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| 1 | +<h2><a href="https://leetcode.com/problems/number-of-islands-ii/">305. Number of Islands II</a></h2><h3>Hard</h3><hr><div><p>You are given an empty 2D binary grid <code>grid</code> of size <code>m x n</code>. The grid represents a map where <code>0</code>'s represent water and <code>1</code>'s represent land. Initially, all the cells of <code>grid</code> are water cells (i.e., all the cells are <code>0</code>'s).</p> |
| 2 | + |
| 3 | +<p>We may perform an add land operation which turns the water at position into a land. You are given an array <code>positions</code> where <code>positions[i] = [r<sub>i</sub>, c<sub>i</sub>]</code> is the position <code>(r<sub>i</sub>, c<sub>i</sub>)</code> at which we should operate the <code>i<sup>th</sup></code> operation.</p> |
| 4 | + |
| 5 | +<p>Return <em>an array of integers</em> <code>answer</code> <em>where</em> <code>answer[i]</code> <em>is the number of islands after turning the cell</em> <code>(r<sub>i</sub>, c<sub>i</sub>)</code> <em>into a land</em>.</p> |
| 6 | + |
| 7 | +<p>An <strong>island</strong> is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.</p> |
| 8 | + |
| 9 | +<p> </p> |
| 10 | +<p><strong class="example">Example 1:</strong></p> |
| 11 | +<img alt="" src="https://assets.leetcode.com/uploads/2021/03/10/tmp-grid.jpg" style="width: 500px; height: 294px;"> |
| 12 | +<pre><strong>Input:</strong> m = 3, n = 3, positions = [[0,0],[0,1],[1,2],[2,1]] |
| 13 | +<strong>Output:</strong> [1,1,2,3] |
| 14 | +<strong>Explanation:</strong> |
| 15 | +Initially, the 2d grid is filled with water. |
| 16 | +- Operation #1: addLand(0, 0) turns the water at grid[0][0] into a land. We have 1 island. |
| 17 | +- Operation #2: addLand(0, 1) turns the water at grid[0][1] into a land. We still have 1 island. |
| 18 | +- Operation #3: addLand(1, 2) turns the water at grid[1][2] into a land. We have 2 islands. |
| 19 | +- Operation #4: addLand(2, 1) turns the water at grid[2][1] into a land. We have 3 islands. |
| 20 | +</pre> |
| 21 | + |
| 22 | +<p><strong class="example">Example 2:</strong></p> |
| 23 | + |
| 24 | +<pre><strong>Input:</strong> m = 1, n = 1, positions = [[0,0]] |
| 25 | +<strong>Output:</strong> [1] |
| 26 | +</pre> |
| 27 | + |
| 28 | +<p> </p> |
| 29 | +<p><strong>Constraints:</strong></p> |
| 30 | + |
| 31 | +<ul> |
| 32 | + <li><code>1 <= m, n, positions.length <= 10<sup>4</sup></code></li> |
| 33 | + <li><code>1 <= m * n <= 10<sup>4</sup></code></li> |
| 34 | + <li><code>positions[i].length == 2</code></li> |
| 35 | + <li><code>0 <= r<sub>i</sub> < m</code></li> |
| 36 | + <li><code>0 <= c<sub>i</sub> < n</code></li> |
| 37 | +</ul> |
| 38 | + |
| 39 | +<p> </p> |
| 40 | +<p><strong>Follow up:</strong> Could you solve it in time complexity <code>O(k log(mn))</code>, where <code>k == positions.length</code>?</p> |
| 41 | +</div> |
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