695 Max Area of Island

Techniques Used

• Graph
• Simple DFS

Prerequisite Problem Recommended

• 200 - Number of Islands

Approach

It is similar to the Number of Islands problem. We just need an additional variable to count the area of every island that we find. Then find the maximum area one.

• Initialize the visited matrix and max_area_island variable.
• Apply a nested for loop, to visited all the elements of the grid with the following conditions
  • if the current element has not been visited and is not water. ( != 0)
    • initialize the count variable (it will store the area of the island formed by current element).
    • we are using count as an 1 element array to pass it by reference.
    • apply dfs for the current element to find its island area.
    • store the greater value between max_island_area and count[0] in the max_island_area variable.
• In the dfs utility function,
  • Check for the boundary conditions, AND if the current element has been visited or not AND if the current element is land ( contains value of 1), and return accordingly.
  • Now, mark the current element as visited.
  • increment the count variable.
  • Apply the same dfs function in all the 4 directions of this element.

Complexity

• Time Complexity: O(mn) - Maximum area can be equal to whole grid.
• Space Complexity: O(mn) - Space for visited matrix.

Code

class Solution {
    public int maxAreaOfIsland(int[][] grid) {


        // find all the islands
        // keep track of the number of elements in that island
        // find the island with max_count

        int m = grid.length;
        int n = grid[0].length;

        int max_area_island = 0;

        boolean[][] visited = new boolean[m][n];

        for(int i =  0; i < m; i++){
            for(int j =  0; j < n; j++){
                if(!visited[i][j] && grid[i][j] != 0){
                    int[] count = new int[1];
                    dfs(grid, i, j, visited, count);

                    max_area_island = Math.max(max_area_island, count[0]);
                }

            }
        }

        return max_area_island;

    }


    static void dfs(int[][] grid, int row, int col, boolean[][] visited, int[] count){

        if(row < 0 || col < 0 || row >= grid.length || col >= grid[0].length || visited[row][col] || grid[row][col] == 0 ) return;


        visited[row][col] = true;
        count[0]++;

        dfs(grid, row - 1, col, visited, count);
        dfs(grid, row + 1, col, visited, count);
        dfs(grid, row, col  + 1, visited, count);
        dfs(grid, row, col - 1, visited, count);

        return;



    }
}