golang_max_area_of_island

You are given an m x n binary matrix grid. 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.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Examples

Example 1:

Input: grid = [[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]]
Output: 6
Explanation: The answer is not 11, because the island must be connected 4-directionally.

Example 2:

Input: grid = [[0,0,0,0,0,0,0,0]]
Output: 0

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 50
• grid[i][j] is either 0 or 1.

解析

這題與 200. Number of Islands 類似

不同的是這次找出最大的 island 面積，也就是連結 cell 的個數

題目給定一個 m by n 的 0-1 矩陣 grid , 1 代表陸地，0代表海洋

定義水平或垂直方向都是 1 的 cell 是相連的

這些連結的 cell 所形成的群叫作 island

求最大的 island 所包含的 cell 個數

直觀的作法是透過 dfs 來累計 cell 個數

對於 grid 上的每一個值為 1 的 cell 用 dfs 去尋找相連的 cell 並且累計

就是以下個關係式

dfs(row, col) = grid[row][col] + dfs(row-1, col) + dfs(row+1, col) + dfs(row, col - 1) + dfs(row, col+1)

要注意的是已經累加過的cell 不能重複加，所以需要一個 hashset 去做紀錄

程式碼

package sol

type Pair struct {
	row, col int
}

func maxAreaOfIsland(grid [][]int) int {
	ROW := len(grid)
	COL := len(grid[0])
	visit := make(map[Pair]struct{})
	var dfs func(row int, col int) int
	dfs = func(row int, col int) int {
		if row < 0 || row >= ROW || col < 0 || col >= COL ||
			grid[row][col] == 0 {
			return 0
		}
		if _, ok := visit[Pair{row: row, col: col}]; ok {
			return 0
		}
		visit[Pair{row: row, col: col}] = struct{}{}
		return 1 + dfs(row-1, col) + dfs(row+1, col) + dfs(row, col-1) + dfs(row, col+1)
	}
	area := 0
	for row := 0; row < ROW; row++ {
		for col := 0; col < COL; col++ {
			total := dfs(row, col)
			if total > area {
				area = total
			}
		}
	}
	return area
}

困難點

1. 理解如何找尋連結的 cell

Solve Point

• Understand how to calculate connected area
• Use HashMap to reduce TimeComplexity