題目

Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

Find the maximum area of an island in the given 2D array. (If there is no island, the maximum area is 0.)

Example 1:

[[0,0,1,0,0,0,0,1,0,0,0,0,0],
 [0,0,0,0,0,0,0,1,1,1,0,0,0],
 [0,1,1,0,1,0,0,0,0,0,0,0,0],
 [0,1,0,0,1,1,0,0,1,0,1,0,0],
 [0,1,0,0,1,1,0,0,1,1,1,0,0],
 [0,0,0,0,0,0,0,0,0,0,1,0,0],
 [0,0,0,0,0,0,0,1,1,1,0,0,0],
 [0,0,0,0,0,0,0,1,1,0,0,0,0]]

Example 2:

[[0,0,0,0,0,0,0,0]]

Note: The length of each dimension in the given grid does not exceed 50.

題意

給定一個二維陣列，計算其中最大島嶼的面積。（注意形成島嶼的規則）

分析及解答

• 【遍歷法】下面的解法，將問題當作圖來進行求解（使用了visiteds陣列用來記錄訪問狀態）。
• 【實現方式】深度優先遍歷 ，回溯法。

class Solution {
    
	public int maxAreaOfIsland(int[][] grid) {
		if (grid == null || grid.length == 0) {
			return 0;
		}
		
		int[][] visited = new int[grid.length][grid[0].length];
		int max = 0;
		for (int i = 0; i < grid.length; i++) {
			for (int j = 0; j < grid[0].length; j++) {

				if (grid[i][j] == 0) {
					continue;
				}
				int result = find(grid,i,j,visited);
				if(max < result){
					max = result;
				}
			}
		}
		return max;
	}
public int find(int[][] grid ,int x,int y, int[][] visited){
		if(grid[x][y] == 0 || visited[x][y] == 1){ //邊界溢位。
			return 0;
		}
		int result = 1;
		visited[x][y] = 1;
		if(x + 1 < grid.length){
			result += find(grid, x+1, y, visited);
		}
		if(x -1 >= 0){
			result += find(grid, x-1, y, visited);
		}
		if(y + 1 < grid[0].length){
			result += find(grid,x,y+1,visited);
		}
		if(y -1 >= 0){
			result += find(grid,x,y-1,visited);
		}
		return result;
	}
}