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, Problem 5P
a.
Program Plan Intro
To show how to compute the convex hull of all
b.
Program Plan Intro
To show how to compute the convex hull of a set of n points with
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The Partitioning Problem: Given a set ofnpositive integers, partition the integers into two subsets of equal or almost equal sum. The goal is to partition the input numbers into two groups such that the difference between the sums of the elements in the two group is minimum or as small as possible.
a) Since no polynomial solutions are known for the above problem, implement an exponential algorithm for finding the optimal solution for any instance of the problem and test it for small input samples. Identify the maximum input size for which an optimal solution is possible to obtain using your algorithm in reasonable time (for example 3 hours). Hint: Every possible partition (solution) can be represented by a binary array of sizen
Consider a text corpus consisting of N tokens of d distinct words and the number of times each distinct word w appears is given by . We want to apply a version of Laplace smoothing that estimates a word's probability as: xw+a/ N+ad for some constant a (Laplace recommended a = 1, but other values are possible.) In the following problems, assume N is 100,000, d is 10,000 and a is 2.
A. Give both the unsmoothed maximum likelihood probability estimate and the Laplace smoothed estimate of a word that appears 1,000 times in the corpus.
B. Do the same for a word that does not appear at all.
C. You are running a Naive Bayes text classifier with Laplace Smoothing, and you suspect that you are overfitting the data. How would you increase or decrease the parameter a?
D. Could increasing a increase or decrease training set error? Increase or decrease validation set error?
Conditional Probability
How do I find P(A) and also P(B) given P(C) P(C') P(AlC) P(BlC) P(AlC') and P(BlC').
And how do I find out if P(A) and P(B) are independent?
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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