Question

802. Find Eventual Safe States

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Description

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:

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].

Solutions

Solution 1

class Solution:
  def eventualSafeNodes(self, graph: List[List[int]]) -> List[int]:
    rg = defaultdict(list)
    indeg = [0] * len(graph)
    for i, vs in enumerate(graph):
      for j in vs:
        rg[j].append(i)
      indeg[i] = len(vs)
    q = deque([i for i, v in enumerate(indeg) if v == 0])
    while q:
      i = q.popleft()
      for j in rg[i]:
        indeg[j] -= 1
        if indeg[j] == 0:
          q.append(j)
    return [i for i, v in enumerate(indeg) if v == 0]

class Solution {
  public List<Integer> eventualSafeNodes(int[][] graph) {
    int n = graph.length;
    int[] indeg = new int[n];
    List<Integer>[] rg = new List[n];
    Arrays.setAll(rg, k -> new ArrayList<>());
    Deque<Integer> q = new ArrayDeque<>();
    for (int i = 0; i < n; ++i) {
      for (int j : graph[i]) {
        rg[j].add(i);
      }
      indeg[i] = graph[i].length;
      if (indeg[i] == 0) {
        q.offer(i);
      }
    }
    while (!q.isEmpty()) {
      int i = q.pollFirst();
      for (int j : rg[i]) {
        if (--indeg[j] == 0) {
          q.offer(j);
        }
      }
    }
    List<Integer> ans = new ArrayList<>();
    for (int i = 0; i < n; ++i) {
      if (indeg[i] == 0) {
        ans.add(i);
      }
    }
    return ans;
  }
}

class Solution {
public:
  vector<int> eventualSafeNodes(vector<vector<int>>& graph) {
    int n = graph.size();
    vector<int> indeg(n);
    vector<vector<int>> rg(n);
    queue<int> q;
    for (int i = 0; i < n; ++i) {
      for (int j : graph[i]) rg[j].push_back(i);
      indeg[i] = graph[i].size();
      if (indeg[i] == 0) q.push(i);
    }
    while (!q.empty()) {
      int i = q.front();
      q.pop();
      for (int j : rg[i])
        if (--indeg[j] == 0) q.push(j);
    }
    vector<int> ans;
    for (int i = 0; i < n; ++i)
      if (indeg[i] == 0) ans.push_back(i);
    return ans;
  }
};

func eventualSafeNodes(graph [][]int) []int {
  n := len(graph)
  indeg := make([]int, n)
  rg := make([][]int, n)
  q := []int{}
  for i, vs := range graph {
    for _, j := range vs {
      rg[j] = append(rg[j], i)
    }
    indeg[i] = len(vs)
    if indeg[i] == 0 {
      q = append(q, i)
    }
  }
  for len(q) > 0 {
    i := q[0]
    q = q[1:]
    for _, j := range rg[i] {
      indeg[j]--
      if indeg[j] == 0 {
        q = append(q, j)
      }
    }
  }
  ans := []int{}
  for i, v := range indeg {
    if v == 0 {
      ans = append(ans, i)
    }
  }
  return ans
}

/**
 * @param {number[][]} graph
 * @return {number[]}
 */
var eventualSafeNodes = function (graph) {
  const n = graph.length;
  const rg = new Array(n).fill(0).map(() => new Array());
  const indeg = new Array(n).fill(0);
  const q = [];
  for (let i = 0; i < n; ++i) {
    for (let j of graph[i]) {
      rg[j].push(i);
    }
    indeg[i] = graph[i].length;
    if (indeg[i] == 0) {
      q.push(i);
    }
  }
  while (q.length) {
    const i = q.shift();
    for (let j of rg[i]) {
      if (--indeg[j] == 0) {
        q.push(j);
      }
    }
  }
  let ans = [];
  for (let i = 0; i < n; ++i) {
    if (indeg[i] == 0) {
      ans.push(i);
    }
  }
  return ans;
};

Solution 2

class Solution:
  def eventualSafeNodes(self, graph: List[List[int]]) -> List[int]:
    def dfs(i):
      if color[i]:
        return color[i] == 2
      color[i] = 1
      for j in graph[i]:
        if not dfs(j):
          return False
      color[i] = 2
      return True

    n = len(graph)
    color = [0] * n
    return [i for i in range(n) if dfs(i)]

class Solution {
  private int[] color;
  private int[][] g;

  public List<Integer> eventualSafeNodes(int[][] graph) {
    int n = graph.length;
    color = new int[n];
    g = graph;
    List<Integer> ans = new ArrayList<>();
    for (int i = 0; i < n; ++i) {
      if (dfs(i)) {
        ans.add(i);
      }
    }
    return ans;
  }

  private boolean dfs(int i) {
    if (color[i] > 0) {
      return color[i] == 2;
    }
    color[i] = 1;
    for (int j : g[i]) {
      if (!dfs(j)) {
        return false;
      }
    }
    color[i] = 2;
    return true;
  }
}

class Solution {
public:
  vector<int> color;

  vector<int> eventualSafeNodes(vector<vector<int>>& graph) {
    int n = graph.size();
    color.assign(n, 0);
    vector<int> ans;
    for (int i = 0; i < n; ++i)
      if (dfs(i, graph)) ans.push_back(i);
    return ans;
  }

  bool dfs(int i, vector<vector<int>>& g) {
    if (color[i]) return color[i] == 2;
    color[i] = 1;
    for (int j : g[i])
      if (!dfs(j, g)) return false;
    color[i] = 2;
    return true;
  }
};

func eventualSafeNodes(graph [][]int) []int {
  n := len(graph)
  color := make([]int, n)
  var dfs func(int) bool
  dfs = func(i int) bool {
    if color[i] > 0 {
      return color[i] == 2
    }
    color[i] = 1
    for _, j := range graph[i] {
      if !dfs(j) {
        return false
      }
    }
    color[i] = 2
    return true
  }
  ans := []int{}
  for i := range graph {
    if dfs(i) {
      ans = append(ans, i)
    }
  }
  return ans
}

/**
 * @param {number[][]} graph
 * @return {number[]}
 */
var eventualSafeNodes = function (graph) {
  const n = graph.length;
  const color = new Array(n).fill(0);
  function dfs(i) {
    if (color[i]) {
      return color[i] == 2;
    }
    color[i] = 1;
    for (const j of graph[i]) {
      if (!dfs(j)) {
        return false;
      }
    }
    color[i] = 2;
    return true;
  }
  let ans = [];
  for (let i = 0; i < n; ++i) {
    if (dfs(i)) {
      ans.push(i);
    }
  }
  return ans;
};