695. Max Area of Island

695_max_area_of_island/problem.md

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+## 問題: [695. Max Area of Island](https://leetcode.com/problems/max-area-of-island/description/)

695_max_area_of_island/step1.md

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+# Step 1
+
+- 各セルで１かつ訪れていなかったらdfsを行う
+  - dfs
+    - セルがgridの外、すでに訪れている、もしくは1でない場合は0を返す
+    - セルが1だったら、隣接するセルのdfsの戻り値に1を足した値を返す
+
+```python
+class Solution:
+    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
+        row_length = len(grid)
+        column_length = len(grid[0])
+        visited = set()
+        max_area = 0
+
+        def dfs(r, c):
+            if not (0 <= r < row_length and 0 <= c < column_length) or (r, c) in visited or grid[r][c] != 1:
+                return 0
+            visited.add((r, c))
+            return 1 + dfs(r + 1, c) + dfs(r - 1, c) + dfs(r, c + 1) + dfs(r, c - 1)
+
+        for r in range(row_length):
+            for c in range(column_length):
+                max_area = max(max_area, dfs(r, c))
+
+        return max_area
+```
+
+時間計算量: $O(mn)$
+
+空間計算量: $O(mn)$
+
+アルゴリズム最大実行時間(概算): 時間計算量 / Pythonの1秒あたりの計算ステップ数 -> $(50 \times 50) \div 10,000,000 = 0.000025 (s)$

695_max_area_of_island/step2.md

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+# Step 2
+
+```python
+class Solution:
+    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
+        num_rows = len(grid)
+        num_columns = len(grid[0])
+        visited = set()
+        max_area = 0
+
+        def measure_island(r, c):
+            if not (0 <= r < num_rows and 0 <= c < num_columns) or (r, c) in visited or grid[r][c] != 1:
+                return 0
+            visited.add((r, c))
+            return 1 + measure_island(r + 1, c) + measure_island(r - 1, c) + measure_island(r, c + 1) + measure_island(r, c - 1)
+
+        for r in range(num_rows):
+            for c in range(num_columns):
+                if grid[r][c] == 1 and (r, c) not in visited:
+                    max_area = max(max_area, measure_island(r, c))
+
+        return max_area
+
+```
+
+時間計算量: $O(mn)$
+
+空間計算量: $O(mn)$
+
+アルゴリズム最大実行時間(概算): 時間計算量 / Pythonの1秒あたりの計算ステップ数 -> $(50 \times 50) \div 10,000,000 = 0.000025 (s)$

695_max_area_of_island/step3.md

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+# Step 3
+
+```python
+class Solution:
+    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
+        num_rows = len(grid)
+        num_columns = len(grid[0])
+        visited = set()
+        max_area = 0
+
+        def measure_island(r, c):
+            if not (0 <= r < num_rows and 0 <= c < num_columns) or (r, c) in visited or grid[r][c] != 1:
+                return 0
+            visited.add((r, c))
+            return 1 + measure_island(r + 1, c) + measure_island(r - 1, c) + measure_island(r, c + 1) + measure_island(r, c - 1)
+
+        for r in range(num_rows):
+            for c in range(num_columns):
+                if grid[r][c] == 1 and (r, c) not in visited:
+                    max_area = max(max_area, measure_island(r, c))
+
+        return max_area
+```
+
+1回目: 4分　0秒
+
+2回目: 3分　41秒
+
+3回目: 3分　9秒