lanqiao3517 砍树(LCA+树上差分)

14lanqiao/test10-2.cpp

@@ -0,0 +1,90 @@
+// lanqiao3517 砍树(LCA+树上差分)
+#include<bits/stdc++.h>
+using namespace std;
+const int N = 5e5 + 10;
+// 链式前向量存储图
+int edges[N], next_edge[N], head[N], edge_idx;
+int fa[N][25], depth[N], subtree_pairs[N];
+int n, m;
+// 添加一条边
+void addEdge(int s, int t){
+    edges[edge_idx] = t;
+    next_edge[edge_idx] = head[s];
+    head[s] = edge_idx++;
+}
+// 深度搜索优先并记录每个节点的深度与祖先信息
+void dfs(int cur, int parent, int dep){
+    fa[cur][0] = parent;
+    depth[cur] = dep;
+    for(int i = 1; i <= 20; i++){
+        fa[cur][i] = fa[fa[cur][i-1]][i-1]; // 动态规划处理快速求最近
+    }
+    for(int i = head[cur]; i != -1; i = next_edge[i]){
+        int child = edges[i];
+        if(child == parent) continue;
+        dfs(child, cur, dep + 1);
+    }
+}
+int LCA(int x, int y){
+    if(depth[x] < depth[y]) swap(x, y);
+    // 将x向上跳到与y同一深度或更浅的位置
+    for(int i = 20; i >= 0; i--){
+        if(depth[fa[x][i]] >= depth[y]){
+            x = fa[x][i];
+        }
+    }
+    if(x == y) return x;
+    for(int i = 20; i >= 0; i--){
+        if(fa[x][i] != fa[y][i]){
+            x = fa[x][i];
+            y = fa[y][i];
+        }
+    }
+    return fa[x][0]; // 返回最近公共祖先
+}
+void updateSubtreePairs(int cur, int parent, int edgeId, int& maxEdgeId){
+    for(int i = head[cur]; i != -1; i = next_edge[i]){
+        int child = edges[i];
+        if(child == parent) continue;
+        updateSubtreePairs(child, cur, i, maxEdgeId); // 递归更新子节点
+        subtree_pairs[cur] += subtree_pairs[child];
+    }
+    // 当前节点及其子树内包含m对点对时，更新答案
+    if(subtree_pairs[cur] == m){
+        maxEdgeId = max(maxEdgeId, edgeId / 2 + 1); // 边的编号减半(因为是无向图, 一条边有两个方向的编号)
+    }
+}
+int main(){
+    cin >> n >> m;
+    // 初始化邻接表
+    for(int i = 1; i <= n; i++) head[i] = -1;
+    // 读入树的边并建立邻接表
+    for(int i = 1; i < n; i++){
+        int u, v;
+        cin >> u >> v;
+        addEdge(u, v); addEdge(v, u);
+    }
+    // 深度优先搜索预处理节点深度与祖先信息
+    dfs(1, 0, 1);
+    for(int i = 1; i <= m; i++){
+        int firstNode, secondNode;
+        cin >> firstNode >> secondNode;
+        subtree_pairs[firstNode]++; 
+        subtree_pairs[secondNode]++;
+        subtree_pairs[LCA(firstNode, secondNode)] -= 2;
+    }
+    int ans = -1;
+    updateSubtreePairs(1, 0, 0, ans);
+    cout << ans;
+    return 0;
+}
+/* test samples -> 4
+6 2
+1 2
+2 3
+4 3
+2 5
+6 5
+3 6
+4 5
+*/