[Facebook] Task Scheduling Question

Question

link

有n个任务需要完成（编号1到n），任务之间有一些依赖关系，如果任务a依赖于任务b和c，那么只有当任务b和任务c完成之后才能完成任务a。给定所有的依赖关系，判断这些任务是否能够完成。如果能够完成，请给出一个合法的任务完成序列。

样例：

n=5

1->2,3

3->4

上述样例中任务1依赖于任务2和任务3，任务3依赖于任务4，那么存在合法的任务完成序列4,3,2,1,5

Solution

Classic topology sorting, refer to this nice answer.

My Code

public int[] myJobSchedulerWithoutQueue(Map<Integer, List<Integer>> deps,
		int n) {
	int[] ans = new int[n];

	int[] depCount = new int[n];
	// eg. job 1 depends on job 2 and 3, thus depCount[1-1] = 2
	Map<Integer, List<Integer>> graph = new HashMap<Integer, List<Integer>>();
	// graph would be reversed version of deps, used for topology sorting
	// eg. 2 would point to 1, and 3 would points to 1
	for (int i : deps.keySet()) {
		depCount[i - 1] = deps.get(i).size();
		for (int j : deps.get(i)) {
			// add (j, i) pair into graph
			if (!graph.containsKey(j)) {
				graph.put(j, new ArrayList<Integer>());
			}
			graph.get(j).add(i);
		}
	}
	// now we got depCount[] and graph ready, let's rock
	int sorted = 0;
	while (sorted != n) {
		// first find a 'p' so that depCount[p] = 0
		int p = 0;
		while (p < n && depCount[p] != 0) {
			p++;
		}
		if (p == n) {
			// unable to find a new node to sort, sorting failed
			break;
		}
		// remember p is only the index, the value should be +1
		int val = p + 1;
		ans[sorted++] = val;
		depCount[p] = -1;
		if (graph.containsKey(val)) {
			for (int i : graph.get(val)) {
				depCount[i - 1]--;
			}
		}
	}
	if (sorted == n)
		return ans; // sort sucess
	else
		return null; // sort failed
}

The following is very similar implementation, but using a Queue to store temporary nodes.

public int[] myJobSchedulerWithQueue(Map<Integer, List<Integer>> deps, int n) {
	int[] ans = new int[n];

	int[] depCount = new int[n];
	// eg. job 1 depends on job 2 and 3, thus depCount[1-1] = 2
	Map<Integer, List<Integer>> graph = new HashMap<Integer, List<Integer>>();
	// graph would be reversed version of deps, used for topology sorting
	// eg. 2 would point to 1, and 3 would points to 1
	for (int i : deps.keySet()) {
		depCount[i - 1] = deps.get(i).size();
		for (int j : deps.get(i)) {
			// add (j, i) pair into graph
			if (!graph.containsKey(j)) {
				graph.put(j, new ArrayList<Integer>());
			}
			graph.get(j).add(i);
		}
	}
	// now we got depCount[] and graph ready, let's rock
	int sorted = 0;
	Queue<Integer> queue = new LinkedList<Integer>();
	while (sorted != n) {
		for (int i = 0; i < depCount.length; i++) {
			if (depCount[i] == 0) {
				queue.offer(i + 1);
				depCount[i] = -1;
			}
		}
		if (queue.isEmpty()) {
			break; // sorting failed
		}
		int val = queue.poll();
		ans[sorted++] = val;
		if (graph.containsKey(val)) {
			for (int i : graph.get(val)) {
				depCount[i - 1]--;
			}
		}
	}
	if (sorted == n)
		return ans; // sort sucess
	else
		return null; // sort failed
}