Create 0463-island-perimeter.md

Author: tanyagupta01

dsa-solutions/lc-solutions/0400-0499/0463-island-perimeter.md

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+---
+id: island-perimeter
+title: Island Perimeter
+sidebar_label: 0463-island-perimeter
+tags:
+- Array
+- Depth first search
+- Breadth first search
+- Matrix
+description: "This is a solution to the Island Perimeter problem on LeetCode."
+---
+
+## Problem Description
+
+You are given `row x col` `grid` representing a map where `grid[i][j] = 1` represents land and `grid[i][j] = 0` represents water.
+
+Grid cells are connected horizontally/vertically (not diagonally). The `grid` is completely surrounded by water, and there is exactly one island (i.e., one or more connected land cells).
+
+The island doesn't have "lakes", meaning the water inside isn't connected to the water around the island. One cell is a square with side length 1. The grid is rectangular, width and height don't exceed 100. Determine the perimeter of the island.
+
+### Examples
+
+**Example 1:**
+
+```
+Input: grid = [[0,1,0,0],[1,1,1,0],[0,1,0,0],[1,1,0,0]]
+Output: 16
+Explanation: The perimeter is the 16 yellow stripes in the image above.
+```
+
+**Example 2:**
+
+```
+Input: grid = [[1]]
+Output: 4
+```
+
+### Constraints
+
+- `row == grid.length`
+- `col == grid[i].length`
+- `1 <= row, col <= 100`
+- `grid[i][j]` is `0` or `1`.
+- There is exactly one island in `grid`.
+
+
+### Approach
+
+#### Intuition
+
+To solve this problem, we need to calculate the total perimeter contributed by each land cell in the grid. Since we're working with a grid that has connected cells horizontally and vertically, each land cell that does not touch another land cell contributes 4 units to the perimeter (as it has four sides).
+
+Here's the intuitive step-by-step approach:
+
+1. Initialize a perimeter count to 0.
+2. Iterate through each cell in the grid.
+3. If a cell is land (1), increment the perimeter count by 4 (all possible sides of a single cell).
+4. Then, check the adjacent cells:
+- If there is a land cell to the right (horizontally adjacent), the shared edge does not contribute to the perimeter, so we subtract 2 from the perimeter count (as it removes one edge from each of the two adjacent land cells).
+- Similarly, if there is a land cell below (vertically adjacent), subtract 2 for the shared edge.
+5. Continue this process for all land cells in the grid.
+6. Return the total perimeter count.
+
+This approach works because it dynamically adjusts the perimeter count based on the land cell's adjacency with other land cells, ensuring that shared edges are only counted once.
+
+## Code in Different Languages
+
+<Tabs>
+<TabItem value="cpp" label="C++">
+  <SolutionAuthor name="@tanyagupta01"/>
+
+```cpp
+class Solution {
+ public:
+  int islandPerimeter(vector<vector<int>>& grid) {
+    int islands = 0;
+    int neighbors = 0;
+
+    for (int i = 0; i < grid.size(); ++i)
+      for (int j = 0; j < grid[0].size(); ++j)
+        if (grid[i][j]) {
+          ++islands;
+          if (i - 1 >= 0 && grid[i - 1][j])
+            ++neighbors;
+          if (j - 1 >= 0 && grid[i][j - 1])
+            ++neighbors;
+        }
+
+    return islands * 4 - neighbors * 2;
+  }
+};
+```
+</TabItem>
+<TabItem value="java" label="Java">
+  <SolutionAuthor name="@tanyagupta01"/>
+
+```java
+class Solution {
+  public int islandPerimeter(int[][] grid) {
+    int islands = 0;
+    int neighbors = 0;
+
+    for (int i = 0; i < grid.length; ++i)
+      for (int j = 0; j < grid[0].length; ++j)
+        if (grid[i][j] == 1) {
+          ++islands;
+          if (i - 1 >= 0 && grid[i - 1][j] == 1)
+            ++neighbors;
+          if (j - 1 >= 0 && grid[i][j - 1] == 1)
+            ++neighbors;
+        }
+
+    return islands * 4 - neighbors * 2;
+  }
+}
+```
+
+</TabItem>
+<TabItem value="python" label="Python">
+  <SolutionAuthor name="@tanyagupta01"/>
+
+```python
+class Solution:
+  def islandPerimeter(self, grid: List[List[int]]) -> int:
+    m = len(grid)
+    n = len(grid[0])
+
+    islands = 0
+    neighbors = 0
+
+    for i in range(m):
+      for j in range(n):
+        if grid[i][j] == 1:
+          islands += 1
+          if i + 1 < m and grid[i + 1][j] == 1:
+            neighbors += 1
+          if j + 1 < n and grid[i][j + 1] == 1:
+            neighbors += 1
+
+    return islands * 4 - neighbors * 2
+```
+</TabItem>
+</Tabs>
+
+## Complexity Analysis
+
+### Time Complexity: O(mn)
+
+### Space Complexity: O(1)
+
+## References
+
+- **LeetCode Problem**: [Island Perimeter](https://leetcode.com/problems/island-perimeter/description/)
+
+- **Solution Link**: [Island Perimeter](https://leetcode.com/problems/island-perimeter/solutions/)