CSE116 4-21-2010 Notes

# CSE116 4-21-2010 Notes - The tree is heap ordered Balance...

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Priority Queues A priority queue is a queue in which items are ordered according to their priorities. Traditionally, low numeric values for priorities correspond to high priorities. Implementation Linear list – sorted list in which items are ordered by priority Heap - A binary tree which maintains its items according to a heap order Aside : the queue we saw earlier is a special case of a priority queue in which the priority of an item corresponds to how long it has been in the queue. A head is a binary tree that maintains two invariants: 1) Order property 2) Structure/balance property Heap order Property (min version) For every non-empty heap the value at the root is less than any value in either of its children.

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Unformatted text preview: The tree is heap ordered Balance Property Basic idea : do not start a new level in the tree until the previous one is full In our implementation, the condition is: For every non-empty heap, the size of the left subtree is either the same size as the right subtree, r it is one larger Either: |L| = |R| Or: |L| = |R| + 1 Insertion into a heap: 1a) insert a new item (recursively) into the right subtree 1b) swap the left and right subtrees as we go along 2) Restore the order condition by percolating up any out – of –order item along the insertion path Ex: show what an initially empty min- heap looks like as each of the following items is inserted: 40 60 90 50 20 30 10 D) …...
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