LeetCode-in-All

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

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 <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.

Solution

(define (can-finish num-courses prereqs)
  (let ([adj (make-hash)]
        [seen (make-vector num-courses 0)])
    (for ([x prereqs])
      (hash-set! adj (first x)
                 (cons (second x) (hash-ref adj (first x) '()))))
   
    (define (dfs node)
      (cond ((= 1 (vector-ref seen node)) #f)
            ((= 2 (vector-ref seen node)) #t)
            (else
             (vector-set! seen node 1)
             (if (andmap dfs (hash-ref adj node '()))         
                 (begin
                   (vector-set! seen node 2)
                   #t)
                 #f))))

    (andmap dfs (hash-keys adj))))

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