LeetCode 562 - Longest Line of Consecutive One in Matrix


http://bookshadow.com/weblog/2017/04/23/leetcode-longest-line-of-consecutive-one-in-matrix/
Given a 01 matrix M, find the longest line of consecutive one in the matrix. The line could be horizontal, vertical, diagonal or anti-diagonal.
Example:
Input:
[[0,1,1,0],
 [0,1,1,0],
 [0,0,0,1]]
Output: 3
Hint: The number of elements in the given matrix will not exceed 10,000.
给定01矩阵M,计算矩阵中一条线上连续1的最大长度。一条线可以为横向、纵向、主对角线、反对角线。
提示:给定矩阵元素个数不超过10,000
X.
https://segmentfault.com/a/1190000017237619
    public int longestLine(int[][] M) {
        if (M == null || M.length == 0 || M[0].length == 0) return 0;
        int max = 0, m = M.length, n = M[0].length;
        int[] row = new int[m];
        int[] col = new int[n];
        int[] d = new int[m+n];
        int[] ad = new int[m+n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (M[i][j] == 1) {
                    row[i]++;
                    col[j]++;
                    d[i+j]++;
                    ad[j-i+m]++;
                    max = Math.max(max, Math.max(row[i], col[j]));
                    max = Math.max(max, Math.max(d[i+j], ad[j-i+m]));
                } else {
                    row[i] = 0;
                    col[j] = 0;
                    d[i+j] = 0;
                    ad[j-i+m] = 0;
                }
            }
        }
        return max;
    }
http://www.cnblogs.com/grandyang/p/6900866.html
如果上面的解法的坐标转换不好想的话,我们也可以考虑用DP解法来做,我们建立一个三维dp数组,其中dp[i][j][k]表示从开头遍历到数字nums[i][j]为止,第k种情况的连续1的个数,k的值为0,1,2,3,分别对应水平,竖直,对角线和逆对角线这四种情况。之后就是更新dp数组的过程了,如果如果数字为0的情况直接跳过,然后水平方向就加上前一个的dp值,竖直方向加上上面一个数字的dp值,对角线方向就加上右上方数字的dp值,逆对角线就加上左上方数字的dp值,然后每个值都用来更新结果res
https://www.jianshu.com/p/6bdf7b29b752
dp[i][j][k]表示从开头遍历到数字nums[i][j]为止,第k种情况的连续1的个数.
k的值为0,1,2,3,分别对应水平,竖直,对角线和逆对角线这四种情况。
更新dp数组过程:
如果如果数字为0的情况直接跳过,然后水平方向就加上前一个的dp值,竖直方向加上上面一个数字的dp值,对角线方向就加上右上方数字的dp值,逆对角线就加上左上方数字的dp值,然后每个值都用来更新结果res.
https://discuss.leetcode.com/topic/87197/java-o-nm-time-dp-solution
public int longestLine(int[][] M) {
    int n = M.length, max = 0;
    if (n == 0) return max;
    int m = M[0].length;
    int[][][] dp = new int[n][m][4];
    for (int i=0;i<n;i++) 
        for (int j=0;j<m;j++) {
            if (M[i][j] == 0) continue;
            for (int k=0;k<4;k++) dp[i][j][k] = 1;
            if (j > 0 && M[i][j-1] == 1) dp[i][j][0] += dp[i][j-1][0]; // horizontal line
            if (j > 0 && i > 0 &&  M[i-1][j-1] == 1) dp[i][j][1] += dp[i-1][j-1][1]; // diagonal line
            if (i > 0 && M[i-1][j] == 1) dp[i][j][2] += dp[i-1][j][2]; // vertical line
            if (j < m-1 && i > 0 &&  M[i-1][j+1] == 1) dp[i][j][3] += dp[i-1][j+1][3]; // anti-diagonal line
            max = Math.max(max, Math.max(dp[i][j][0], dp[i][j][1]));
            max = Math.max(max, Math.max(dp[i][j][2], dp[i][j][3]));
        }
    return max;

动态规划(Dynamic Programming)
分表用二维数组h[x][y], v[x][y], d[x][y], a[x][y]表示以元素M[x][y]结尾,横向、纵向、主对角线、反对角线连续1的最大长度
状态转移方程如下:
h[x][y] = M[x][y] * (h[x - 1][y]  + 1)

v[x][y] = M[x][y] * (v[x][y - 1]  + 1)

d[x][y] = M[x][y] * (d[x - 1][y - 1]  + 1)

a[x][y] = M[x][y] * (a[x + 1][y - 1]  + 1)
https://discuss.leetcode.com/topic/87204/verbose-java-solution-hashset-only-search-later-cells
For each unvisited direction of each 1, we search length of adjacent 1s and mark those 1s as visited in that direction. And we only need to search 4 directions: right, down, down-right, down-left. We only access each cell at max 4 times, so time complexity is O(mn). m = number of rows, n = number of columns.
    public int longestLine(int[][] M) {
        int m = M.length;
        if (m <= 0) return 0;
        int n = M[0].length;
        if (n <= 0) return 0;
        
        int max = 0;
        int[][] dirs = {{0, 1}, {1, 0}, {1, 1}, {1, -1}};
        List<Set<String>> memo = new ArrayList<>();
        for (int i = 0; i < 4; i++) {
            memo.add(new HashSet<String>());
        }
        
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (M[i][j] == 0) continue;
                String pos = i + "," + j;
                for (int k = 0; k < 4; k++) {
                    if (!memo.get(k).contains(pos)) {
                        int count = 0;
                        for (int r = i, c = j; r < m && r >= 0 && c < n && c >= 0; r += dirs[k][0], c += dirs[k][1]) {
                            if (M[r][c] == 1) {
                                count++;
                                memo.get(k).add(r + "," + c);
                            }
                            else break;
                        }
                        max = Math.max(max, count);
                    }
                }
            }
        }
        
        return max;
    }
https://discuss.leetcode.com/topic/87389/simple-and-concise-java-solution-easy-to-understand-o-m-n-space

public int longestLine(int[][] M) {
    if (M.length == 0 || M[0].length == 0) {
        return 0;
    }
    int max = 0;
    int[] col = new int[M[0].length];
    int[] diag = new int[M.length + M[0].length];
    int[] antiD = new int[M.length + M[0].length];
    for (int i = 0; i < M.length; i++) {
        int row = 0;
        for (int j = 0; j < M[0].length; j++) {
            if (M[i][j] == 1) {
                row++;
                col[j]++;
                diag[j + i]++;
                antiD[j - i + M.length]++;
                max = Math.max(max, row);
                max = Math.max(max, col[j]);
                max = Math.max(max, diag[j + i]);
                max = Math.max(max, antiD[j - i + M.length]);
            } else {
                row = 0;
                col[j] = 0;
                diag[j + i] = 0;
                antiD[j - i + M.length] = 0;
            }
        }
    }
    return max;
X.
https://www.jianshu.com/p/60d9c17617b8
第一种方法是直接做搜索,LC现在感觉大数据的test case少了,所以繁琐一点也是能过的.
对于每一个点,朝8个方向进行搜索 (其实朝前向的四个方向就可以) 同时将扫过的点记录下来,以便不往回找.
https://blog.csdn.net/katrina95/article/details/79311355
递归的解法,同时maintain一个最大值,注意8个方向中只需要走4个方向即可。
下面我们来优化空间复杂度,用一种类似于DFS的思路来解决问题,我们在遍历到为1的点时,对其水平方向,竖直方向,对角线方向和逆对角线方向分别不停遍历,直到越界或者遇到为0的数字,同时用计数器来累计1的个数,这样就可以用来更新结果res了,就不用把每个中间结果都保存下来

    int longestLine(vector<vector<int>>& M) {
        if (M.empty() || M[0].empty()) return 0;
        int m = M.size(), n = M[0].size(), res = 0;
        vector<vector<int>> dirs{{1,0},{0,1},{-1,-1},{-1,1}};
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (M[i][j] == 0) continue;
                for (int k = 0; k < 4; ++k) {
                    int cnt = 0, x = i, y = j;
                    while (x >= 0 && x < m && y >= 0 && y < n && M[x][y] == 1) {
                        x += dirs[k][0];
                        y += dirs[k][1];
                        ++cnt;
                    }
                    res = max(res, cnt);
                }
            }
        }
        return res;
    }
https://discuss.leetcode.com/topic/87228/java-strightforward-solution
    public int longestLine(int[][] M) {
        if(M == null) return 0;
        int res = 0;
        for(int i =0;i<M.length;i++){
            for(int j = 0;j<M[0].length;j++){
                if(M[i][j] == 1){
                    res = Math.max(res,getMaxOneLine(M, i, j));
                }
            }
        }
        return res;
    }
    final int [][] dirs = new int[][]{{1,0},{0,1},{1,1},{1,-1}};
    private int getMaxOneLine(int [][] M, int x, int y){
        int res = 1;
        for(int [] dir:dirs){
            int i = x+dir[0];
            int j = y+dir[1];
            int count = 1;
            while(isValidPosition(M, i, j) && M[i][j] == 1){
                i+=dir[0];
                j+=dir[1];
                count++;
            }
            res = Math.max(count,res);
        }
        return res;
    }
    
    private boolean isValidPosition(int M[][], int i, int j){
        return (i<M.length && j<M[0].length && i>=0 && j>=0);
    }

lc solution:用三维数组压缩代码
   public int longestLine(int[][] M) {
       int rows = M.length;
       if (rows == 0) return 0;
       int cols = M[0].length;
       int res = 0;
       // 0 horizaental, 1 vertical, 2 diagonal, 3 anti-diagonal
       int[][][] dp = new int[rows][cols][4];
       for (int i = 0 ; i < rows ; i++) {
           for (int j = 0 ; j < cols ; j++) {
               if (M[i][j] == 1) {
                   dp[i][j][0] = j > 0 ? dp[i][j-1][0] + 1 : 1;
                   dp[i][j][1] = i > 0 ? dp[i-1][j][1] + 1 : 1;
                   dp[i][j][2] = (i > 0 && j > 0) ? dp[i-1][j-1][2] + 1 : 1;
                   dp[i][j][3] = (i > 0 && j < cols - 1) ? dp[i-1][j+1][3] + 1 : 1;
                   res = Math.max(dp[i][j][0], res);
                   res = Math.max(dp[i][j][1], res);
                   res = Math.max(dp[i][j][2], res);
                   res = Math.max(dp[i][j][3], res);
               }
           }
       }
       return res;
   }


Labels

LeetCode (1432) GeeksforGeeks (1122) LeetCode - Review (1067) Review (882) Algorithm (668) to-do (609) Classic Algorithm (270) Google Interview (237) Classic Interview (222) Dynamic Programming (220) DP (186) Bit Algorithms (145) POJ (141) Math (137) Tree (132) LeetCode - Phone (129) EPI (122) Cracking Coding Interview (119) DFS (115) Difficult Algorithm (115) Lintcode (115) Different Solutions (110) Smart Algorithm (104) Binary Search (96) BFS (91) HackerRank (90) Binary Tree (86) Hard (79) Two Pointers (78) Stack (76) Company-Facebook (75) BST (72) Graph Algorithm (72) Time Complexity (69) Greedy Algorithm (68) Interval (63) Company - Google (62) Geometry Algorithm (61) Interview Corner (61) LeetCode - Extended (61) Union-Find (60) Trie (58) Advanced Data Structure (56) List (56) Priority Queue (53) Codility (52) ComProGuide (50) LeetCode Hard (50) Matrix (50) Bisection (48) Segment Tree (48) Sliding Window (48) USACO (46) Space Optimization (45) Company-Airbnb (41) Greedy (41) Mathematical Algorithm (41) Tree - Post-Order (41) ACM-ICPC (40) Algorithm Interview (40) Data Structure Design (40) Graph (40) Backtracking (39) Data Structure (39) Jobdu (39) Random (39) Codeforces (38) Knapsack (38) LeetCode - DP (38) Recursive Algorithm (38) String Algorithm (38) TopCoder (38) Sort (37) Introduction to Algorithms (36) Pre-Sort (36) Beauty of Programming (35) Must Known (34) Binary Search Tree (33) Follow Up (33) prismoskills (33) Palindrome (32) Permutation (31) Array (30) Google Code Jam (30) HDU (30) Array O(N) (29) Logic Thinking (29) Monotonic Stack (29) Puzzles (29) Code - Detail (27) Company-Zenefits (27) Microsoft 100 - July (27) Queue (27) Binary Indexed Trees (26) TreeMap (26) to-do-must (26) 1point3acres (25) GeeksQuiz (25) Merge Sort (25) Reverse Thinking (25) hihocoder (25) Company - LinkedIn (24) Hash (24) High Frequency (24) Summary (24) Divide and Conquer (23) Proof (23) Game Theory (22) Topological Sort (22) Lintcode - Review (21) Tree - Modification (21) Algorithm Game (20) CareerCup (20) Company - Twitter (20) DFS + Review (20) DP - Relation (20) Brain Teaser (19) DP - Tree (19) Left and Right Array (19) O(N) (19) Sweep Line (19) UVA (19) DP - Bit Masking (18) LeetCode - Thinking (18) KMP (17) LeetCode - TODO (17) Probabilities (17) Simulation (17) String Search (17) Codercareer (16) Company-Uber (16) Iterator (16) Number (16) O(1) Space (16) Shortest Path (16) itint5 (16) DFS+Cache (15) Dijkstra (15) Euclidean GCD (15) Heap (15) LeetCode - Hard (15) Majority (15) Number Theory (15) Rolling Hash (15) Tree Traversal (15) Brute Force (14) Bucket Sort (14) DP - Knapsack (14) DP - Probability (14) Difficult (14) Fast Power Algorithm (14) Pattern (14) Prefix Sum (14) TreeSet (14) Algorithm Videos (13) Amazon Interview (13) Basic Algorithm (13) Codechef (13) Combination (13) Computational Geometry (13) DP - Digit (13) LCA (13) LeetCode - DFS (13) Linked List (13) Long Increasing Sequence(LIS) (13) Math-Divisible (13) Reservoir Sampling (13) mitbbs (13) Algorithm - How To (12) Company - Microsoft (12) DP - Interval (12) DP - Multiple Relation (12) DP - Relation Optimization (12) LeetCode - Classic (12) Level Order Traversal (12) Prime (12) Pruning (12) Reconstruct Tree (12) Thinking (12) X Sum (12) AOJ (11) Bit Mask (11) Company-Snapchat (11) DP - Space Optimization (11) Dequeue (11) Graph DFS (11) MinMax (11) Miscs (11) Princeton (11) Quick Sort (11) Stack - Tree (11) 尺取法 (11) 挑战程序设计竞赛 (11) Coin Change (10) DFS+Backtracking (10) Facebook Hacker Cup (10) Fast Slow Pointers (10) HackerRank Easy (10) Interval Tree (10) Limited Range (10) Matrix - Traverse (10) Monotone Queue (10) SPOJ (10) Starting Point (10) States (10) Stock (10) Theory (10) Tutorialhorizon (10) Kadane - Extended (9) Mathblog (9) Max-Min Flow (9) Maze (9) Median (9) O(32N) (9) Quick Select (9) Stack Overflow (9) System Design (9) Tree - Conversion (9) Use XOR (9) Book Notes (8) Company-Amazon (8) DFS+BFS (8) DP - States (8) Expression (8) Longest Common Subsequence(LCS) (8) One Pass (8) Quadtrees (8) Traversal Once (8) Trie - Suffix (8) 穷竭搜索 (8) Algorithm Problem List (7) All Sub (7) Catalan Number (7) Cycle (7) DP - Cases (7) Facebook Interview (7) Fibonacci Numbers (7) Flood fill (7) Game Nim (7) Graph BFS (7) HackerRank Difficult (7) Hackerearth (7) Inversion (7) Kadane’s Algorithm (7) Manacher (7) Morris Traversal (7) Multiple Data Structures (7) Normalized Key (7) O(XN) (7) Radix Sort (7) Recursion (7) Sampling (7) Suffix Array (7) Tech-Queries (7) Tree - Serialization (7) Tree DP (7) Trie - Bit (7) 蓝桥杯 (7) Algorithm - Brain Teaser (6) BFS - Priority Queue (6) BFS - Unusual (6) Classic Data Structure Impl (6) DP - 2D (6) DP - Monotone Queue (6) DP - Unusual (6) DP-Space Optimization (6) Dutch Flag (6) How To (6) Interviewstreet (6) Knapsack - MultiplePack (6) Local MinMax (6) MST (6) Minimum Spanning Tree (6) Number - Reach (6) Parentheses (6) Pre-Sum (6) Probability (6) Programming Pearls (6) Rabin-Karp (6) Reverse (6) Scan from right (6) Schedule (6) Stream (6) Subset Sum (6) TSP (6) Xpost (6) n00tc0d3r (6) reddit (6) AI (5) Abbreviation (5) Anagram (5) Art Of Programming-July (5) Assumption (5) Bellman Ford (5) Big Data (5) Code - Solid (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Convex Hull (5) Crazyforcode (5) DFS - Multiple (5) DFS+DP (5) DP - Multi-Dimension (5) DP-Multiple Relation (5) Eulerian Cycle (5) Graph - Unusual (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Java (5) LogN (5) Manhattan Distance (5) Matrix Chain Multiplication (5) N Queens (5) Pre-Sort: Index (5) Quick Partition (5) Quora (5) Randomized Algorithms (5) Resources (5) Robot (5) SPFA(Shortest Path Faster Algorithm) (5) Shuffle (5) Sieve of Eratosthenes (5) Strongly Connected Components (5) Subarray Sum (5) Sudoku (5) Suffix Tree (5) Swap (5) Threaded (5) Tree - Creation (5) Warshall Floyd (5) Word Search (5) jiuzhang (5)

Popular Posts