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 5.1, Problem 1E
Program Plan Intro
To show that the best candidate in line 4 of procedure HIRE-ASSISTANT implies that the total order on the ranks of the candidates.
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Let C={c1,c2,… ,cm} (c1<c2<… <cm) be the arrangement of individuals who hold cardboards of 'C'. Let P={p1,p2,… ,pk} (p1<p2<… <pk) be the arrangement of individuals who hold cardboards of 'P'. The photograph is acceptable if and provided that it fulfills the accompanying requirements:
C∪P={1,2,… ,n}
C∩P=∅.
ci−ci−1≤ci+1−ci(1<i<m).
pi−pi−1≥pi+1−pi(1<i<k).
Given a cluster a1,… ,an, kindly track down the number of good photographs fulfilling the accompanying condition:
∑x∈Cax<∑y∈Pay.
The appropriate response can be huge, so output it modulo 998244353. Two photographs are unique if and provided that there exists no less than one individual who holds a cardboard of 'C' in one photograph yet holds a cardboard of 'P' in the other.
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Chapter 5 Solutions
Introduction to Algorithms
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