Cracking the Coding Interview - Fooo

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Val_D = area(point(0, 0) -> point(x2, y2)) Val_C = area(point(0, 0) -> point(x2, y1)) Val_B = area(point(0, 0) -> point(x1, y2)) Val_A = area(point(0, 0) -> point(x1, y1)) With these values, we know the following: Solutions to Chapter 20 | Hard area(D) = Val_D - area(A union C) - area(A union B) + area(A). Or, written another way: area(D) = Val_D - Val_B - Val_C + Val_A Can we efficiently compute these Val_* values for all points in the matrix? Yes, by using similar logic: Val_(x, y) = Val(x - 1, y) + Val(y - 1, x) - Val(x - 1, y - 1) We can precompute all such values, and then efficiently find the maximum submatrix See the following code for this implementation 1 public static int getMaxMatrix(int[][] original) { 2 int maxArea = Integer.MIN_VALUE; // Important! Max could be < 0 3 int rowCount = original.length; 4 int columnCount = original[0].length; 5 int[][] matrix = precomputeMatrix(original); 6 for (int row1 = 0; row1 < rowCount; row1++) { 7 for (int row2 = row1; row2 < rowCount; row2++) { 8 for (int col1 = 0; col1 < columnCount; col1++) { 9 for (int col2 = col1; col2 < columnCount; col2++) { 10 maxArea = Math.max(maxArea, computeSum(matrix, 11 row1, row2, col1, col2)); 12 } 13 } 14 } 15 } 16 return maxArea; 17 } 18 19 private static int[][] precomputeMatrix(int[][] matrix) { 20 int[][] sumMatrix = new int[matrix.length][matrix[0].length]; 21 for (int i = 0; i < matrix.length; i++) { 22 for (int j = 0; j < matrix.length; j++) { 23 if (i == 0 && j == 0) { // first cell 24 sumMatrix[i][j] = matrix[i][j]; 25 } else if (j == 0) { // cell in first column 26 sumMatrix[i][j] = sumMatrix[i - 1][j] + matrix[i][j]; 27 } else if (i == 0) { // cell in first row 28 sumMatrix[i][j] = sumMatrix[i][j - 1] + matrix[i][j]; 29 } else { 30 sumMatrix[i][j] = sumMatrix[i - 1][j] + 31 sumMatrix[i][j - 1] - sumMatrix[i - 1][j - 1] + CareerCup com 2 9 6
Solutions to Chapter 20 | Hard 32 matrix[i][j]; 33 } 34 } 35 } 36 return sumMatrix; 37 } 38 39 private static int computeSum(int[][] sumMatrix, int i1, int i2, 40 int j1, int j2) { 41 if (i1 == 0 && j1 == 0) { // starts at row 0, column 0 42 return sumMatrix[i2][j2]; 43 } else if (i1 == 0) { // start at row 0 44 return sumMatrix[i2][j2] - sumMatrix[i2][j1 - 1]; 45 } else if (j1 == 0) { // start at column 0 46 return sumMatrix[i2][j2] - sumMatrix[i1 - 1][j2]; 47 } else { 48 return sumMatrix[i2][j2] - sumMatrix[i2][j1 - 1] 49 - sumMatrix[i1 - 1][j2] + sumMatrix[i1 - 1][j1 - 1]; 50 } 51 } 2 9 7 Cracking the Coding Interview | Additional Review Problems
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CRACKING THE C O D I N G I N T E R
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CRACKING THE C O D I N G I N T E R
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Table of Contents Foreword 4 Introd
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Dear Readers, CareerCup com Forewor
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My Approach Introduction The focus
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Behind the Scenes | The Microsoft I
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Behind the Scenes | The Google Inte
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Behind the Scenes | The Yahoo Inter
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Interview War Stories the next few
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Interview War Stories | Failure to
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Interview War Stories | You Can (Ma
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Before the Interview
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Before the Interview | Resume Advic
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Before the Interview | Behavioral P
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What You Need To Know Before the In
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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 | Handling Technic
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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 How This Book i
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Part 1 Data Structures
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Chapter 1 | Arrays and Strings 1 1
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2 1 Write code to remove duplicates
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Chapter 3 | Stacks and Queues 3 1 D
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Chapter 4 | Trees and Graphs 4 1 Im
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Chapter 5 | Bit Manipulation How to
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Chapter 6 | Brain Teasers Do compan
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Chapter 7 | Object Oriented Design
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Chapter 8 | Recursion How to Recogn
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Chapter 9 | Sorting and Searching H
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Chapter 10 | Mathematical How to Ap
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Chapter 11 | Testing Testing Proble
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Chapter 12 | System Design and Memo
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Part 3 Knowledge Based
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Chapter 13 | C++ 13 1 Write a metho
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Chapter 14 | Java 14 1 In terms of
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Chapter 15 | Databases 15 1 Write a
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Chapter 16 | Low Level 16 1 Explain
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Chapter 17 | Networking 17 1 Explai
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Chapter 18 | Threads and Locks 18 1
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Chapter 19 | Moderate 19 1 Write a
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Chapter 20 | Hard 20 1 Write a func
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Each problem may have many 'optimal
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Solutions to Chapter 1 | Arrays and
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Solutions to Chapter 2 | Linked Lis
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Approach 2: Solutions to Chapter 3
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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 6 | Brain Teas
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Solutions to Chapter 7 | Object Ori
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Solutions to Chapter 8 | Recursion
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Solutions to Chapter 9 | Sorting an
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Solutions to Chapter 13 | C++ 13 1
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Solutions to Chapter 14 | Java 14 1
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Solutions to Chapter 15 | Databases
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Page 310: About the Author Gayle Laakmann’s
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Cracking the Coding Interview - Fooo

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