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

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Solutions to Chapter 11 | System Design and Memory Limits Follow Up: What if we have only 10 MB memory? It’s possible to find a missing integer with just two passes of the data set. We can divide up the integers into blocks of some size (we’ll discuss how to decide on a size later). Let’s just assume that we divide up the integers into blocks of 1000. So, block 0 represents the numbers 0 through 999, block 1 represents blocks 1000 - 1999, etc. Since the range of ints is finite, we know that the number of blocks needed is finite. In the first pass, we count how many ints are in each block. That is, if we see 552, we know that that is in block 0, we increment counter[0]. If we see 1425, we know that that is in block 1, so we increment counter[1]. At the end of the first pass, we’ll be able to quickly spot a block that is missing a number. If our block size is 1000, then any block which has fewer than 1000 numbers must be missing a number. Pick any one of those blocks. In the second pass, we’ll actually look for which number is missing. We can do this by creating a simple bit vector of size 1000. We iterate through the file, and for each number that should be in our block, we set the appropriate bit in the bit vector. By the end, we’ll know which number (or numbers) is missing. Now we just have to decide what the block size is. A quick answer is 2^20 values per block. We will need an array with 2^12 block counters and a bit vector in 2^17 bytes. Both of these can comfortably fit in 10*2^20 bytes. What’s the smallest footprint? When the array of block counters occupies the same memory as the bit vector. Let N = 2^32. counters (bytes): blocks * 4 bit vector (bytes): (N / blocks) / 8 blocks * 4 = (N / blocks) / 8 blocks^2 = N / 32 blocks = sqrt(N/2)/4 It’s possible to find a missing integer with just under 65KB (or, more exactly, sqrt(2)*2^15 bytes). 1 int bitsize = 1048576; // 2^20 bits (2^17 bytes) 2 int blockNum = 4096; // 2^12 3 byte[] bitfield = new byte[bitsize/8]; 4 int[] blocks = new int[blockNum]; 5 6 void findOpenNumber() throws FileNotFoundException { 7 int starting = -1; 8 Scanner in = new Scanner (new FileReader (“input_file_q11_4.txt”)); 2 0 3 Cracking the Coding Interview | Concepts and Algorithms
Solutions to Chapter 11 | System Design and Memory Limits 9 while (in.hasNextInt()) { 10 int n = in.nextInt(); 11 blocks[n / (bitfield.length * 8)]++; 12 } 13 14 for (int i = 0; i < blocks.length; i++) { 15 if (blocks[i] < bitfield.length * 8){ 16 /* if value < 2^20, then at least 1 number is missing in 17 * that section. */ 18 starting = i * bitfield.length * 8; 19 break; 20 } 21 } 22 23 in = new Scanner(new FileReader(“input_file_q11_4.txt”)); 24 while (in.hasNextInt()) { 25 int n = in.nextInt(); 26 /* If the number is inside the block that’s missing numbers, 27 * we record it */ 28 if( n >= starting && n < starting + bitfield.length * 8){ 29 bitfield [(n-starting) / 8] |= 1
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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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Solutions
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Solutions to Chapter 1 | Arrays and
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Solutions to Chapter 2 | Linked Lis
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Solutions to Chapter 3 | Stacks and
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Solutions to Chapter 4 | Trees and
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Solutions to Chapter 5 | Bit Manipu
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Solutions to Chapter 6 | Brain Teas
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Page 143 and 144: Solutions to Chapter 7 | Object Ori
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Solutions to Chapter 17 | Networkin
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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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