Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

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Solutions to Chapter 6 | Brain Teasers »» Condition one (P(1) is true) ignites this chain, with truth cascading off into infinity. Base Case: c = 1 (See previous page). Assume true for c hats. i.e., if there are c hats, it will take c nights to remove all of them. Prove true for c+1 hats. Each man with a hat sees c hat, and can not be immediately sure whether there are c hats or c+1 hats. However, he knows that if there are c hats, it will take exactly c nights to remove them. Therefore, when c nights have passed and everyone still has a hat, he can only conclude that there are c+1 hats. He must know that he is wearing a hat. Each man makes the same conclusion and simultaneously removes the hats on night c+1. Therefore, we have met the principles of induction. We have proven that it will take c nights to remove c hats. 1 4 7 Cracking the Coding Interview | Concepts and Algorithms
Solutions to Chapter 6 | Brain Teasers 6.5 There is a building of 100 floors. If an egg drops from the Nth floor or above it will break. If it’s dropped from any floor below, it will not break. You’re given 2 eggs. Find N, while minimizing the number of drops for the worst case. SOLUTION pg 60 Observation: Regardless of how we drop Egg1, Egg2 must do a linear search. i.e., if Egg1 breaks between floor 10 and 15, we have to check every floor in between with the Egg2 The Approach: A First Try: Suppose we drop an egg from the 10th floor, then the 20th, … »» If the first egg breaks on the first drop (Floor 10), then we have at most 10 drops total. »» If the first egg breaks on the last drop (Floor 100), then we have at most 19 drops total (floors 10, 20, ...,90, 100, then 91 through 99). »» That’s pretty good, but all we’ve considered is the absolute worst case. We should do some “load balancing” to make those two cases more even. Goal: Create a system for dropping Egg1 so that the most drops required is consistent, whether Egg1 breaks on the first drop or the last drop. 1. A perfectly load balanced system would be one in which Drops of Egg1 + Drops of Egg2 is always the same, regardless of where Egg1 broke. 2. For that to be the case, since each drop of Egg1 takes one more step, Egg2 is allowed one fewer step. 3. We must, therefore, reduce the number of steps potentially required by Egg2 by one drop each time. For example, if Egg1 is dropped on Floor 20 and then Floor 30, Egg2 is potentially required to take 9 steps. When we drop Egg1 again, we must reduce potential Egg2 steps to only 8. That is, we must drop Egg1 at floor 39. 4. We know, therefore, Egg1 must start at Floor X, then go up by X-1 floors, then X-2, …, until it gets to 100. 5. Solve for X+(X-1)+(X-2)+…+1 = 100. X(X+1)/2 = 100 -> X = 14 We go to Floor 14, then 27, then 39, … This takes 14 steps maximum. CareerCup.com 1 4 8
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CRACKING THE FOURTH EDITION C O D I
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Table of Contents Chapter 7 | Objec
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Introduction Something’s Wrong We
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Behind the Scenes For many candidat
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Behind the Scenes | The Amazon Inte
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Behind the Scenes | The Apple Inter
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Interview War Stories The View from
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Interview War Stories | Pop Divas P
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Interview War Stories | You Can (Ma
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Interview War Stories | Spider Sens
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Before the Interview | Resume Advic
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Before the Interview | Behavioral P
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Before the Interview | Technical Pr
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The Interview and Beyond
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At the Interview | Handling Behavio
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At the Interview | Handling Technic
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At the Interview | Five Algorithm A
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At the Interview | Five Algorithm A
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At the Interview | The Offer and Be
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At the Interview | Top Ten Mistakes
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At the Interview | Frequently Asked
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Interview Questions
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Chapter 1 | Arrays and Strings Hash
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Chapter 2 | Linked Lists How to App
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Chapter 3 | Stacks and Queues How t
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Chapter 4 | Trees and Graphs How to
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Part 2 Concepts and Algorithms
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Chapter 5 | Bit Manipulation 5.1 Yo
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Chapter 6 | Brain Teasers 6.1 Add a
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Chapter 7 | Object Oriented Design
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Chapter 8 | Recursion 8.1 Write a m
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Chapter 9 | Sorting and Searching 9
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Chapter 10 | Mathematical 10.1 You
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Chapter 11 | Testing 11.1 Find the
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Chapter 12 | System Design and Memo
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Chapter 13 | C++ How To Approach: A
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Chapter 14 | Java How to Approach:
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Chapter 15 | Databases How to Appro
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Chapter 16 | Low Level How to Appro
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Chapter 17 | Networking How to Appr
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Chapter 18 | Threads and Locks How
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Part 4 Additional Review Problems
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Chapter 19 | Moderate _____________
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Chapter 20 | Hard Input: DAMP, LIKE
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Page 91 and 92: Solutions to Chapter 1 | Arrays and
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Solutions to Chapter 11 | System De
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Solutions to Chapter 12 | Testing 1
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Solutions to Chapter 13 | C++ 13.2
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Solutions to Chapter 13 | C++ Then
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Solutions to Chapter 14 | Java 14.2
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Solutions to Chapter 15 | Databases
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Solutions to Chapter 16 | Low Level
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Solutions to Chapter 17 | Networkin
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Solutions to Chapter 18 | Threads a
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Solutions to Chapter 19 | Moderate
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Solutions to Chapter 20 | Hard 2. O
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Solutions to Chapter 20 | Hard 20.3
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Solutions to Chapter 20 | Hard 10 1
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Solutions to Chapter 20 | Hard 28 i
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Solutions to Chapter 20 | Hard 23 }
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Solutions to Chapter 20 | Hard Val_
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Index A arithmetic 108, 131, 143, 1
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Mock Interviews Mock Interviews Stu
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Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

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