By Gilles Brassard
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7). 5. 8). This is much better than the first algorithm. However, there exists a third algorithm that gives as great an improvement over the second algorithm as the second does over the first. 9). It will be explained in Chapter 4. function fib3(n) i <-1; j -0; kwhile n > 0 do 0; h - I if n is odd then t v-- jh j e- ih + jk + t i <- ik + t t -- 1h2 h <- 2kh + t k <-k2+ t n -- n div 2 return j Once again, we programmed the three algorithms in Pascal on a CDC CYBER 835 in order to compare their execution times empirically.
A) The starting situation. Q Ta0 (b) The level I subtrees are made into heaps. (c) One level 2 subtree is made into a heap (the other already is a heap). 9. Making a heap. Preliminaries 30 Chap. 2. Let T[l .. 12] be an array such that T[i] =i for each i < 12. Exhibit the state of the array after each of the following procedure calls: make-heap (T) alter-heap(T, 12, 10) alter-heap (T. 1, 6) alter-heap(T, 5, 8) . 3. Exhibit a heap T [1 n] containing distinct values, such that the following sequence results in a different heap: m v- find-max (T) delete-max (T) insert-node(T[1 ..
These are exactly the operations we need implement dynamic priority lists efficiently: the value of a node gives the priority the corresponding event. The event with highest priority is always found at the root it, to of of 28 Preliminaries Chap. 1 the heap, and the priority of an event can be changed dynamically at all times. This is particularly useful in computer simulations. function find-max (T [1 .. n ]) Ireturns the largest element of the heap T [ I .. n ] return T l] procedure delete-max (T [I ..
Algorithmics: Theory and Practice by Gilles Brassard