Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 16.3, Problem 7E
Program Plan Intro
To generalize Huffman
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Given an array of digits D[1, . . . , n], find the largest multiple of three that can be formed by concatenating some of the given digits in ANY order. Return -1 if there is no answer.
Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
Given a set S of n planar points, construct an efficient algorithm to determine whether or not there exist three points in S that are collinear. Hint: While there are Θ(n3) triples of members of S, you should be able to construct an algorithm that runs in o(n3) sequential time.
Imagine that you have a problem P that you know is N P-complete. For
this problem you have two algorithms to solve it. For each algorithm, some
problem instances of P run in polynomial time and others run in exponential time (there are lots of heuristic-based algorithms for real N P-complete
problems with this behavior). You can’t tell beforehand for any given problem instance whether it will run in polynomial or exponential time on either
algorithm. However, you do know that for every problem instance, at least
one of the two algorithms will solve it in polynomial time.
(a) What should you do?
(b) What is the running time of your solution?
564 Chap. 17 Limits to Computation
(c) What does it say about the question of P = N P if the conditions
described in this problem existed?
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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