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] = [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

class Solution {
    const WHITE = 0;
    const GRAY = 1;
    const BLACK = 2;

    /**
     * @param Integer $numCourses
     * @param Integer[][] $prerequisites
     * @return Boolean
     */
    public function canFinish($numCourses, $prerequisites) {
        $adj = array_fill(0, $numCourses, []);
        foreach ($prerequisites as $pre) {
            array_push($adj[$pre[1]], $pre[0]);
        }
        $colors = array_fill(0, $numCourses, self::WHITE);
        for ($i = 0; $i < $numCourses; $i++) {
            if ($colors[$i] == self::WHITE && !empty($adj[$i]) && $this->hasCycle($adj, $i, $colors)) {
                return false;
            }
        }
        return true;
    }

    private function hasCycle($adj, $node, &$colors) {
        $colors[$node] = self::GRAY;
        foreach ($adj[$node] as $nei) {
            if ($colors[$nei] == self::GRAY) {
                return true;
            }
            if ($colors[$nei] == self::WHITE && $this->hasCycle($adj, $nei, $colors)) {
                return true;
            }
        }
        $colors[$node] = self::BLACK;
        return false;
    }
}

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