0785-is-graph-bipartite.rb

# frozen_string_literal: true

# 785. Is Graph Bipartite?
# https://leetcode.com/problems/is-graph-bipartite
# Medium

=begin
There is an undirected graph with n nodes, where each node is numbered between 0 and n - 1. You are given a 2D array graph, where graph[u] is an array of nodes that node u is adjacent to. More formally, for each v in graph[u], there is an undirected edge between node u and node v. The graph has the following properties:

There are no self-edges (graph[u] does not contain u).
There are no parallel edges (graph[u] does not contain duplicate values).
If v is in graph[u], then u is in graph[v] (the graph is undirected).
The graph may not be connected, meaning there may be two nodes u and v such that there is no path between them.
A graph is bipartite if the nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A and a node in set B.

Return true if and only if it is bipartite.

Example 1:
Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
Output: false
Explanation: There is no way to partition the nodes into two independent sets such that every edge connects a node in one and a node in the other.

Example 2:
Input: graph = [[1,3],[0,2],[1,3],[0,2]]
Output: true
Explanation: We can partition the nodes into two sets: {0, 2} and {1, 3}.

Constraints:
graph.length == n
1 <= n <= 100
0 <= graph[u].length < n
0 <= graph[u][i] <= n - 1
graph[u] does not contain u.
All the values of graph[u] are unique.
If graph[u] contains v, then graph[v] contains u.
=end

# @param {Integer[][]} graph
# @return {Boolean}
def is_bipartite(graph)
  @graph = graph
  n = @graph.count
  @group = [-1] * n

  n.times do |i|
    if @group[i] == -1
      @group[i] = 0
      return false unless dfs(i)
    end
  end

  true
end

def dfs(i)
  @graph[i].each do |j|
    if @group[j] != -1
      return false if @group[j] == @group[i]
    else
      @group[j] = 1 - @group[i]
      return false unless dfs(j)
    end
  end

  true
end

# ********************#
#       TEST         #
# ********************#

require "test/unit"
class Test_is_bipartite < Test::Unit::TestCase
  def test_
    assert_equal false, is_bipartite([[1, 2, 3], [0, 2], [0, 1, 3], [0, 2]])
    assert_equal true, is_bipartite([[1, 3], [0, 2], [1, 3], [0, 2]])
  end
end