Question

Formatted question description: https://leetcode.ca/all/200.html

 200	Number of Islands

 Given a 2d grid map of '1's (land) and '0's (water), count the number of islands.

 An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically.
 You may assume all four edges of the grid are all surrounded by water.

 Example 1:

 11110
 11010
 11000
 00000
 Answer: 1

 Example 2:

 11000
 11000
 00100
 00011
 Answer: 3

Algorithm

Need to use DFS to solve, create a visited array to record whether a certain location has been visited.

For a location that is ‘1’ and has not been visited, recursively enter the number of ‘1’ in its up, down, left, and right positions, assign its visited corresponding value to true, and continue to enter all its adjacent neighbors, so that this Find all the numbers in the connected area, and assign true to the value in the visited.

After finding the adjacent area, increment the result by 1, and then continue to find the next position that is ‘1’ and has not been visited, and so on until the entire original array is traversed.

Or, skipping the visited array to record, just set all visited ‘1’ to be ‘0’. (Assuming we can alter the original array) grid[i][j] = '0';

Code

Java

public class Number_of_Islands {

    public static void main (String[] args) {

        Number_of_Islands out = new Number_of_Islands();
        Solution s = out.new Solution();

        System.out.println(s.numIslands(new char[][]{ {'1', '1', '0', '0', '0'}, {'1', '1', '0', '0', '0'}, {'0', '0', '1', '0', '0'}, {'0', '0', '0', '1', '1'} }));
    }

    // from online, directly overrite visited 1s
    public class Solution {

        private int n;
        private int m;

        public int numIslands(char[][] grid) {
            int count = 0;
            n = grid.length;
            if (n == 0) return 0;
            m = grid[0].length;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++)
                    if (grid[i][j] == '1') {
                        dfs(grid, i, j);
                        ++count;
                    }
            }
            return count;
        }

        private void dfs(char[][] grid, int i, int j) {
            // @note: grid[i][j] != '1', should last of if(), or else index out of boundary
            if (i < 0 || j < 0 || i >= n || j >= m || grid[i][j] != '1') {
                return;
            }

            grid[i][j] = '0';
            dfs(grid, i + 1, j);
            dfs(grid, i - 1, j);
            dfs(grid, i, j + 1);
            dfs(grid, i, j - 1);
        }
    }

    class Solution_bfs {
        public int numIslands(char[][] grid) {
            int h = grid.length; // height
            if (h == 0)
                return 0;
            int w = grid[0].length; // width
            int count = 0;

            boolean[][] visited = new boolean[h][w];

            Queue<Integer[]> queue = new LinkedList<>();
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    if (!visited[i][j] && grid[i][j] == '1') {
                        queue.add(new Integer[]{i, j});
                        BFS(queue, grid, visited);
                        count++;
                    }
                }
            }

            return count;
        }

        private void BFS(Queue<Integer[]> queue, char[][] islandGrid, boolean[][] visited) {

            int H = islandGrid.length;
            int L = islandGrid[0].length;

            while (!queue.isEmpty()) {

                Integer[] x = queue.remove();
                int row = x[0];
                int col = x[1];

                if (row < 0 || col < 0 || row >= H || col >= L || visited[row][col] || islandGrid[row][col] != '1')
                    continue;

                visited[row][col] = true;
                queue.add(new Integer[]{row, (col - 1)});
                queue.add(new Integer[]{row, (col + 1)});
                queue.add(new Integer[]{(row - 1), col});
                queue.add(new Integer[]{(row + 1), col});
            }
        }
    }

    // union find
    class Solution_uf {

        final int d[][] = { // direction
            {0, 1},
            {1, 0},
            {0, -1},
            {-1, 0}
        };

        public int numIslands(char[][] grid) {
            int h = grid.length;
            if (h == 0)
                return 0;
            int w = grid[0].length;

            int N = 0; // id for each point, prepare for UF
            List<Point> ptlist = new ArrayList<Point>(); // each position, Point list
            Map<String, Integer> map = new HashMap<String, Integer>(); // (i,j) => count

            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    if (grid[i][j] == '1') {
                        Point pt = new Point(i,j);
                        ptlist.add(pt);
                        map.put(i+","+j, N++);
                    }
                }
            }

            UF uf = new UF(N);
            for (int i = 0; i < N; i++) {
                Point curr = ptlist.get(i);
                int row = curr.x;
                int col = curr.y;
                for (int k = 0; k < 4; k++) {
                    int x = row + d[k][0];
                    int y = col + d[k][1];
                    if (isValid(grid, h, w, x, y)) {
                        uf.union(i, map.get(x + "," + y));
                    }
                }
            }

            return uf.count();
        }


        private boolean isValid(char[][] grid, int width, int height, int row, int col) {
            return (row >= 0) && (row < width) && (col >= 0) && (col < height) && grid[row][col] == '1';
        }

        class Point {
            int x;
            int y;

            public Point(int x, int y) {
                this.x = x;
                this.y = y;
            }
        }
    }

    class UF {
        private int[] parent;
        private byte[] rank;
        private int count;

        public UF(int n) {
            if (n < 0) throw new IllegalArgumentException();
            count = n;
            parent = new int[n];
            rank = new byte[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                rank[i] = 0;
            }
        }

        public int find(int p) {
            validate(p);
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public int count() {
            return count;
        }

        public void union(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP == rootQ) return;

            if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
            else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
            else {
                parent[rootQ] = rootP;
                rank[rootP]++;
            }
            count--;
        }

        private void validate(int p) {
            int n = parent.length;
            if (p < 0 || p >= n) {
                throw new IllegalArgumentException("index " + p + " is not between 0 and " + (n-1));
            }
        }
    }

}

// OJ: https://leetcode.com/problems/number-of-islands/
// Time: O(MN)
// Space: O(MN)
class UnionFind {
    vector<int> id;
public:
    UnionFind(int N) : id(N) {
        iota(begin(id), end(id), 0);
    }
    void connect(int x, int y) {
        int a = find(x), b = find(y);
        if (a == b) return;
        id[a] = b;
    }
    int find(int x) {
        return id[x] == x ? x : (id[x] = find(id[x]));
    }
};
class Solution {
    int M, N;
    int key(int x, int y) { return x * N + y; }
    int dirs[4][2] = { {0,1},{0,-1},{1,0},{-1,0} };
public:
    int numIslands(vector<vector<char>>& A) {
        if (A.empty() || A[0].empty()) return 0;
        M = A.size(), N = A[0].size();
        UnionFind uf(M * N);
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (A[i][j] == '0') continue;
                for (auto &dir : dirs) {
                    int x = i + dir[0], y = j + dir[1];
                    if (x < 0 || y < 0 || x >= M || y >= N || A[x][y] == '0') continue;
                    uf.connect(key(i, j), key(x, y));
                }
            }
        }
        unordered_set<int> s;
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (A[i][j] == '0') continue;
                s.insert(uf.find(key(i, j)));
            }
        }
        return s.size();
    }
};

'''
>>> a = set()
>>>
>>> a |= {(1, 1)}
>>> a
{(1, 1)}
>>>
>>> a |= {(2, 2)}
>>> a
{(1, 1), (2, 2)}
>>>
>>> a.add((3, 3))
>>> a
{(1, 1), (3, 3), (2, 2)}
>>>
>>> (1,1) in a
True
>>> (10,10) in a
False
'''
class Solution(object):
  def numIslands(self, grid):
    """
    :type grid: List[List[str]]
    :rtype: int
    """
    visited = set()
    ans = 0

    def dfs(grid, i, j, visited):
      if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] == "0" or (i, j) in visited:
        return False
      visited |= {(i, j)}
      for di, dj in [(-1, 0), (1, 0), (0, 1), (0, -1)]:
        newi, newj = i + di, j + dj
        dfs(grid, newi, newj, visited)
      return True

    for i in range(0, len(grid)):
      for j in range(0, len(grid[0])):
        if dfs(grid, i, j, visited):
          ans += 1
    return ans

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