Count the Number of Lakes Within the Island Containing a Given Cell

Problem: Count the Number of Lakes Within the Island Containing a Given Cell You are given an m x n binary matrix grid: 1 represents land 0 represents water You are also given a coordinate (r, c) (0-indexed). Definitions: Island: a set of land cells connected via 4-directional adjacency. Lake: a 4-directionally connected water component that lies inside that island and does not touch the grid boundary (i.e., it is fully enclosed by land). Return the number of lakes inside the island that contains (r, c). Special cases If grid[r][c] == 0, output 0. If the island containing (r, c) has no lakes, output 0. Input (stdin) m n <m lines of 0/1 strings of length n> r c Output (stdout) lakes Constraints 1 <= m, n <= 2000 Target near O(mn) time. Example 1 Input: 5 5 11111 10001 10101 10001 11111 2 2 Output: 1 Example 2 Input: 3 3 010 010 010 1 1 Output: 0 Example Input 5 5 11111 10001 10101 10001 11111 2 2 Output 1