695. Max Area of Island

Description

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.

Constraints

• m == grid.length

• n == grid[i].length

• 1 <= m, n <= 50

• grid[i][j] is either 0 or 1.

Approach

Links

• Binarysearch

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

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

Solutions

Solution 1

/**
 * Time complexity : O(R*C), where R is the number of rows in the given grid, 
 *    and C is the number of columns. We visit every square once.
 * Space complexity : O(R*C), the space used by seen to keep track of 
 *    visited squares, and the space used by stack.
 */

class Solution {
    public int maxAreaOfIsland(int[][] grid) {
        int maxArea = 0;
        if(grid != null && grid.length != 0) {
            int rows = grid.length, cols = grid[0].length;
            for(int i = 0; i < rows; i++) {
                for(int j = 0; j < cols; j++) {
                    if(grid[i][j] == 1) {
                        maxArea = Math.max(maxArea, calcArea(grid, i, j));
                    }
                }
            }
        }
        return maxArea;
    }
    
    private int calcArea(int[][] grid, int x, int y) {
        if(x < 0 || x >= grid.length || 
            y < 0 || y >= grid[0].length || grid[x][y] != 1) {
            return 0;
        }
        grid[x][y] = 2;
        return 1 + calcArea(grid, x-1, y) + calcArea(grid, x, y+1) + 
                calcArea(grid, x+1, y) + calcArea(grid, x, y-1);
    }
}

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