Saturday, July 9, 2016

[CareerCup] 18.13 Largest Rectangle of Letters - Grandyang - 博客园


[CareerCup] 18.13 Largest Rectangle of Letters - Grandyang - 博客园
18.13 Given a list of millions of words, design an algorithm to create the largest possible rectangle of letters such that every row forms a word (reading left to right) and every column forms a word (reading top to bottom). The words need not be chosen consecutively from the list, but all rows must be the same length and all columns must be the same height.

private int maxWordLength;
private WordGroup[] groupList ;
private Trie trieList[];

public Question(String[] list) {
groupList = WordGroup.createWordGroups(list);
maxWordLength = groupList.length;
// Initialize trieList to store trie of groupList[i] at ith position.
trieList = new Trie[maxWordLength];
}

/* This function finds a rectangle of letters of the largest
* possible area (length x breadth) such that every row forms a
* word (reading left to right) from the list and every column
* forms a word (reading top to bottom) from the list.
*/
public Rectangle maxRectangle() {
// The dimensions of the largest possible rectangle.
int maxSize = maxWordLength * maxWordLength;

for (int z = maxSize; z > 0; z--) {
// Find out all pairs i,j less than maxWordLength
// such that i * j = z
for (int i = 1; i <= maxWordLength; i ++ ) {
if (z % i == 0) {
int j = z / i;
if (j <= maxWordLength) {
// Check if a Rectangle of length i and height
// j can be created.
Rectangle rectangle = makeRectangle(i,j);
if (rectangle != null) {
return rectangle;
}
}
}
}
}
return null;
}
/* This function takes the length and height of a rectangle as
* arguments. It tries to form a rectangle of the given length and
* height using words of the specified length as its rows, in which
* words whose length is the specified height form the columns. It
* returns the rectangle so formed, and null if such a rectangle
* cannot be formed.
*/
private Rectangle makeRectangle(int length, int height) {
if (groupList[length - 1] == null || groupList[height - 1] == null) {
return null;
}
if (trieList[height - 1] == null) {
ArrayList<String> words = groupList[height - 1].getWords();
trieList[height - 1] = new Trie(words);
}
return makePartialRectangle(length, height, new Rectangle(length));
}


/* This function recursively tries to form a rectangle with words
* of length l from the dictionary as rows and words of length h
* from the dictionary as columns. To do so, we start with an empty
* rectangle and add in a word with length l as the first row. We
* then check the trie of words of length h to see if each partial
* column is a prefix of a word with length h. If so we branch
* recursively and check the next word till we've formed a complete
* rectangle. When we have a complete rectangle check if every
* column is a word in the dictionary.
*/
private Rectangle makePartialRectangle(int l, int h, Rectangle rectangle) {

// Check if we have formed a complete rectangle by seeing if each column
// is in the dictionary
if (rectangle.height == h) {
if (rectangle.isComplete(l, h, groupList[h - 1])) {
return rectangle;
} else {
return null;
}
}

// If the rectangle is not empty, validate that each column is a
// substring of a word of length h in the dictionary using the
// trie of words of length h.
if (!rectangle.isPartialOK(l, trieList[h - 1])) {
return null;
}

// For each word of length l, try to make a new rectangle by adding
// the word to the existing rectangle.
for (int i = 0; i < groupList[l-1].length(); i++) {
Rectangle orgPlus = rectangle.append(groupList[l-1].getWord(i));
Rectangle rect = makePartialRectangle(l, h, orgPlus);
if (rect != null) {
return rect;
}
}
return null;
}
public class WordGroup {
private HashMap<String, Boolean> lookup = new HashMap<String, Boolean>();
   private ArrayList<String> group = new ArrayList<String>();  
   public boolean containsWord(String s) {
    return lookup.containsKey(s);
   }  
   public void addWord(String s) {
       group.add(s);
       lookup.put(s, true);
   }
 
   public int length() {
       return group.size();
   }
 
   public String getWord(int i) {
       return group.get(i);
   }
 
   public ArrayList<String> getWords(){
       return group;
   }
 
   public static WordGroup[] createWordGroups(String[] list) {
    WordGroup[] groupList;
    int maxWordLength = 0;
// Find out the length of the longest word
for (int i = 0; i < list.length; i++) {
if (list[i].length() > maxWordLength) {
maxWordLength = list[i].length();
}
}

/* Group the words in the dictionary into lists of words of
* same length.groupList[i] will contain a list of words, each
* of length (i+1). */
groupList = new WordGroup[maxWordLength];
for (int i = 0; i < list.length; i++) {
/* We do wordLength - 1 instead of just wordLength since this is used as
* an index and no words are of length 0 */
int wordLength = list[i].length() - 1;
if (groupList[wordLength] == null) {
groupList[wordLength] = new WordGroup();
}
groupList[wordLength].addWord(list[i]);
}
return groupList;
   }
}
public class Rectangle {
 
   // Rectangle data.
   public int height;
   public int length;
   public char [][] matrix;

   public Rectangle(int len) {
       this.length = len;
   }

   /* Construct a rectangular array of letters of the specified length
    * and height, and backed by the specified matrix of letters. (It is
    * assumed that the length and height specified as arguments are
    * consistent with the array argument's dimensions.)
    */
   public Rectangle(int length, int height, char[][] letters) {
       this.height = letters.length;
       this.length = letters[0].length;
       matrix = letters;
   }

   /* Return the letter present at the specified location in the array.
    */
   public char getLetter (int i, int j) {
       return matrix[i][j];
   }
 
   public String getColumn(int i) {
char[] column = new char[height];
for (int j = 0; j < height; j++) {
column[j] = getLetter(j, i);
}
return new String(column);
   }
 
   public boolean isComplete(int l, int h, WordGroup groupList) {
// Check if we have formed a complete rectangle.
if (height == h) {
// Check if each column is a word in the dictionary.
for (int i = 0; i < l; i++) {
String col = getColumn(i);
if (!groupList.containsWord(col)) {
return false; // Invalid rectangle.
}
}
return true; // Valid Rectangle!
}
return false;
   }
 
   public boolean isPartialOK(int l, Trie trie) {
    if (height == 0) {
    return true;
    }
for (int i = 0; i < l ; i++ ) {
String col = getColumn(i);
if (!trie.contains(col)) {
return false; // Invalid rectangle.
}
}
return true;
   }

   /* If the length of the argument s is consistent with that of this
    * Rectangle object, then return a Rectangle whose matrix is constructed by
    * appending s to the underlying matrix. Otherwise, return null. The
    * underlying matrix of this Rectangle object is /not/ modified.
    */
   public Rectangle append(String s) {
       if (s.length() == length) {
           char temp[][] = new char[height + 1][length];
           for (int i = 0; i < height; i++) {
               for (int j = 0; j < length; j++) {
                   temp[i][j] = matrix[i][j];
               }
           }
           s.getChars(0, length, temp[height], 0);

           return new Rectangle(length, height + 1, temp);
       }
       return null;
   }
}

https://github.com/wzhishen/cracking-the-coding-interview/blob/master/src/chap18/Q13.java
Read full article from [CareerCup] 18.13 Largest Rectangle of Letters - Grandyang - 博客园

No comments:

Post a Comment

Labels

GeeksforGeeks (976) Algorithm (811) LeetCode (652) to-do (599) Review (360) Classic Algorithm (334) Classic Interview (298) Dynamic Programming (263) Google Interview (233) LeetCode - Review (233) Tree (146) POJ (137) Difficult Algorithm (136) EPI (127) Different Solutions (119) Bit Algorithms (110) Cracking Coding Interview (110) Smart Algorithm (109) Math (91) HackerRank (85) Lintcode (83) Binary Search (73) Graph Algorithm (73) Greedy Algorithm (61) Interview Corner (61) Binary Tree (58) List (58) DFS (56) Algorithm Interview (53) Advanced Data Structure (52) Codility (52) ComProGuide (52) LeetCode - Extended (47) USACO (46) Geometry Algorithm (45) BFS (43) Data Structure (42) Mathematical Algorithm (42) ACM-ICPC (41) Jobdu (39) Interval (38) Recursive Algorithm (38) Stack (38) String Algorithm (38) Binary Search Tree (37) Knapsack (37) Codeforces (36) Introduction to Algorithms (36) Matrix (36) Must Known (36) Beauty of Programming (35) Sort (35) Space Optimization (34) Array (33) Trie (33) prismoskills (33) Segment Tree (32) Union-Find (32) Backtracking (31) HDU (31) Google Code Jam (30) Permutation (30) Puzzles (30) Array O(N) (29) Data Structure Design (29) Company-Zenefits (28) Microsoft 100 - July (28) to-do-must (28) Random (27) Sliding Window (27) GeeksQuiz (25) Logic Thinking (25) hihocoder (25) High Frequency (23) Palindrome (23) Algorithm Game (22) Company - LinkedIn (22) Graph (22) Hash (22) Queue (22) DFS + Review (21) TopCoder (21) Binary Indexed Trees (20) Brain Teaser (20) CareerCup (20) Company - Twitter (20) Pre-Sort (20) Company-Facebook (19) UVA (19) Probabilities (18) Follow Up (17) Codercareer (16) Company-Uber (16) Game Theory (16) Heap (16) Shortest Path (16) String Search (16) Topological Sort (16) Tree Traversal (16) itint5 (16) Iterator (15) Merge Sort (15) O(N) (15) Bisection Method (14) Difficult (14) Number (14) Number Theory (14) Post-Order Traverse (14) Priority Quieue (14) Amazon Interview (13) BST (13) Basic Algorithm (13) Codechef (13) Majority (13) mitbbs (13) Combination (12) Computational Geometry (12) KMP (12) Long Increasing Sequence(LIS) (12) Modify Tree (12) Reconstruct Tree (12) Reservoir Sampling (12) 尺取法 (12) AOJ (11) DFS+Backtracking (11) Fast Power Algorithm (11) Graph DFS (11) LCA (11) LeetCode - DFS (11) Ordered Stack (11) Princeton (11) Tree DP (11) 挑战程序设计竞赛 (11) Binary Search - Bisection (10) Company - Microsoft (10) Company-Airbnb (10) Euclidean GCD (10) Facebook Hacker Cup (10) HackerRank Easy (10) Reverse Thinking (10) Rolling Hash (10) SPOJ (10) Theory (10) Tutorialhorizon (10) X Sum (10) Coin Change (9) Divide and Conquer (9) Lintcode - Review (9) Mathblog (9) Max-Min Flow (9) Stack Overflow (9) Stock (9) Two Pointers (9) Book Notes (8) Bottom-Up (8) DP-Space Optimization (8) Graph BFS (8) LeetCode - DP (8) LeetCode Hard (8) Prefix Sum (8) Prime (8) Suffix Tree (8) System Design (8) Tech-Queries (8) Time Complexity (8) Use XOR (8) 穷竭搜索 (8) Algorithm Problem List (7) DFS+BFS (7) Facebook Interview (7) Fibonacci Numbers (7) Game Nim (7) HackerRank Difficult (7) Hackerearth (7) Interval Tree (7) Linked List (7) Longest Common Subsequence(LCS) (7) Math-Divisible (7) Miscs (7) O(1) Space (7) Probability DP (7) Radix Sort (7) Simulation (7) Xpost (7) n00tc0d3r (7) 蓝桥杯 (7) Bucket Sort (6) Catalan Number (6) Classic Data Structure Impl (6) DFS+DP (6) DP - Tree (6) How To (6) Interviewstreet (6) Kadane’s Algorithm (6) Knapsack - MultiplePack (6) Level Order Traversal (6) Manacher (6) Minimum Spanning Tree (6) One Pass (6) Programming Pearls (6) Quick Select (6) Rabin-Karp (6) Randomized Algorithms (6) Sampling (6) Schedule (6) Suffix Array (6) Threaded (6) reddit (6) AI (5) Art Of Programming-July (5) Big Data (5) Brute Force (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Crazyforcode (5) DFS+Cache (5) DP-Multiple Relation (5) DP-Print Solution (5) Dutch Flag (5) Fast Slow Pointers (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Inversion (5) Java (5) Kadane - Extended (5) Matrix Chain Multiplication (5) Microsoft Interview (5) Morris Traversal (5) Pruning (5) Quadtrees (5) Quick Partition (5) Quora (5) SPFA(Shortest Path Faster Algorithm) (5) Subarray Sum (5) Sweep Line (5) Traversal Once (5) TreeMap (5) jiuzhang (5) to-do-2 (5) 单调栈 (5) 树形DP (5) 1point3acres (4) Anagram (4) Approximate Algorithm (4) Backtracking-Include vs Exclude (4) Brute Force - Enumeration (4) Chess Game (4) Company-Amazon (4) Consistent Hash (4) Convex Hull (4) Cycle (4) DP-Include vs Exclude (4) Dijkstra (4) Distributed (4) Eulerian Cycle (4) Flood fill (4) Graph-Classic (4) HackerRank AI (4) Histogram (4) Kadane Max Sum (4) Knapsack - Mixed (4) Knapsack - Unbounded (4) Left and Right Array (4) MinMax (4) Multiple Data Structures (4) N Queens (4) Nerd Paradise (4) Parallel Algorithm (4) Practical Algorithm (4) Pre-Sum (4) Probability (4) Programcreek (4) Quick Sort (4) Spell Checker (4) Stock Maximize (4) Subsets (4) Sudoku (4) Symbol Table (4) TreeSet (4) Triangle (4) Water Jug (4) Word Ladder (4) algnotes (4) fgdsb (4) 最大化最小值 (4) A Star (3) Abbreviation (3) Algorithm - Brain Teaser (3) Algorithm Design (3) Anagrams (3) B Tree (3) Big Data Algorithm (3) Binary Search - Smart (3) Caterpillar Method (3) Coins (3) Company - Groupon (3) Company - Indeed (3) Cumulative Sum (3) DP-Fill by Length (3) DP-Two Variables (3) Dedup (3) Dequeue (3) Dropbox (3) Easy (3) Edit Distance (3) Expression (3) Finite Automata (3) Forward && Backward Scan (3) Github (3) GoLang (3) Include vs Exclude (3) Joseph (3) Jump Game (3) Knapsack-多重背包 (3) LeetCode - Bit (3) LeetCode - TODO (3) Linked List Merge Sort (3) LogN (3) Master Theorem (3) Maze (3) Min Cost Flow (3) Minesweeper (3) Missing Numbers (3) NP Hard (3) Online Algorithm (3) Pascal's Triangle (3) Pattern Match (3) Project Euler (3) Rectangle (3) Scala (3) SegmentFault (3) Stack - Smart (3) State Machine (3) Streaming Algorithm (3) Subset Sum (3) Subtree (3) Transform Tree (3) Two Pointers Window (3) Warshall Floyd (3) With Random Pointer (3) Word Search (3) bookkeeping (3) codebytes (3) Activity Selection Problem (2) Advanced Algorithm (2) AnAlgorithmADay (2) Application of Algorithm (2) Array Merge (2) BOJ (2) BT - Path Sum (2) Balanced Binary Search Tree (2) Bellman Ford (2) Binomial Coefficient (2) Bit Mask (2) Bit-Difficult (2) Bloom Filter (2) Book Coding Interview (2) Branch and Bound Method (2) Clock (2) Codesays (2) Company - Baidu (2) Complete Binary Tree (2) DFS+BFS, Flood Fill (2) DP - DFS (2) DP-3D Table (2) DP-Classical (2) DP-Output Solution (2) DP-Slide Window Gap (2) DP-i-k-j (2) DP-树形 (2) Distributed Algorithms (2) Divide and Conqure (2) Doubly Linked List (2) GoHired (2) Graham Scan (2) Graph - Bipartite (2) Graph BFS+DFS (2) Graph Coloring (2) Graph-Cut Vertices (2) Hamiltonian Cycle (2) Huffman Tree (2) In-order Traverse (2) Include or Exclude Last Element (2) Information Retrieval (2) Interview - Linkedin (2) Invariant (2) Islands (2) Knuth Shuffle (2) LeetCode - Recursive (2) Linked Interview (2) Linked List Sort (2) Longest SubArray (2) Lucene-Solr (2) MST (2) MST-Kruskal (2) Math-Remainder Queue (2) Matrix Power (2) Minimum Vertex Cover (2) Negative All Values (2) Number Each Digit (2) Numerical Method (2) Object Design (2) Order Statistic Tree (2) Palindromic (2) Parentheses (2) Parser (2) Peak (2) Programming (2) Range Minimum Query (2) Reuse Forward Backward (2) Robot (2) Rosettacode (2) Scan from right (2) Search (2) Shuffle (2) Sieve of Eratosthenes (2) SimHash (2) Simple Algorithm (2) Skyline (2) Spatial Index (2) Stream (2) Strongly Connected Components (2) Summary (2) TV (2) Tile (2) Traversal From End (2) Tree Sum (2) Tree Traversal Return Multiple Values (2) Word Break (2) Word Graph (2) Word Trie (2) Young Tableau (2) 剑指Offer (2) 数位DP (2) 1-X (1) 51Nod (1) Akka (1) Algorithm - How To (1) Algorithm - New (1) Algorithm Series (1) Algorithms Part I (1) Analysis of Algorithm (1) Array-Element Index Negative (1) Array-Rearrange (1) Auxiliary Array (1) Auxiliary Array: Inc&Dec (1) BACK (1) BK-Tree (1) BZOJ (1) Basic (1) Bayes (1) Beauty of Math (1) Big Integer (1) Big Number (1) Binary (1) Binary Tree Variant (1) Bipartite (1) Bit-Missing Number (1) BitMap (1) BitMap index (1) BitSet (1) Bug Free Code (1) BuildIt (1) C/C++ (1) CC Interview (1) Cache (1) Calculate Height at Same Recusrion (1) Cartesian tree (1) Check Tree Property (1) Chinese (1) Circular Buffer (1) Code Quality (1) Codesolutiony (1) Company - Alibaba (1) Company - Palantir (1) Company - WalmartLabs (1) Company-Apple (1) Company-Epic (1) Company-Salesforce (1) Company-Snapchat (1) Company-Yelp (1) Compression Algorithm (1) Concurrency (1) Convert BST to DLL (1) Convert DLL to BST (1) Custom Sort (1) Cyclic Replacement (1) DFS-Matrix (1) DP - Probability (1) DP Fill Diagonal First (1) DP-Difficult (1) DP-End with 0 or 1 (1) DP-Fill Diagonal First (1) DP-Graph (1) DP-Left and Right Array (1) DP-MaxMin (1) DP-Memoization (1) DP-Node All Possibilities (1) DP-Optimization (1) DP-Preserve Previous Value (1) DP-Print All Solution (1) Database (1) Detect Negative Cycle (1) Directed Graph (1) Do Two Things at Same Recusrion (1) Domino (1) Dr Dobb's (1) Duplicate (1) Equal probability (1) External Sort (1) FST (1) Failure Function (1) Fraction (1) Front End Pointers (1) Funny (1) Fuzzy String Search (1) Game (1) Generating Function (1) Generation (1) Genetic algorithm (1) GeoHash (1) Geometry - Orientation (1) Google APAC (1) Graph But No Graph (1) Graph Transpose (1) Graph Traversal (1) Graph-Coloring (1) Graph-Longest Path (1) Gray Code (1) HOJ (1) Hanoi (1) Hard Algorithm (1) How Hash (1) How to Test (1) Improve It (1) In Place (1) Inorder-Reverse Inorder Traverse Simultaneously (1) Interpolation search (1) Interview (1) Interview - Easy (1) Interview - Facebook (1) Isomorphic (1) JDK8 (1) K Dimensional Tree (1) Knapsack - Fractional (1) Knapsack - ZeroOnePack (1) Knight (1) Kosaraju’s algorithm (1) Kruskal (1) Kruskal MST (1) Kth Element (1) Least Common Ancestor (1) LeetCode - Binary Tree (1) LeetCode - Coding (1) LeetCode - Detail (1) LeetCode - Related (1) LeetCode Diffcult (1) Linked List Reverse (1) Linkedin (1) Linkedin Interview (1) Local MinMax (1) Logic Pattern (1) Longest Common Subsequence (1) Longest Common Substring (1) Longest Prefix Suffix(LPS) (1) Manhattan Distance (1) Map && Reverse Map (1) Math - Induction (1) Math-Multiply (1) Math-Sum Of Digits (1) Matrix - O(N+M) (1) Matrix BFS (1) Matrix Graph (1) Matrix Search (1) Matrix+DP (1) Matrix-Rotate (1) Max Min So Far (1) Median (1) Memory-Efficient (1) MinHash (1) MinMax Heap (1) Monotone Queue (1) Monto Carlo (1) Multi-Reverse (1) Multiple DFS (1) Multiple Tasks (1) Next Successor (1) Offline Algorithm (1) PAT (1) Parent-Only Tree (1) Partition (1) Path Finding (1) Patience Sort (1) Persistent (1) Pigeon Hole Principle (1) Power Set (1) Pratical Algorithm (1) Probabilistic Data Structure (1) Proof (1) Python (1) Queue & Stack (1) RSA (1) Ranking (1) Rddles (1) ReHash (1) Realtime (1) Recurrence Relation (1) Recursive DFS (1) Recursive to Iterative (1) Red-Black Tree (1) Region (1) Regular Expression (1) Resources (1) Reverse Inorder Traversal (1) Robin (1) Selection (1) Self Balancing BST (1) Similarity (1) Sort && Binary Search (1) String Algorithm. Symbol Table (1) String DP (1) String Distance (1) SubMatrix (1) Subsequence (1) System of Difference Constraints(差分约束系统) (1) TSP (1) Ternary Search Tree (1) Test (1) Thread (1) TimSort (1) Top-Down (1) Tournament (1) Tournament Tree (1) Transform Tree in Place (1) Tree Diameter (1) Tree Rotate (1) Trie + DFS (1) Trie and Heap (1) Trie vs Hash (1) Trie vs HashMap (1) Triplet (1) Two Data Structures (1) Two Stacks (1) USACO - Classical (1) USACO - Problems (1) UyHiP (1) Valid Tree (1) Vector (1) Wiggle Sort (1) Wikipedia (1) Yahoo Interview (1) ZOJ (1) baozitraining (1) codevs (1) cos126 (1) javabeat (1) jum (1) namic Programming (1) sqrt(N) (1) 两次dijkstra (1) 九度 (1) 二进制枚举 (1) 夹逼法 (1) 归一化 (1) 折半枚举 (1) 枚举 (1) 状态压缩DP (1) 男人八题 (1) 英雄会 (1) 逆向思维 (1)

Popular Posts