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;
     }
 }