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 7E
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Let's say you're going to invite some people to a party. You're considering n friends, but you know that they will
have a good time only if each of them knows at least k others at the party. (Assume that if A knows B, then B
automatically knows A.) Solve your problem by designing an algorithm for finding the largest possible subset of
your friends where everyone knows at least k of the others, if such a subset exists. Please comment on code and
show all work so I can better understand the problem and please use python thank you,
To help you get started l've made a graph of "my friends":
G={'Rachel':['Ross Monica'], 'Ross':['Rachel', 'Monica'], 'Monica':['Rachel', 'Ross'], 'Jon
Snow':['Daenerys' "Sansa' "Arya'), 'Daenerys':['Jon Snow "Sansa "Arya' Khal Drogo'), 'Sansa':['Jon
Snow DaenerysArya'), 'Arya':['Jon Snow "Daenerys' Sansa'), 'Khal Drogo':['Daenerys'], 'Cersei':['Jaime'],
'Jaime':['Cersei'], 'Bart':['Milhouse'], 'Milhouse':['Bart','Lisa'], 'Lisa':['Milhouse'],…
Suppose you are given two sets A and B, each containing n positive integers. Let
be the i th element of set A, and let b; be the i th element of set B.
bi
You would like to receive maximum payoff [I?-, a;'.
Give an algorithm that will maximize your payoff. Explain that how/why your
algorithm maximizes the payoff, and analyze the running time.
This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos.
Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at
random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total
number of matches to be played altogether, in all the rounds of the tournament?
Your answer:
Hint: This is much simpler than you think. When you see the answer you will say "of course".
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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