Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 7 ppsx
... to go to get to 1 or 1/4, starting from 1/2, rate of increase of differs. • For α to go from 1/ 2to1 ,num increases from size /2tosize, for a total increase of size /2. increases from 0 to size. ... moves to a higher-indexed array, i.e., from A i to A i+1 . It can Lecture Notes for Chapter 17: Amortized Analysis 17- 5 Binary counter Charge $2 to set a bit to 1. • $1 pays...
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... Structures Lecture Notes 14-1 Solutions 14-9 Preface This document is an instructor’s manual to accompany Introduction to Algorithms, Second Edition, by Thomas H. Cormen, Charles E. Leiserson, Ronald L. ... invariants is like mathematical induction: Instructor’s Manual by Thomas H. Cormen Clara Lee Erica Lin to Accompany Introduction to Algorithms Second Edition...
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... 2, 3 4/ 27 1, 3, 2 5/ 27 2, 1, 3 5/ 27 2, 3, 1 5/ 27 3, 1, 2 4/ 27 3, 2, 1 4/ 27 6-6 Lecture Notes for Chapter 6: Heapsort (a) (b) (c) (d) (e) 123 47 2 13 47 1 23 47 3 21 74 4 23 71 7 43 21 A i i i i Analysis • BUILD-MAX-HEAP: ... 5. • MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4. 1 23 45 67 8910 1 23 45 67 8910 4 13 2910 14 8 7...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 3 docx
... overview [The treatment in the second edition differs from that of the Þrst edition. We use a different partitioning method—known as “Lomuto partitioning”—in the second edition, rather than the “Hoare ... program may need to scale a set of (x, y) data to Þt onto a rectangular display. To do so, the program must Þrst Þnd the minimum and maximum of each coordinate. A simple algori...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 4 pot
... could have picked, say, n ≥ 71 , so that for all n ≥ 71 , the fraction would be ≤ 71 / (71 − 70 ) = 71 . Then we would have had 20a ≥ 71 0a, so we’d have needed to choose c ≥ 71 0a. Notice that S ELECT ... c n/5 + c(7n/10 + 6) +an ≤ cn/5 + c + 7cn/10 + 6c + an = 9cn/10 + 7c + an = cn + (−cn/10 + 7c +an). • This last quantity is ≤ cn if −cn/10 + 7c + an ≤ 0 cn/10 −7c ≥ an cn 70 c...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 5 potx
... O(h) time, analogous to the changes we made for persistence in insertion. But to do so without using parent pointers we need to walk down the tree to the node to be deleted, to build up a stack ... keys are not distinct, because in order to Þnd the path to the node to delete—a particular node with a given key—we have to make some changes to how we store things in the tre...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 6 pps
... row-major order, i.e., row-by-row from top to bottom, and left to right within each row. Column- major order (column-by-column from left to right, and top to bottom within each column) would also ... 365, we wish to print the sequence p 7 , p 6 , p 4 , p 3 , p 1 , p 2 , p 5 . Our code is recursive. The right -to- left subpath is printed as we go deeper into the recursion, and the...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 8 potx
... into A right after the Þrst element of A. We have to traverse B to update representative pointers anyway, so we can just make the last element of B point to the second element of A. Solution to ... edge it visits to the cycle C, which is then added to the Euler tour T , when we return from a call to VISIT(u), all edges entering or leaving vertex u have been added to the tour...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 9 pdf
... + E) to compute G . • O(VE) to run BELLMAN-FORD. • (E) to compute w. • O(V 2 lg V +VE) to run Dijkstra’s algorithm | V | times (using Fibonacci heap). • (V 2 ) to compute D matrix. Total: ... t (k−1) kj . T RANSITIVE-CLOSURE(E, n) for i ← 1 to n do for j ← 1 to n do if i = j or (i, j) ∈ E[G] then t (0) ij ← 1 else t (0) ij ← 0 for k ← 1 to n do for i ← 1 to n do for j...
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Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 10 potx
... 26-20 Exercise 27. 1-4, 27- 8 Exercise 27. 1-5, 27- 8 Exercise 27. 1-6, 27- 2 Exercise 27. 1 -7, 27- 8 Exercise 27. 2-2, 27- 9 Exercise 27. 5-1, 27- 9 Exercise 27. 5-2, 27- 10 27- 4 Lecture Notes for Chapter 27: Sorting ... 16-13 Exercise 16.2 -7, 16-13 Exercise 16.4-2, 16-14 Exercise 16.4-3, 16-14 Exercise 17. 1-3, 17- 14 Exercise 17. 2-1, 17- 14 Exercise 17. 2-2, 17- 15 Exercise 17. 2-3, 1...
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