Number of Islands

问题描述

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

算法思想

问题类似于图的遍历问题，我们假设每一个点都是顶点，利用图的优先搜索算法，进行遍历。
1. 每次选择一个点，并且访问这个点的4上下左右四个方向上的点，直到访问完所有的临接点。
2. 每次重新选择点就是一个新的岛的存在。

算法实现

public class Solution {
    boolean[][] visitPoint = null;
    int cols=0,rows=0;
    public void visitIsland(char[][] grid, int i, int j) {
        visitPoint[i][j]=true;
        if(i-1>=0&&visitPoint[i-1][j]==false&&grid[i-1][j]==‘1‘)
            visitIsland(grid,i-1,j);
        if(i+1<rows&&visitPoint[i+1][j]==false&&grid[i+1][j]==‘1‘)
            visitIsland(grid,i+1,j);
        if(j-1>=0&&visitPoint[i][j-1]==false&&grid[i][j-1]==‘1‘)
            visitIsland(grid,i,j-1);
        if(j+1<cols&&visitPoint[i][j+1]==false&&grid[i][j+1]==‘1‘)
            visitIsland(grid,i,j+1);
    }

    public int numIslands(char[][] grid) {
        if(grid==null)
            return 0;

        rows = grid.length;
        if(rows==0)
            return 0;

        cols = grid[0].length;

        visitPoint = new boolean[rows][cols];
        for(int i=0;i<rows;i++){
            for(int j=0;j<cols;j++){
                visitPoint[i][j]=false;
            }
        }
        int num = 0;
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (visitPoint[i][j] == false && grid[i][j] == ‘1‘) {
                    num++;
                    visitIsland(grid, i, j);
                }
            }

        }
        return num;
    }
}

算法时间

$T(n) = O(n^2)$

演示结果

import static org.junit.Assert.*;

import org.junit.After;
import org.junit.Before;
import org.junit.Test;

public class SolutionTest {
    private Solution s = new Solution();

    @Before
    public void setUp() throws Exception {
    }

    @After
    public void tearDown() throws Exception {
    }

    @Test
    public void testNumIslands() {
        char[][] grid3 = { 
                { ‘1‘, ‘1‘, ‘0‘, ‘0‘, ‘0‘ }, 
                { ‘1‘, ‘1‘, ‘0‘, ‘0‘, ‘0‘},
                { ‘0‘, ‘0‘, ‘1‘, ‘0‘, ‘0‘ }, 
                { ‘0‘, ‘0‘, ‘0‘, ‘1‘, ‘1‘} 
        };
        assertEquals(3,s.numIslands(grid3));

        char[][] grid1 = { 
                { ‘1‘, ‘1‘, ‘1‘, ‘1‘, ‘0‘ }, 
                { ‘1‘, ‘1‘, ‘0‘, ‘1‘, ‘0‘},
                { ‘1‘, ‘1‘, ‘0‘, ‘0‘, ‘0‘ }, 
                { ‘0‘, ‘0‘, ‘0‘, ‘0‘, ‘0‘} 
        };
        assertEquals(1,s.numIslands(grid1));

        char[][] grid = {};
        assertEquals(0,s.numIslands(grid));
        assertEquals(0,s.numIslands(null));
    }

}