LeetCode: Max Area of Island

Posted on February 27, 2018July 26, 2020 by braindenny

Max Area of Island

Similar Problems:

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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

Solution DFS

## https://code.dennyzhang.com/max-area-of-island
## Basic Ideas: DFS
##
##  Find a starting point of one island, then do a DFS
##
## Complexity: Time O(n*m), Space O(1)
class Solution:
    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
        n, m = len(grid), len(grid[0])
        def dfs(i, j):
            if 0<=i<n and 0<=j<m and grid[i][j]:
                # mark as visited
                grid[i][j] = 0
                return 1+dfs(i+1, j)+dfs(i-1, j)+dfs(i, j+1)+dfs(i, j-1)
            return 0

        res = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    res = max(res, dfs(i, j))
        return res

Solution BFS

## https://code.dennyzhang.com/max-area-of-island
## Basic Ideas: BFS
##
##  Find a starting point of one island, then do a DFS
##
## Complexity: Time O(n*m), Space O(1)
class Solution:
    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
        n, m = len(grid), len(grid[0])
        def bfs(i, j):
            q = collections.deque([(i, j)])
            grid[i][j] = 0
            res = 0
            while len(q)>0:
                for i in range(len(q)):
                    (x, y) = q.popleft()
                    res += 1
                    for dx, dy in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                        x2, y2 = x+dx, y+dy
                        if 0<=x2<n and 0<=y2<m and grid[x2][y2]:
                            grid[x2][y2] = 0
                            q.append((x2, y2))
            return res

        area = [bfs(i, j) for i in range(n) for j in range(m) if grid[i][j]]
        return max(area) if area else 0

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