Merge pull request #2780 from Jasonyou-boy/feature/冗余连接II

Feature/冗余连接ii

Author: youngyangyang04

problems/kamacoder/0109.冗余连接II.md

@@ -250,105 +250,131 @@ int main() {
 ## 其他语言版本
 
 ### Java 
-```java
-import java.util.ArrayList;
-import java.util.List;
-import java.util.Scanner;
 
+```java
+import java.util.*;
+
+/* 
+ * 冗余连接II。主要问题是存在入度为2或者成环，也可能两个问题同时存在。
+ * 1.判断入度为2的边 
+ * 2.判断是否成环（并查集）
+ */
+ 
 public class Main {
-    static int n;
-    static int[] father = new int[1001]; // 并查集数组
+    /**
+     * 并查集模板
+     */
+    static class Disjoint {
+
+        private final int[] father;
 
-    // 并查集初始化
-    public static void init() {
-        for (int i = 1; i <= n; ++i) {
-            father[i] = i;
+        public Disjoint(int n) {
+            father = new int[n];
+            for (int i = 0; i < n; i++) {
+                father[i] = i;
+            }
+        }
+
+        public void join(int n, int m) {
+            n = find(n);
+            m = find(m);
+            if (n == m) return;
+            father[n] = m;
+        }
+
+        public int find(int n) {
+            return father[n] == n ? n : (father[n] = find(father[n]));
         }
-    }
 
-    // 并查集里寻根的过程
-    public static int find(int u) {
-        if (u == father[u]) return u;
-        return father[u] = find(father[u]); // 路径压缩
+        public boolean isSame(int n, int m) {
+            return find(n) == find(m);
+        }
     }
 
-    // 将 v->u 这条边加入并查集
-    public static void join(int u, int v) {
-        u = find(u);
-        v = find(v);
-        if (u != v) {
-            father[v] = u; // 合并两棵树
+    static class Edge {
+        int s;
+        int t;
+
+        public Edge(int s, int t) {
+            this.s = s;
+            this.t = t;
         }
     }
 
-    // 判断 u 和 v 是否有同一个根
-    public static boolean same(int u, int v) {
-        return find(u) == find(v);
+    static class Node {
+        int id;
+        int in;
+        int out;
     }
 
-    // 在有向图里找到删除的那条边，使其变成树
-    public static void getRemoveEdge(List<int[]> edges) {
-        init(); // 初始化并查集
-        for (int i = 0; i < n; i++) { // 遍历所有的边
-            if (same(edges.get(i)[0], edges.get(i)[1])) { // 如果构成有向环了，就是要删除的边
-                System.out.println(edges.get(i)[0] + " " + edges.get(i)[1]);
-                return;
+    public static void main(String[] args) {
+        Scanner scanner = new Scanner(System.in);
+        int n = scanner.nextInt();
+        List<Edge> edges = new ArrayList<>();
+        Node[] nodeMap = new Node[n + 1];
+        for (int i = 1; i <= n; i++) {
+            nodeMap[i] = new Node();
+        }
+        Integer doubleIn = null;
+        for (int i = 0; i < n; i++) {
+            int s = scanner.nextInt();
+            int t = scanner.nextInt();
+            //记录入度
+            nodeMap[t].in++;
+            if (!(nodeMap[t].in < 2)) doubleIn = t;
+            Edge edge = new Edge(s, t);
+            edges.add(edge);
+        }
+        Edge result = null;
+        //存在入度为2的节点，既要消除入度为2的问题同时解除可能存在的环
+        if (doubleIn != null) {
+            List<Edge> doubleInEdges = new ArrayList<>();
+            for (Edge edge : edges) {
+                if (edge.t == doubleIn) doubleInEdges.add(edge);
+                if (doubleInEdges.size() == 2) break;
+            }
+            Edge edge = doubleInEdges.get(1);
+            if (isTreeWithExclude(edges, edge, nodeMap)) {
+                result = edge;
             } else {
-                join(edges.get(i)[0], edges.get(i)[1]);
+                result = doubleInEdges.get(0);
             }
+        } else {
+            //不存在入度为2的节点,则只需要解除环即可
+            result = getRemoveEdge(edges, nodeMap);
         }
+
+        System.out.println(result.s + " " + result.t);
     }
 
-    // 删一条边之后判断是不是树
-    public static boolean isTreeAfterRemoveEdge(List<int[]> edges, int deleteEdge) {
-        init(); // 初始化并查集
-        for (int i = 0; i < n; i++) {
-            if (i == deleteEdge) continue;
-            if (same(edges.get(i)[0], edges.get(i)[1])) { // 如果构成有向环了，一定不是树
+    public static boolean isTreeWithExclude(List<Edge> edges, Edge exculdEdge, Node[] nodeMap) {
+        Disjoint disjoint = new Disjoint(nodeMap.length + 1);
+        for (Edge edge : edges) {
+            if (edge == exculdEdge) continue;
+            //成环则不是树
+            if (disjoint.isSame(edge.s, edge.t)) {
                 return false;
             }
-            join(edges.get(i)[0], edges.get(i)[1]);
+            disjoint.join(edge.s, edge.t);
         }
         return true;
     }
 
-    public static void main(String[] args) {
-        Scanner sc = new Scanner(System.in);
-        List<int[]> edges = new ArrayList<>(); // 存储所有的边
-
-        n = sc.nextInt(); // 顶点数
-        int[] inDegree = new int[n + 1]; // 记录每个节点的入度
-        for (int i = 0; i < n; i++) {
-            int s = sc.nextInt(); // 边的起点
-            int t = sc.nextInt(); // 边的终点
-            inDegree[t]++;
-            edges.add(new int[]{s, t}); // 将边加入列表
-        }
-
-        List<Integer> vec = new ArrayList<>(); // 记录入度为2的边（如果有的话就两条边）
-        // 找入度为2的节点所对应的边，注意要倒序，因为优先删除最后出现的一条边
-        for (int i = n - 1; i >= 0; i--) {
-            if (inDegree[edges.get(i)[1]] == 2) {
-                vec.add(i);
-            }
-        }
+    public static Edge getRemoveEdge(List<Edge> edges, Node[] nodeMap) {
+        int length = nodeMap.length;
+        Disjoint disjoint = new Disjoint(length);
 
-        // 情况一、情况二
-        if (vec.size() > 0) {
-            // vec里的边已经按照倒叙放的，所以优先删 vec.get(0) 这条边
-            if (isTreeAfterRemoveEdge(edges, vec.get(0))) {
-                System.out.println(edges.get(vec.get(0))[0] + " " + edges.get(vec.get(0))[1]);
-            } else {
-                System.out.println(edges.get(vec.get(1))[0] + " " + edges.get(vec.get(1))[1]);
-            }
-            return;
+        for (Edge edge : edges) {
+            if (disjoint.isSame(edge.s, edge.t)) return edge;
+            disjoint.join(edge.s, edge.t);
         }
-
-        // 处理情况三：明确没有入度为2的情况，一定有有向环，找到构成环的边返回即可
-        getRemoveEdge(edges);
+        return null;
     }
+
 }
+
 ```
+
 ### Python
 
 ```python