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

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Solutions to Chapter 6 | Brain Teasers 6.3 You have a five quart jug and a three quart jug, and an unlimited supply of water (but no measuring cups). How would you come up with exactly four quarts of water? NOTE: The jugs are oddly shaped, such that filling up exactly ‘half’ of the jug would be impossible. SOLUTION We can pour water back and forth between the two jugs as follows: 5 Quart Contents 3 Quart Contents Note 5 0 Filled 5 quart jug 2 3 Filled 3Q with 5Q’s contents 0 2 Dumped 3Q 5 2 Filled 5Q 4 3 Fill remainder of 3Q with 5Q 4 Done! We have four quarts. OBSERVATIONS AND SUGGESTIONS: pg 60 » » Many brain teasers have a math / CS root to them—this is one of them! Note that as long as the two jug sizes are relatively prime (i.e., have no common prime factors), you can find a pour sequence for any value between 1 and the sum of the jug sizes. 1 4 5 Cracking the Coding Interview | Concepts and Algorithms
Solutions to Chapter 6 | Brain Teasers 6.4 A bunch of men are on an island. A genie comes down and gathers everyone together and places a magical hat on some people’s heads (i.e., at least one person has a hat). The hat is magical: it can be seen by other people, but not by the wearer of the hat himself. To remove the hat, those (and only those who have a hat) must dunk themselves underwater at exactly midnight. If there are n people and c hats, how long does it take the men to remove the hats? The men cannot tell each other (in any way) that they have a hat. FOLLOW UP SOLUTION Prove that your solution is correct. This problem seems hard, so let’s simplify it by looking at specific cases. Case c = 1: Exactly one man is wearing a hat. pg 60 Assuming all the men are intelligent, the man with the hat should look around and realize that no one else is wearing a hat. Since the genie said that at least one person is wearing a hat, he must conclude that he is wearing a hat. Therefore, he would be able to remove it that night. Case c = 2: Exactly two men are wearing hats. The two men with hats see one hat, and are unsure whether c = 1 or c = 2. They know, from the previous case, that if c = 1, the hats would be removed on Night #1. Therefore, if the other man still has a hat, he must deduce that c = 2, which means that he has a hat. Both men would then remove the hats on Night #2 Case General: If c = 3, then each man is unsure whether c = 2 or 3. If it were 2, the hats would be removed on Night #2. If they are not, they must deduce that c = 3, and therefore they have a hat. We can follow this logic for c = 4, 5, … Proof by Induction Using induction to prove a statement P(n) If (1) P(1) = TRUE (e.g., the statement is true when n = 1) AND (2) if P(n) = TRUE -> P(n+1) = TRUE (e.g., P(n+1) is true whenever P(2) is true). THEN P(n) = TRUE for all n >= 1. Explanation » » Condition 2 sets up an infinite deduction chain: P(1) implies P(2) implies P(3) implies ... P(n) implies P(n+1) implies ... CareerCup.com 1 4 6
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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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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 18 | Threads a
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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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