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207. Course Schedule

Medium

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

• For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]

Output: true

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]

Output: false

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

• 1 <= numCourses <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique.

Solution

WHITE = 0
GRAY = 1
BLACK = 2

# @param {Integer} num_courses
# @param {Integer[][]} prerequisites
# @return {Boolean}
def can_finish(num_courses, prerequisites)
  adj = Array.new(num_courses) {[]}

  prerequisites.each do |pre|
    adj[pre[1]] << pre[0]
  end

  colors = Array.new(num_courses, WHITE)

  (0...num_courses).each do |i|
    if colors[i] == WHITE && !adj[i].empty? && has_cycle(adj, i, colors)
      return false
    end
  end

  true
end

private

def has_cycle(adj, node, colors)
  colors[node] = GRAY

  adj[node].each do |nei|
    return true if colors[nei] == GRAY
    return true if colors[nei] == WHITE && has_cycle(adj, nei, colors)
  end

  colors[node] = BLACK
  false
end

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