Calculate Number Of Islands And Lakes 解答

Question

1 1 1 1 1 0
1 0 1 0 0 1
1 0 1 0 0 1
1 1 0 1 1 1

1 is earth, 0 is water.

i) count the number of 'islands' that the matrix has.
ii) count the number of 'lakes' that the matrix has i.e. connected clump of zeros that is entirely surrounded by a single island

Solution

这是Number of Islands的升级版。关键在于lake的定义，必须被同一个岛包围。

所以我们在dfs遍历岛的时候，给相同的岛同样的标号。然后在遍历水的时候，检查包围的岛是否是相同标号。

import java.util.*;
import java.io.*;

public class Islands {
    private static final int[][] directions = {{0,1},{0,-1},{1,0},{-1,0}};

    public static void main(String[] args) {
        int[][] island = {
            {1, 1, 1, 1, 1, 0},
            {1, 0, 1, 0, 0, 1},
            {1, 0, 1, 0, 0, 1},
            {1, 1, 0, 1, 1, 1}
        };
        int m = island.length, n = island[0].length;
        // Calculate island number
        int color = 2;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (island[i][j] == 1) {
                    dfs(island, color, i, j);
                    color++;
                }
            }
        }
        int islandNum = color - 2;
        int lakeNum = 0;
        int surround = -2;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (island[i][j] == 0) {
                    if (dfs2(island, surround, i, j)) {
                        lakeNum++;
                    }
                }
            }
        }
        System.out.println(islandNum);
        System.out.println(lakeNum);

    }

    private static void dfs(int[][] island, int color, int x, int y) {
        int m = island.length, n = island[0].length;
        island[x][y] = color;
        int newX, newY;
        for (int i = 0; i < 4; i++) {
            newX = x + directions[i][0];
            newY = y + directions[i][1];
            if (newX < 0 || newX >= m || newY < 0 || newY >= n)
                continue;
            if (island[newX][newY] != 1)
                continue;
            dfs(island, color, newX, newY);
        }
    }

    private static boolean dfs2(int[][] island, int surround, int x, int y) {
        int m = island.length, n = island[0].length;
        island[x][y] = -1;
        int newX, newY;
        for (int i = 0; i < 4; i++) {
            newX = x + directions[i][0];
            newY = y + directions[i][1];
            if (newX < 0 || newX >= m || newY < 0 || newY >= n)
                continue;
            int color = island[newX][newY];
            if (color == -1)
                continue;
            if (color != 0) {
                // This point is earth
                if (surround == -2) {
                    surround = color;
                } else if (surround != color) {
                    return false;
                }
            } else {
                if (!dfs2(island, surround, newX, newY))
                    return false;
            }

        }
        return true;
    }
}