bzoj 3237 连通图 - 并查集 - 线段树

Input

Output

Sample Input

4 5
1 2
2 3
3 4
4 1
2 4
3
1 5
2 2 3
2 1 2

Sample Output

Connected
Disconnected
Connected

Hint

N<=100000 M<=200000 K<=100000

---

　　题目大意 给出一个有n个节点和m条边的图，然后有k个询问，每个询问是删掉一些边，然后判断图是否连通，询问之间互相独立。

　　连通性问题通常的做法是并查集，然而并查集不支持删边，但是可以撤销上次操作，所以只能考虑把一条一条边加入并查集，为了高效的确定边是否存在，可以用一个时间戳(其实就是确定某条边在询问时是否存在)。因为存在的时间段是连续的，所以呢就用一个线段树，每个点开一个vector，记录恰好存在时间段为当前区间的的边有哪些。

　　接着开始遍历整棵树，每到一个点就把它存的边一一塞进并查集

　　1)如果不是叶节点，然后访问左右子树，访问完后O(1)撤销这个点加入的所有边

　　2)如果是叶节点，就随便找个点的最高级father(就是f[father] = father)看下它的size是否为n(然后一个操作就"水"完了)

　　因为并查集要支持撤销，所以不能压缩路径了，只能按秩合并(把小的合并到大的中)。

　　注意题目输入中的数据范围是错的(然后我就RE了一次)

Code

 /**
  * bzoj
  * Problem#3237
  * Accepted
  * Time:19508ms
  * Memory:72656k
  */
 #include <iostream>
 #include <cstdio>
 #include <ctime>
 #include <cmath>
 #include <cctype>
 #include <cstring>
 #include <cstdlib>
 #include <fstream>
 #include <sstream>
 #include <algorithm>
 #include <map>
 #include <set>
 #include <stack>
 #include <queue>
 #include <vector>
 #include <stack>
 #ifndef WIN32
 #define Auto "%lld"
 #else
 #define Auto "%I64d"
 #endif
 using namespace std;
 typedef bool boolean;
 const signed int inf = (signed)((1u << ) - );
 const signed long long llf = (signed long long)((1ull << ) - );
 const double eps = 1e-;
 const int binary_limit = ;
 #define smin(a, b) a = min(a, b)
 #define smax(a, b) a = max(a, b)
 #define max3(a, b, c) max(a, max(b, c))
 #define min3(a, b, c) min(a, min(b, c))
 template<typename T>
 inline boolean readInteger(T& u){
     char x;
     int aFlag = ;
     while(!isdigit((x = getchar())) && x != '-' && x != -);
     if(x == -) {
         ungetc(x, stdin);
         return false;
     }
     if(x == '-'){
         x = getchar();
         aFlag = -;
     }
     for(u = x - ''; isdigit((x = getchar())); u = (u * ) + x - '');
     ungetc(x, stdin);
     u *= aFlag;
     return true;
 }
 
 typedef class SegTreeNode {
     public:
         vector< pair<int, int> > e;
         SegTreeNode *l, *r;
 
         SegTreeNode() {        }
         SegTreeNode(SegTreeNode* l, SegTreeNode* r):l(l), r(r) {        }
 }SegTreeNode;
 
 SegTreeNode pool[];
 SegTreeNode *top = pool;
 SegTreeNode null = SegTreeNode(&null, &null);
 
 inline SegTreeNode* newnode() {
     *top = SegTreeNode(&null, &null);
     return top++;
 }
 
 typedef class union_found {
     public:
         int n;
         SegTreeNode* root;
         int* f;
         int* s;
         stack< pair<int, int> > trace;
         stack< pair<int, int> > ss;
         union_found():root(NULL) {        }
         union_found(int n):root(&null), n(n) {
             f = new int[(n + )];
             s = new int[(n + )];
             fill(s, s + n + , );
             for(int i = ; i <= n; i++)
                 f[i] = i;
         }
 
         int find(int x) {
             return (f[x] == x) ? (x) : (find(f[x]));
         }
 
         inline void unit(int fa, int so) {
             int ffa = find(fa);
             int fso = find(so);
             if(ffa == fso)    trace.push(pair<int, int>(, ));
             else {
                 if(s[ffa] < s[fso])
                     swap(ffa, fso);
                 trace.push(pair<int, int>(fso, f[fso]));
                 ss.push(pair<int, int>(ffa, s[ffa]));
                 s[ffa] += s[fso];
                 f[fso] = ffa;
             }
         }
 
         inline void undo() {
             pair<int, int> p = trace.top();
             pair<int, int> sp = ss.top();
             trace.pop();
             if(p.first == )    return;
             f[p.first] = p.second;
             s[sp.first] = sp.second;
             ss.pop();
         }
 
         void update(SegTreeNode*& node, int l, int r, int ql, int qr, pair<int, int> &val) {
             if(node == &null)    node = newnode();
             if(l == ql && r == qr) {
 //                printf("Update at segment [%d, %d] with the edge (%d, %d)\n", l, r, val.first, val.second);
                 node->e.push_back(val);
                 return;
             }
             int mid = (l + r) >> ;
             if(qr <= mid)    update(node->l, l, mid, ql, qr, val);
             else if(ql > mid)    update(node->r, mid + , r, ql, qr, val);
             else {
                 update(node->l, l, mid, ql, mid, val);
                 update(node->r, mid + , r, mid + , qr, val);
             }
         }
 
         void query(SegTreeNode* node, int l, int r, boolean *res) {
             pair<int, int> p;
             for(int i = ; i < (signed)node->e.size(); i++) {
                 p = node->e[i];
                 unit(p.first, p.second);
 //                printf("Connect %d and %d\n", p.first, p.second);
             }
             if(l == r) {
                 res[l] = (s[find()] == n);
             } else {
                 int mid = (l + r) >> ;
                 query(node->l, l, mid, res);
                 query(node->r, mid + , r, res);
             }
             for(int i = ; i < (signed)node->e.size(); i++)
                 undo();
         }
 }union_found;
 
 int n, m, q;
 pair<int, int> *es;
 vector<int> *exists;
 union_found uf;
 
 inline void init() {
     readInteger(n);
     readInteger(m);
     es = new pair<int, int>[(m + )];
     for(int i = ; i <= m; i++) {
         readInteger(es[i].first);
         readInteger(es[i].second);
     }
     exists = new vector<int>[(m + )];
     readInteger(q);
     for(int i = , c, x; i <= q; i++) {
         readInteger(c);
         while(c--) {
             readInteger(x);
             exists[x].push_back(i);
         }
     }
 }
 
 inline void mktree() {
     uf = union_found(n);
     for(int i = ; i <= m; i++) {
         exists[i].push_back(q + );
         for(int j = , last = ; j < (signed)exists[i].size(); j++) {
             if(last == exists[i][j])
                 last++;
             else {
 //                cout << exists[i][j] << endl;
                 uf.update(uf.root, , q, last, exists[i][j] - , es[i]);
                 last = exists[i][j] + ;
             }
         }
     }
 }
 
 boolean *res;
 inline void solve() {
     res = new boolean[(q + )];
     uf.query(uf.root, , q, res);
     for(int i = ; i <= q; i++)
         puts((res[i]) ? ("Connected") : ("Disconnected"));
 }
 
 int main() {
     init();
     mktree();
     solve();
     return ;
 }