Add: Add 2025/1/24

Author: whats2000

802-Find Eventual Safe States/Note.md

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+# 802. Find Eventual Safe States
+
+There is a directed graph of `n` nodes with each node labeled from `0` to `n - 1`. 
+The graph is represented by a 0-indexed 2D integer array `graph` where 
+`graph[i]` is an integer array of nodes adjacent to node `i`, 
+meaning there is an edge from node `i` to each node in `graph[i]`.
+
+A node is a terminal node if there are no outgoing edges. 
+A node is a safe node if every possible path starting from that node leads to a terminal node (or another safe node).
+
+Return an array containing all the safe nodes of the graph. The answer should be sorted in ascending order.
+
+## 基礎思路
+對於每個 Node 做 DFS，為了減少重複運算，我們用一個 visited 陣列來記錄每個 Node 的狀態，分為三種狀態：
+
+- 0: 未訪問
+- 1: 訪問中繼點
+- 2: 安全
+
+我們只對未訪問的 Node 做 DFS，如果 DFS 過程中遇到訪問中繼點，則表示有環，此 Node 不安全，直接回傳 false，並把該 Node 設為不安全。
+如果 DFS 過程中沒有遇到不安全的 Node，則會把該 Node 設為安全，表示到達此解點的路徑都是安全的。
+
+## 解題步驟
+
+### Step 1: 紀錄 Graph 長度
+
+```typescript
+const n = graph.length;
+```
+
+### Step 2: 初始化 visited 陣列
+
+```typescript
+// 0: 未訪問, 1: 訪問中繼點, 2: 安全
+const visited = new Array(n).fill(0);
+```
+
+### Step 3: 定義 DFS 函數
+
+```typescript
+function dfs(node: number): boolean {
+  // 如果該 Node 已經訪問過，則直接回傳該 Node 是否是安全
+  if (visited[node] > 0) {
+    return visited[node] === 2;
+  }
+
+  // 設定該 Node 為訪問中繼點
+  visited[node] = 1;
+
+  // 持續檢查下一個 Node 是否安全
+  // Note: 如果陣列是空的，則不會進入迴圈，會直接跳過 for 迴圈
+  for (const next of graph[node]) {
+    // 如果下一個 Node 不安全，則設定當前 Node 為不安全
+    if (!dfs(next)) {
+      return false;
+    }
+  }
+
+  // 設定該 Node 為安全
+  visited[node] = 2;
+  return true;
+}
+```
+
+### Step 4: 開始 DFS
+
+```typescript
+// 紀錄結果
+const result: number[] = [];
+
+// 檢查每個 Node 是否安全
+for (let i = 0; i < n; i++) {
+  // 如果 Node 是安全的，則加入結果中
+  if (dfs(i)) {
+    result.push(i);
+  }
+}
+```
+
+## 時間複雜度
+- 每個 Node 與 Edge 都只會被訪問一次，所以時間複雜度為 $O(V + E)$
+
+> $O(V + E)$
+
+## 空間複雜度
+- 額外使用了 visited 陣列，所以空間複雜度為 $O(V)$
+
+> $O(V)$

802-Find Eventual Safe States/answer.ts

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+function eventualSafeNodes(graph: number[][]): number[] {
+  const n = graph.length;
+
+  // 0: unvisited, 1: visiting, 2: safe
+  const visited = new Array(n).fill(0);
+
+  function dfs(node: number): boolean {
+    // If the node is visited, return the safety of the node
+    if (visited[node] > 0) {
+      return visited[node] === 2;
+    }
+
+    // Mark the node as visiting
+    visited[node] = 1;
+
+    // Check the safety of the next nodes
+    // Note: While the array is empty, the for loop will not run
+    for (const next of graph[node]) {
+      // If the next node is not safe, then the current node is not safe
+      if (!dfs(next)) {
+        return false;
+      }
+    }
+
+    // Mark the node as safe
+    visited[node] = 2;
+    return true;
+  }
+
+
+  // Now traverse all the nodes and check if they are safe
+  const result: number[] = [];
+
+  for (let i = 0; i < n; i++) {
+    // If the node is safe, then add it to the result
+    if (dfs(i)) {
+      result.push(i);
+    }
+  }
+
+  return result;
+}