diff --git a/problems/kamacoder/0109.冗余连接II.md b/problems/kamacoder/0109.冗余连接II.md index 2bd4eac6..56959d87 100644 --- a/problems/kamacoder/0109.冗余连接II.md +++ b/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; +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 { - // 并查集初始化 - public static void init() { - for (int i = 1; i <= n; ++i) { - father[i] = i; - } - } + private final int[] father; - // 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 - } - - // 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 - } - } - - // 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); - } - - // 在有向图里找到删除的那条边,使其变成树 - public static void getRemoveEdge(List 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; - } else { - join(edges.get(i)[0], edges.get(i)[1]); + 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])); + } + + public boolean isSame(int n, int m) { + return find(n) == find(m); + } } - // 删一条边之后判断是不是树 - public static boolean isTreeAfterRemoveEdge(List edges, int deleteEdge) { - init(); // 初始化并查集 + static class Edge { + int s; + int t; + + public Edge(int s, int t) { + this.s = s; + this.t = t; + } + } + + static class Node { + int id; + int in; + int out; + } + + public static void main(String[] args) { + Scanner scanner = new Scanner(System.in); + int n = scanner.nextInt(); + List 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++) { - 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 + 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 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 { + 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); + } + + public static boolean isTreeWithExclude(List 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 edges = new ArrayList<>(); // 存储所有的边 + public static Edge getRemoveEdge(List edges, Node[] nodeMap) { + int length = nodeMap.length; + Disjoint disjoint = new Disjoint(length); - 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 + for (Edge edge : edges) { + if (disjoint.isSame(edge.s, edge.t)) return edge; + disjoint.join(edge.s, edge.t); } - - List 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); - } - } - - // 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; - } - - // 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