695. Max Area of Island

max-area-of-island/memo.md

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+## 問題
+
+[Max Area of Island - LeetCode](https://leetcode.com/problems/max-area-of-island/description/)
+
+- 入力
+    - `grid`: バイナリ行列
+        - `1` は陸を表す
+        - 高さ `m`
+            - 1以上50以下
+        - 幅: `n`
+            - 1以上50以下
+- 出力
+    - 島の最大面積
+
+## 解法
+
+### 1. 幅優先探索で島を探索し、面積の最大値を求める
+
+- 以前やった島を数えるのとだいたい同じ
+- grid をコピーする
+- 島を探索し、面積を出す
+- 面積の最大値を更新する
+- grid の探索が終わったら面積の最大値を返す
+    - 島がない場合は `0` を返す
+- 時間計算量はO(mn)
+- 空間計算量はO(mn)
+    - grid のコピー
+
+## Step1
+
+### 1.
+
+```go
+const (
+    WATER = 0
+    LAND = 1
+)
+
+func maxAreaOfIsland(grid [][]int) int {
+    // コピーした grid を扱う
+    grid = copyGrid(grid)
+
+    var maxArea int
+    for row := range grid {
+        for column := range grid[row] {
+            // 陸でなければスキップ
+            if grid[row][column] != LAND {
+                continue
+            }
+
+            startCell := Cell{
+                row: row,
+                column: column,
+            }
+            area := exploreIsland(startCell, grid)
+            maxArea = max(maxArea, area)
+        }
+    }
+
+    return maxArea
+}
+
+func copyGrid(grid [][]int) [][]int {
+    g := make([][]int, len(grid))
+    for row := range g {
+        g[row] = slices.Clone(grid[row])
+    }
+
+    return g
+}
+
+type Cell struct {
+    row int
+    column int
+}
+
+// 島を探索する
+// 探索した島の大きさを返す
+func exploreIsland(startCell Cell, grid [][]int) int {
+    rowSize := len(grid)
+    columnSize := len(grid[0])
+
+    offsets := []Cell{
+        // up
+        {row: -1, column: 0},
+        // right
+        {row: 0, column: 1},
+        // down
+        {row: 1, column: 0},
+        // left
+        {row: 0, column: -1},
+    }
+
+    // 最初の土地を登録する
+    // 重複して訪問しないよう水にする
+    area := 1
+    grid[startCell.row][startCell.column] = WATER
+
+    queue := []Cell{startCell}
+    for len(queue) > 0 {
+        cell := queue[0]
+        queue = queue[1:]
+
+        for _, offset := range offsets {
+            // 隣接セル
+            adjacent := Cell{
+                row: cell.row + offset.row,
+                column: cell.column + offset.column,
+            }
+
+            // 行が範囲外
+            if adjacent.row < 0 || rowSize <= adjacent.row {
+                continue
+            }
+            // 列が範囲外
+            if adjacent.column < 0 || columnSize <= adjacent.column {
+                continue
+            }
+            // 陸でない
+            if grid[adjacent.row][adjacent.column] != LAND {
+                continue
+            }
+
+            // エリアとgridを更新する
+            area++
+            grid[adjacent.row][adjacent.column] = WATER
+
+            queue = append(queue, adjacent)
+        }
+    }
+
+    return area
+}
+```
+
+## Step2
+
+- グリッド内か判定する処理を関数にまとめる
+- スタックを使うようにするとメモリ効率が多少改善される
+
+```go
+const (
+    WATER = 0
+    LAND = 1
+)
+
+func maxAreaOfIsland(grid [][]int) int {
+    grid = copyGrid(grid)
+
+    var maxArea int
+    for row := range grid {
+        for column := range grid[row] {
+            if grid[row][column] != LAND {
+                continue
+            }
+
+            startCell := Cell{
+                row: row,
+                column: column,
+            }
+            area := exploreIsland(startCell, grid)
+            maxArea = max(maxArea, area)
+        }
+    }
+
+    return maxArea
+}
+
+func copyGrid(grid [][]int) [][]int {
+    g := make([][]int, len(grid))
+    for row := range g {
+        g[row] = slices.Clone(grid[row])
+    }
+
+    return g
+}
+
+type Cell struct {
+    row int
+    column int
+}
+
+func exploreIsland(startCell Cell, grid [][]int) int {
+    rowSize := len(grid)
+    columnSize := len(grid[0])
+    isValidLand := func(row, column int) bool {
+        if row < 0 || rowSize <= row {
+            return false
+        }
+        if column < 0 || columnSize <= column {
+            return false
+        }
+
+        return grid[row][column] == LAND
+    }
+
+    offsets := []Cell{
+        {row: -1, column: 0},
+        {row: 0, column: 1},
+        {row: 1, column: 0},
+        {row: 0, column: -1},
+    }
+
+    area := 1
+    grid[startCell.row][startCell.column] = WATER
+
+    nextLands := []Cell{startCell}
+    for len(nextLands) > 0 {
+        land := nextLands[len(nextLands) - 1]
+        nextLands = nextLands[:len(nextLands) - 1]
+
+        for _, offset := range offsets {
+            adjacent := Cell{
+                row: land.row + offset.row,
+                column: land.column + offset.column,
+            }
+
+            if !isValidLand(adjacent.row, adjacent.column) {
+                continue
+            }
+
+            area++
+            grid[adjacent.row][adjacent.column] = WATER
+
+            nextLands = append(nextLands, adjacent)
+        }
+    }
+
+    return area
+}
+```
+
+### レビューを依頼する方のPR
+
+- [695. Max Area of Island by mamo3gr · Pull Request #18 · mamo3gr/arai60](https://github.com/mamo3gr/arai60/pull/18)
+    - DFS
+- [695. Max Area of Island by dxxsxsxkx · Pull Request #18 · dxxsxsxkx/leetcode](https://github.com/dxxsxsxkx/leetcode/pull/18)
+    - DFS
+- [695. Max Area of Island by TakayaShirai · Pull Request #18 · TakayaShirai/leetcode_practice](https://github.com/TakayaShirai/leetcode_practice/pull/18)
+    - BFS
+- [695_max_area_of_island by Hiroto-Iizuka · Pull Request #18 · Hiroto-Iizuka/coding_practice](https://github.com/Hiroto-Iizuka/coding_practice/pull/18)
+    - `frontier` という言葉がよく使われている
+    - 再帰版
+- [695.max area of island by PafsCocotte · Pull Request #2 · PafsCocotte/leetcode](https://github.com/PafsCocotte/leetcode/pull/2)
+
+## Step3
+
+- 10分ギリギリ
+
+```go
+const (
+    WATER = 0
+    LAND = 1
+)
+
+func maxAreaOfIsland(grid [][]int) int {
+    grid = copyGrid(grid)
+
+    var maxArea int
+    for row := range grid {
+        for column := range grid[row] {
+            if grid[row][column] != LAND {
+                continue
+            }
+
+            area := exploreIsland(Cell{row: row, column: column}, grid)
+            maxArea = max(area, maxArea)
+        }
+    }
+
+    return maxArea
+}
+
+func copyGrid(grid [][]int) [][]int {
+    g := make([][]int, len(grid))
+    for row := range grid {
+        g[row] = slices.Clone(grid[row])
+    }
+    return g
+}
+
+type Cell struct {
+    row int
+    column int
+}
+
+func exploreIsland(start Cell, grid [][]int) int {
+    rowSize := len(grid)
+    columnSize := len(grid[0])
+    isValidLand := func(cell Cell) bool {
+        if cell.row < 0 || rowSize <= cell.row {
+            return false
+        }
+        if cell.column < 0 || columnSize <= cell.column {
+            return false
+        }
+
+        return grid[cell.row][cell.column] == LAND 
+    }
+    offsets := []Cell{
+        {row: -1, column: 0},
+        {row: 0, column: 1},
+        {row: 1, column: 0},
+        {row: 0, column: -1},
+    }
+
+    area := 1
+    grid[start.row][start.column] = WATER
+
+    nextLands := []Cell{start}
+    for len(nextLands) > 0 {
+        land := nextLands[len(nextLands) - 1]
+        nextLands = nextLands[:len(nextLands) - 1]
+
+        for _, offset := range offsets {
+            adjacent := Cell{
+                row: land.row + offset.row,
+                column: land.column + offset.column,
+            }
+
+            if !isValidLand(adjacent) {
+                continue
+            }
+
+            area++
+            grid[adjacent.row][adjacent.column] = WATER
+
+            nextLands = append(nextLands, adjacent)
+        }
+    }
+
+    return area
+}
+```