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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

import scala.collection.mutable.ArrayBuffer

object Solution {
    val WHITE = 0
    val GRAY = 1
    val BLACK = 2

    def canFinish(numCourses: Int, prerequisites: Array[Array[Int]]): Boolean = {
        val adj = Array.fill(numCourses)(new ArrayBuffer[Int]())
        prerequisites.foreach { pre =>
            adj(pre(1)).append(pre(0))
        }

        val colors = Array.fill(numCourses)(WHITE)
        (0 until numCourses).forall { i =>
            if (colors(i) == WHITE && adj(i).nonEmpty && hasCycle(adj, i, colors)) {
                false
            } else {
                true
            }
        }
    }

    private def hasCycle(adj: Array[ArrayBuffer[Int]], node: Int, colors: Array[Int]): Boolean = {
        colors(node) = GRAY
        adj(node).foreach { nei =>
            if (colors(nei) == GRAY) {
                return true
            }
            if (colors(nei) == WHITE && hasCycle(adj, nei, colors)) {
                return true
            }
        }
        colors(node) = BLACK
        false
    }
}

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