Skip to content

886. Possible Bipartition 👍

  • Time: $O(|V| + |E|)$
  • Space: $O(|V|)$
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
enum Color { kWhite, kRed, kGreen };

class Solution {
 public:
  bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
    vector<vector<int>> graph(n + 1);
    vector<Color> colors(n + 1, Color::kWhite);

    for (const vector<int>& d : dislikes) {
      const int u = d[0];
      const int v = d[1];
      graph[u].push_back(v);
      graph[v].push_back(u);
    }

    // Reduce to 785. Is Graph Bipartite?
    for (int i = 1; i <= n; ++i)
      if (colors[i] == Color::kWhite &&
          !isValidColor(graph, i, colors, Color::kRed))
        return false;

    return true;
  }

 private:
  bool isValidColor(const vector<vector<int>>& graph, int u,
                    vector<Color>& colors, Color color) {
    // Always paint red for a white node.
    if (colors[u] != Color::kWhite)
      return colors[u] == color;

    colors[u] = color;  // Always paint the node with `color`.

    // All the children should have valid colors.
    for (const int v : graph[u])
      if (!isValidColor(graph, v, colors,
                        color == Color::kRed ? Color::kGreen : Color::kRed))
        return false;

    return true;
  }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
enum Color { kWhite, kRed, kGreen }

class Solution {
  public boolean possibleBipartition(int n, int[][] dislikes) {
    List<Integer>[] graph = new List[n + 1];
    Color[] colors = new Color[n + 1];
    Arrays.fill(colors, Color.kWhite);

    for (int i = 1; i <= n; ++i)
      graph[i] = new ArrayList<>();

    for (int[] d : dislikes) {
      final int u = d[0];
      final int v = d[1];
      graph[u].add(v);
      graph[v].add(u);
    }

    // Reduce to 785. Is Graph Bipartite?
    for (int i = 1; i <= n; ++i)
      if (colors[i] == Color.kWhite && !isValidColor(graph, i, colors, Color.kRed))
        return false;

    return true;
  }

  private boolean isValidColor(List<Integer>[] graph, int u, Color[] colors, Color color) {
    // Always paint red for a white node.
    if (colors[u] != Color.kWhite)
      return colors[u] == color;

    colors[u] = color; // Always paint the node with `color`.

    // All the children should have valid colors.
    for (final int v : graph[u])
      if (!isValidColor(graph, v, colors, color == Color.kRed ? Color.kGreen : Color.kRed))
        return false;

    return true;
  }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
from enum import Enum


class Color(Enum):
  kWhite = 0
  kRed = 1
  kGreen = 2


class Solution:
  def possibleBipartition(self, n: int, dislikes: list[list[int]]) -> bool:
    graph = [[] for _ in range(n + 1)]
    colors = [Color.kWhite] * (n + 1)

    for u, v in dislikes:
      graph[u].append(v)
      graph[v].append(u)

    # Reduce to 785. Is Graph Bipartite?
    def isValidColor(u: int, color: Color) -> bool:
      # Always paint red for a white node.
      if colors[u] != Color.kWhite:
        return colors[u] == color

      colors[u] = color  # Always paint the node with `color`.

      # All the children should have valid colors.
      childrenColor = Color.kRed if colors[u] == Color.kGreen else Color.kGreen
      return all(isValidColor(v, childrenColor) for v in graph[u])

    return all(colors[i] != Color.kWhite or isValidColor(i, Color.kRed)
               for i in range(1, n + 1))