minimum height trees

Author: JoshuaJiangFD

src/main/java/joshua/leetcode/bfs/MinimumHeightTrees.java

@@ -0,0 +1,76 @@
+package joshua.leetcode.bfs;
+
+import java.util.List;
+
+/**
+ * 310. Minimum Height Trees<br/>
+ * <p/>
+ * <a href = "https://leetcode.com/problems/minimum-height-trees/">leetcode link</a>
+ * <p/>
+ * Created by joshu on 2016/5/19.
+ */
+public abstract class MinimumHeightTrees {
+
+    /**
+     * For a undirected graph with tree characteristics, we can choose any node as the root.
+     * The result graph is then a rooted tree.
+     * Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs).
+     * Given such a graph, write a function to find all the MHTs and return a list of their root labels.
+     * <p/>
+     * <b>Format</b>
+     * <ul>
+     * <li>The graph contains n nodes which are labeled from 0 to n - 1. You will be given the number n and a list of undirected edges (each edge is a pair of labels).</li>
+     * <li>You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.</li>
+     * </ul>
+     * <p/>
+     *
+     * Example 1:
+     * <p/>
+     * Given n = 4, edges = [[1, 0], [1, 2], [1, 3]]
+     * <p/>
+     *  0<br/>
+     *  |<br/>
+     *  1<br/>
+     * / \<br/>
+     * 2   3<br/>
+     * return [1]
+     * <p/>
+     * Example 2:
+     * <p/>
+     *
+     * Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
+     * <p/>
+     * 0  1  2<br/>
+     *  \ | /<br/>
+     *   3<br/>
+     *   |<br/>
+     *   4<br/>
+     *   |<br/>
+     *   5<br/>
+     * return [3, 4]
+     *
+     * @param n the number of vertexes in graph
+     * @param edges the edges in graph
+     * @return
+     */
+    public abstract List<Integer> findMinHeightTrees(int n, int[][] edges);
+
+    /**
+     * 思路来自拓扑排序。
+     * 这个问题先简化为假如能找到图的最长路径，那么minimum height tree的顶点就是这条路径的中间节点，如果路径长度为奇数就是1个，
+     * 路径长度为偶数就是2个。
+     * 如何找到这个中间节点可以用两端出发，步长为1同时移动，相遇时的节点就是中间节点。
+     * 这个方法借鉴到这个问题上，从所有的叶子节点出发，每次剪去所有的叶子节点，然后更新所有其他节点的degree，直到只剩下不多于两个节点
+     * 迭代终止。
+     * <p/>
+     * <a href="https://leetcode.com/discuss/71763/share-some-thoughts">leetcode 解答</a>
+     *
+     */
+    public static class Solution1 extends MinimumHeightTrees {
+
+        @Override
+        public List<Integer> findMinHeightTrees(int n, int[][] edges) {
+            return null;
+        }
+    }
+}