Saturday, December 5, 2015

LeetCode 37 - Sudoku Solver


http://blog.csdn.net/linhuanmars/article/details/20748761
Write a program to solve a Sudoku puzzle by filling the empty cells.
Empty cells are indicated by the character '.'.
You may assume that there will be only one unique solution.
这道题的方法就是用在N-Queens中介绍的常见套路。简单地说思路就是循环处理子问题,对于每个格子,带入不同的9个数,然后判合法,如果成立就递归继续,结束后把数字设回空。大家可以看出代码结构和N-Queens是完全一样的。判合法可以用Valid Sudoku做为subroutine,但是其实在这里因为每次进入时已经保证之前的board不会冲突,所以不需要判断整个盘,只需要看当前加入的数字和之前是否冲突就可以,这样可以大大提高运行效率,毕竟判合法在程序中被多次调用。
这个方法是一个非常典型的套路,大部分NP问题的都是可以这个方法,比如N-QueensCombination SumCombinationsPermutations等。
public void solveSudoku(char[][] board) {
    if(board == null || board.length != 9 || board[0].length !=9)
        return;
    helper(board,0,0);
}
private boolean helper(char[][] board, int i, int j)
{
    if(j>=9)
        return helper(board,i+1,0);
    if(i==9)
    {
        return true;
    }
    if(board[i][j]=='.')
    {
        for(int k=1;k<=9;k++)
        {
            board[i][j] = (char)(k+'0');
            if(isValid(board,i,j))
            {
                if(helper(board,i,j+1))
                    return true;
            }
            board[i][j] = '.';
        }
    }
    else
    {
        return helper(board,i,j+1);
    }
    return false;
}
private boolean isValid(char[][] board, int i, int j)
{
    for(int k=0;k<9;k++)
    {
        if(k!=j && board[i][k]==board[i][j])
            return false;
    }
    for(int k=0;k<9;k++)
    {
        if(k!=i && board[k][j]==board[i][j])
            return false;
    }        
    for(int row = i/3*3; row<i/3*3+3; row++)
    {
        for(int col=j/3*3; col<j/3*3+3; col++)
        {
            if((row!=i || col!=j) && board[row][col]==board[i][j])
                return false;
        }
    }
    return true;
}
http://www.jiuzhang.com/solutions/sudoku-solver/
http://www.cnblogs.com/springfor/p/3884252.html
    public void solveSudoku(char[][] board){
        solve(board);
    }

    public boolean solve(char[][] board) {
        for(int i = 0; i < 9; i++) {
            for(int j = 0; j < 9; j++){
                if(board[i][j] != '.'){
                    continue;
                }
                for(int k = 1; k <= 9; k++){
                    board[i][j] = (char) (k + '0'); // set value
                    if (isValid(board, i, j) && solve(board)){
                        return true;
                    }
                    board[i][j] = '.';// backtrack
                }
                return false;
            }
        }
        return true;
    }
    
    
     public boolean isValid(char[][] board, int a, int b){
        Set<Character> contained = new HashSet<Character>();
        for(int j=0;j<9;j++){
            if(contained.contains(board[a][j])) return false;
            if(board[a][j]>'0' && board[a][j]<='9')
                contained.add(board[a][j]);
        }
            
        
    
        contained = new HashSet<Character>(); // or call set.clear()
        for(int j=0;j<9;j++){
            if (contained.contains(board[j][b])) {
                return false;
            }
            if (board[j][b]>'0' && board[j][b]<='9') {
                contained.add(board[j][b]);
            }
        }
        
    
        contained = new HashSet<Character>();
        for (int m = 0; m < 3; m++) {
            for (int n = 0; n < 3; n++){
                int x = a / 3 * 3 + m, y = b / 3 * 3 + n;
                if (contained.contains(board[x][y])) {
                    return false;
                }
                if (board[x][y] > '0' && board[x][y] <= '9') {
                        contained.add(board[x][y]);
                }
            } 
        }
    
        return true;
    }
http://blog.csdn.net/u011095253/article/details/9158497
    public boolean isValid(int v, int row, int col, char[][] board){
        for(int i=0;i<9;i++){
            if(board[row][i] - '0'==v) return false;
            if(board[i][col] - '0'==v) return false;
            int row_s = 3*(row/3) + i/3;
            int col_s = 3*(col/3) + i%3;
            if(board[row_s][col_s] - '0'==v) return false;
        }
        return true;
    }
http://huangyawu.com/leetcode-sudoku-solver-java/
    private boolean isValid(char[][] board, int row, int col){
        for(int i=0; i<9; i++){
            if(i!=row && board[i][col] == board[row][col]) return false;
            if(i!=col && board[row][i] == board[row][col]) return false;
        }
         
        int r = row / 3 * 3;
        int c = col / 3 * 3;
        for(int i=0; i<3; i++)
            for(int j=0; j<3; j++){
                if(r + i != row && c + j != col
                        && board[r+i][c+j] == board[row][col])
                    return false;
            }
        return true;
    }
https://leetcode.com/discuss/30482/straight-forward-java-solution-using-backtracking
 Backtracking algorithms generally have exponential worst-case running time. However, the efficient pruning isValid makes it fast enough in practice :-)
public void solveSudoku(char[][] board) {
    if(board == null || board.length == 0)
        return;
    solve(board);
}
public boolean solve(char[][] board){
    for(int i = 0; i < board.length; i++){
        for(int j = 0; j < board[0].length; j++){
            if(board[i][j] == '.'){
                for(char c = '1'; c <= '9'; c++){//trial. Try 1 through 9 for each cell
                    if(isValid(board, i, j, c)){
                        board[i][j] = c; //Put c for this cell

                        if(solve(board))
                            return true; //If it's the solution return true
                        else
                            board[i][j] = '.'; //Otherwise go back
                    }
                }
                return false;
            }
        }
    }
    return true;
}
public boolean isValid(char[][] board, int i, int j, char c){
    //Check colum
    for(int row = 0; row < 9; row++)
        if(board[row][j] == c)
            return false;

    //Check row
    for(int col = 0; col < 9; col++)
        if(board[i][col] == c)
            return false;

    //Check 3 x 3 block
    for(int row = (i / 3) * 3; row < (i / 3) * 3 + 3; row++)
        for(int col = (j / 3) * 3; col < (j / 3) * 3 + 3; col++)
            if(board[row][col] == c)
                return false;
    return true;
}
https://leetcode.com/discuss/51308/two-very-simple-and-neat-java-dfs-backtracking-solutions
https://leetcode.com/discuss/7086/there-is-a-dancing-links-x-algorithm
Dr. Donald Knuth’s Dancing Links Algorithm solves an Exact Cover situation. The Exact Cover problem can be extended to a variety of applications that need to fill constraints. Sudoku is one such special case of the Exact Cover problem.
NOTE:This is a very complicate solution.
http://huntfor.iteye.com/blog/2087778
DFS在找到一个结果的时候会继续回溯寻找下一个可能的结果,因此我又设置了一个全局变量来添加控制。这无疑让代码可读性变差
// only check condition(over) at first, no need check condition before every recursive call.

Determine whether a Sudoku has a unique solution
If you return a number instead of a boolean, you can destinguish between cases where there are 0, 1, or more than 1 solution(s).
To return all solutions: clone the matrix, and put it into list.

No comments:

Post a Comment

Labels

GeeksforGeeks (959) Algorithm (811) LeetCode (639) to-do (598) Review (343) Classic Algorithm (334) Classic Interview (299) Dynamic Programming (263) Google Interview (233) LeetCode - Review (229) Tree (146) POJ (137) Difficult Algorithm (136) EPI (127) Different Solutions (118) 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) List (58) Binary Tree (56) 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) Interval (38) Jobdu (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) Array (33) Trie (33) prismoskills (33) Segment Tree (32) Space Optimization (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 (26) GeeksQuiz (25) Logic Thinking (25) hihocoder (25) High Frequency (23) Palindrome (23) Algorithm Game (22) Company - LinkedIn (22) Graph (22) Queue (22) DFS + Review (21) Hash (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) 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) Divide and Conquer (8) Graph BFS (8) LeetCode - DP (8) LeetCode Hard (8) Prefix Sum (8) Prime (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) Suffix Tree (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) 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) Kadane’s Algorithm (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) 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