802. Find Eventual Safe States

Medium (Trung bình) C++ 🔗 Xem trên LeetCode

📋 Đề Bài

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.

 

Example 1:

Illustration of graph 
Input: graph = [[1,2],[2,3],[5],[0],[5],[],[]]
Output: [2,4,5,6]
Explanation: The given graph is shown above.
Nodes 5 and 6 are terminal nodes as there are no outgoing edges from either of them.
Every path starting at nodes 2, 4, 5, and 6 all lead to either node 5 or 6.

Example 2:

Input: graph = [[1,2,3,4],[1,2],[3,4],[0,4],[]]
Output: [4]
Explanation:
Only node 4 is a terminal node, and every path starting at node 4 leads to node 4.

 

Constraints:

  • n == graph.length
  • 1 <= n <= 104
  • 0 <= graph[i].length <= n
  • 0 <= graph[i][j] <= n - 1
  • graph[i] is sorted in a strictly increasing order.
  • The graph may contain self-loops.
  • The number of edges in the graph will be in the range [1, 4 * 104].

🧠 Thuật Toán & Kỹ Thuật

DFS (Tìm kiếm theo chiều sâu)Graph (Đồ thị)Bit Manipulation (Thao tác bit)
⏱️ Thời gian O(V+E)
💾 Không gian O(V)

💻 Lời Giải

C++ 0802-find-eventual-safe-states.cpp 
#define WHITE 0
#define GRAY 1
#define BLACK 2

class Solution {
private:
    vector<vector<int>> graph;
    vector<int> color;
    int n;
        
public:
    bool dfs(int u) {
        if (color[u] == BLACK) {
            return true;
        }
        if (color[u] == GRAY) {
            return false;
        }
        color[u] = GRAY;
        for (int v : graph[u]) {
            bool check = dfs(v);
            if (!check) {
                return false;
            }
        }
        color[u] = BLACK;
        return true;
    }
    vector<int> eventualSafeNodes(vector<vector<int>>& graph) {
        this->graph = graph;
        this->n = (int)graph.size();
        color.resize(n, WHITE);
        
        for (int i = 0; i < n; ++i) {
            if (graph[i].size() == 0) {
                color[i] = BLACK;
            }
        }
        
        for (int i = 0; i < n; ++i) {
            if (color[i] == WHITE) {
                dfs(i);
            }
        }
        
        vector<int> ans;
        
        for (int i = 0; i < n; ++i) {
            if (color[i] == BLACK) {
                ans.push_back(i);
            }
        }
        
        return ans;
    }
};