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 33.4, Problem 5E
Program Plan Intro
To show thathow to determine the sets
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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).
Let T be a sorted array of n elements. An element x is said to be a majority element in T if the number of elements i, with T[i] = x, is greater than n/2.
Give an algorithm (code or pseudo-code) that can decide whether T includes a majority element (it cannot have more than one), and if so, find it. Your algorithm must run
in linear time.
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 È(n3) triples of members of S, you should be able to construct an algorithm that runs in o(n3) sequential time.
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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