Implementation a a a a a a p m p p p l l l e e q p p

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Unformatted text preview: plementation A A A A A A P M P P P L L L E E Q P P P E E E E E E E public UnorderedArrayMaxPQ(int capacity) { pq = (Key) new Comparable[capacity]; Q X P M M M L E E no generic array creation } public boolean isEmpty() { return N == 0; } X P P P M L L public void insert(Key x) { pq[N++] = x; } X P P M M P P P public Key delMax() { int max = 0; for (int i = 1; i < N; i++) if (less(max, i)) max = i; exch(max, N-1); should null out entry return pq[--N]; to prevent loitering } P A sequence of operations on a priority queue less() and exch() similar to sorting methods (but don't pass pq) } 9 10 Priority queue elementary implementations Challenge. Implement all operations efficiently. 2.4 P RIORITY Q UEUES order of growth of running time for priority queue with N items implementation insert del max max unordered array 1 N N ordered array N 1 1 goal log N log N log N ‣ API and elementary implementations ‣ binary heaps Algorithms R OBERT S EDGEWICK | K EVIN W AYNE 11 ‣ heapsort ‣ event-driven simulation Complete binary tree A complete binary tree in nature Binary tree. Empty or node with links to left and right binary trees. Complete tree. Perfectly balanced, except for bottom level. complete tree with N = 16 nodes (height = 4) Property. Height of complete tree with N nodes is ⎣ྏlg N⎦ྏ. Pf. Height only increases when N is a power of 2. 13 14 Binary heap representations Binary heap properties Binary heap. Array representation of a heap-ordered complete binary tree. Proposition. Largest key is a[1], which is root of binary tree. Heap-ordered binary tree. Proposition. Can use array indices to move through tree. ・ ・Parent's key no smaller than ・Parent of node at k is at k/2. ・Children of node at k are at 2k and 2k+1. Keys in nodes. children's keys. i a[i] 0 - 1 T 2 S 3 R S 4 P 5 N 6 O 7 A 8 E 9 10 11 IHG i a[i] 0 - R P N 1 9I O 4 P R 5 N 6 O 7 A P A E I H G N O A 1 T 3R 2S 4P 3 R 8 E 9 10 11 IHG E I T ・Indices start at 1. ・Take nodes in level order. ・No explicit links needed! 8E 2 S...
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