting

tree. The first two items in the queue are removed, merged, and placed back into the queue. O(n)

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In a min (max) winner tree, the player with the smaller (larger) value wins.

In a loser tree, in each internal node, the loser of the match played at that node is recorded.◦ Reduces the work needed to determine the

players of each match after replacing the winner.

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Properties:◦ Every element has a key (or value), and no

elements have the same key.◦ The keys in the left subtree of the root are smaller

than the key in the root.◦ The keys in the right subtree of the root are larger

than the key in the root.◦ The left and right subtrees of the root are also

binary search trees.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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Insert the keys 9, 2, 7, 11, 16, 15, 1 into the tree in this order.

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