[Leetcode] Max Area of Island 最大岛屿面积

最新推荐文章于 2025-09-07 20:32:33 发布

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最新推荐文章于 2025-09-07 20:32:33 发布

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文章标签：数据结构与算法

原文链接：https://segmentfault.com/a/1190000018086001

本文介绍了一种基于深度优先搜索的算法，用于解决二维数组中最大岛屿面积的问题。通过递归方式测量每个岛屿的面积，并返回最大面积。适用于网格长度不超过50的场景。

Max Area of Island

最新更新请见：https://yanjia.me/zh/2019/02/...

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]]
Given the above grid, return 6. Note the answer is not 11, because the island must be connected 4-directionally.
Example 2:
[[0,0,0,0,0,0,0,0]]
Given the above grid, return 0.
Note: The length of each dimension in the given grid does not exceed 50.

深度优先搜索

思路

该题基本上就是Number of Islands的变形题，唯一的区别是在Number of Islands中我们只需要将搜索到的陆地置为0，保证其不会再被下次探索所用就行了。但这题多了一要求就是要同时返回岛屿的面积。那么最简单的方式就是在递归的时候，每个搜索到的格子都将自身的面积1，加上四个方向搜索出来的延伸面积都加上，再返回给调用递归的那个格子作为延伸面积使用，这样一直返回到岛屿的起始格子时，面积之和就是岛屿的总面积了。

代码

Go

func maxAreaOfIsland(grid [][]int) int {
    maxArea := 0
    for i := range grid {
        for j := range grid[i] {
            area := measureIsland(grid, i, j)
            if area > maxArea {
                maxArea = area
            }
        }
    }
    return maxArea
}

func measureIsland(grid [][]int, x, y int) int {
    if grid[x][y] == 0 {
        return 0
    }
    area := 1
    grid[x][y] = 0
    if x > 0 {
        area += measureIsland(grid, x-1, y)
    }
    if x < len(grid)-1 {
        area += measureIsland(grid, x+1, y)
    }
    if y > 0 {
        area += measureIsland(grid, x, y-1)
    }
    if y < len(grid[0])-1 {
        area += measureIsland(grid, x, y+1)
    }
    return area
}