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 16.2, Problem 5E
Program Plan Intro
To describe an efficient
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Let Z be the set of all integers. An integer a has f as a factor if a = fj for some
integer j. An integer is even if it has 2 as a factor. An integer a is odd if it is not even.
Prove by contradiction that an odd number cannot have an even number as a factor.
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.
Analyze the approximation algorithm of the problem consists of a finite set X and a family F of subsets of X, such that every element of X belongs to at least one subset.
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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- Let m be a randomly chosen non-negative integer having at most n decimal digits, i.e. an integer in the range 0 sms 10" - 1. Consider the following problem: determine m by asking only 5- way questions, i.e. questions with at most 5 possible responses. For instance, one could ask which of 5 specific sets m belongs to. Prove that any algorithm restricted to such questions, and which correctly solves this problem, runs in time Q(n).arrow_forwardAbout a set X of numbers we say that it is almost sum-free if the sum of two different elements of X never belongs to X. For instance, the set {1, 2, 4} is almost sum-free. Almost-Schur number A(k) is the largest integer n for which the interval {1, . . . , n} can be partitioned into k almost sum-free sets. Use clingo to find the exact values of A(1), A(2), A(3) and try to find the largest lower bound for A(4), i.e., the largest number l such that A(4) ≥ l. Hint: you do not need to find all partitions to find the values of A(k). PLEASE USE CLINGO.arrow_forwardHow do we define that a function f(n) has an upper bound g(n), i.e., f(n) ∈ O(g(n))?arrow_forward
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