310. Minimum Height Trees

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BFS + Topological Sort

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class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if (n == 1) {
            // 仅有一个节点时没有边，需要特判
            return Collections.singletonList(0);
        }

        int[] nodeEdges = new int[n]; // 每个节点关联了几条无向边
        List<List<Integer>> nodeMappingList = new ArrayList<>(n);
        for (int i = 0; i < n; i++) {
            nodeMappingList.add(new ArrayList<>());
        }
        for (int[] edge : edges) {
            int nodeA = edge[0], nodeB = edge[1];
            nodeEdges[nodeA]++;
            nodeEdges[nodeB]++;
            nodeMappingList.get(nodeA).add(nodeB);
            nodeMappingList.get(nodeB).add(nodeA);
        }

        Queue<Integer> leafNodeQueue = new LinkedList<>();
        for (int i = 0; i < nodeEdges.length; i++) {
            if (nodeEdges[i] == 1) {
                leafNodeQueue.offer(i);
            }
        }

        List<Integer> minHeightRootList = new ArrayList<>();
        while (!leafNodeQueue.isEmpty()) {
            minHeightRootList.clear();
            for (int i = leafNodeQueue.size(); i > 0; i--) {
                int node = leafNodeQueue.poll();
                minHeightRootList.add(node);

                for (int neighbor : nodeMappingList.get(node)) {
                    nodeEdges[neighbor]--; // 切断与当前节点连接的边
                    if (nodeEdges[neighbor] == 1) { // 邻接节点是叶子节点
                        leafNodeQueue.offer(neighbor);
                    }
                }
            }
        }

        return minHeightRootList;
    }
}

References

310. Minimum Height Trees