Data structures and algorithms in C++
2nd Edition
ISBN: 9780470460443
Author: Goodrich
Publisher: WILEY

#### Concept explainers

Chapter 4, Problem 1R

## Preconditions assumed for solving the problem:Consider the city with people who have a habit of enjoying the meal only if it is the best from the experiences in life. Otherwise, they do not accept the meal. Let us assume that the meal is distributed uniformly then the expected number of times the people are happy with their meals are given as follows:Harmonic series:It is the sum of reciprocals of first “n” Natural numbers. It is represented in the form as:Hn=1+ 12 +13+...+ 1n = ∑i=1N1iExpected number of people happy with the meals:To determine the number of people who are happy with their meals are estimated using the harmonic series.Consider the harmonic series into given scenario, let us take Xi as sequence of independent variables that is uniformly distributed over the interval (0, 1).The quality of the meal of a person is represented using the variable Xi. So, the probability of the people happy at “n” number of meal is,P(Xn >Xi,∀i<n)= 1nThus, the expected value of people who has happy meal is as follows:∑n=1N1nWhere, “N” represents the count of number of meals in life.

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