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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Question
Chapter 7, Problem 6P
(a)
Program Plan Intro
To design an overlapping based general randomized
(b)
Program Plan Intro
To argue the expected running time of the algorithm is
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Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. Prove this.Next,show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable.
A magic square of order n is an arrangement of the integers from 1 to n2 in an n × n matrix, with each number occurring exactly once, so that each row, each column, and each main diagonal has the same sum Design and implement an exhaustive-search algorithm for generating all magic squares of order n.
Java Programming
Consider a set of n intervals I1,...,In, each given as an integer tuple (si,fi) with si<fi, such that the ith interval starts at si and ends at fi. We want to determine the maximum number of nonoverlapping intervals. More formally, we want to determine the size of a largest subset S⊆{1,...,n} such that for i, j∈S, with i≠j we have fj≤si or fi≤sj. Note that the intervals [1,2] and [2,3] are not considered to be overlapping.
Input
The first line of input consists of an integer n∈{1,...,105}, the number of intervals. Each of the following n lines consists of two space-separated integers ss and ff, indicating an interval starting at s and ending at f, with 0≤s<f≤109.
requirements:
CPU Time limit: 4 seconds
Memory limit: 1024 MB
Output
Output a single integer, the largest number of nonoverlapping intervals.
Chapter 7 Solutions
Introduction to Algorithms
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