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| 1 | +// https://leetcode.com/problems/parallel-courses |
| 2 | +// T: O(N + E) |
| 3 | +// S: O(N + E) |
| 4 | + |
| 5 | +import java.util.HashMap; |
| 6 | +import java.util.HashSet; |
| 7 | +import java.util.Map; |
| 8 | +import java.util.Set; |
| 9 | + |
| 10 | +public class ParallelCourses { |
| 11 | + public int minimumSemesters(int n, int[][] relations) { |
| 12 | + final Map<Integer, Set<Integer>> graph = createGraph(relations); |
| 13 | + final int[] inDegree = computeInDegree(relations, n); |
| 14 | + return minimumSemesters(graph, inDegree); |
| 15 | + } |
| 16 | + |
| 17 | + // Kahn's algorithm T: O(N + E), S: O(N) |
| 18 | + private static int minimumSemesters(Map<Integer, Set<Integer>> graph, int[] inDegree) { |
| 19 | + Set<Integer> noPrerequisites = coursesWithoutPrerequisites(inDegree); |
| 20 | + int minSemesters = 0; |
| 21 | + |
| 22 | + while (!noPrerequisites.isEmpty()) { |
| 23 | + final Set<Integer> newCourses = new HashSet<>(); |
| 24 | + for (int course : noPrerequisites) { |
| 25 | + inDegree[course]--; |
| 26 | + for (int neighbour : graph.getOrDefault(course, new HashSet<>())) { |
| 27 | + inDegree[neighbour]--; |
| 28 | + if (inDegree[neighbour] == 0) { |
| 29 | + newCourses.add(neighbour); |
| 30 | + } |
| 31 | + } |
| 32 | + graph.remove(course); |
| 33 | + } |
| 34 | + noPrerequisites = newCourses; |
| 35 | + minSemesters++; |
| 36 | + } |
| 37 | + |
| 38 | + return graph.isEmpty() ? minSemesters : -1; |
| 39 | + } |
| 40 | + |
| 41 | + // T: O(E), S: O(N) |
| 42 | + private static int[] computeInDegree(int[][] edges, int n) { |
| 43 | + final int[] inDegree = new int[n]; |
| 44 | + for (int[] edge : edges) { |
| 45 | + final int to = edge[1] - 1; |
| 46 | + inDegree[to]++; |
| 47 | + } |
| 48 | + return inDegree; |
| 49 | + } |
| 50 | + |
| 51 | + // T: O(N), S: O(N) |
| 52 | + private static Set<Integer> coursesWithoutPrerequisites(int[] inDegree) { |
| 53 | + final Set<Integer> set = new HashSet<>(); |
| 54 | + for (int i = 0 ; i < inDegree.length ; i++) { |
| 55 | + if (inDegree[i] == 0) { |
| 56 | + set.add(i); |
| 57 | + } |
| 58 | + } |
| 59 | + return set; |
| 60 | + } |
| 61 | + |
| 62 | + // T: O(E), S: O(E) |
| 63 | + private static Map<Integer, Set<Integer>> createGraph(int[][] edges) { |
| 64 | + final Map<Integer, Set<Integer>> graph = new HashMap<>(); |
| 65 | + for (int[] edge : edges) { |
| 66 | + final int from = edge[0] - 1, to = edge[1] - 1; |
| 67 | + final Set<Integer> fromNeighbours = graph.getOrDefault(from, new HashSet<>()); |
| 68 | + fromNeighbours.add(to); |
| 69 | + graph.putIfAbsent(from, fromNeighbours); |
| 70 | + } |
| 71 | + return graph; |
| 72 | + } |
| 73 | +} |
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