uva 1479 - Graph and Queries(伸展树)

题目链接：uva 1479 - Graph and Queries

题目大意：有一张m条边的无向图，每个节点都有一个权值，现在有若干个操作，

• D x：删除ID为x的节点
• Q x k：计算与节点x联通的节点当中，第k大的权值
• C x v：把节点x的权值改为v

解题思路：把所有操作反过来处理，先执行所有的D操作，获得最终的图，然后逆操作的时候对于D来说即为合并操作，Q和C则是查询和修改操作。

#include <cstdio>#include <cstring>#include <cstdlib>#include <vector>#include <algorithm>using namespace std;typedef long long ll;const int maxn = 20005;const int maxm = 60005;const int maxc = 500005;// Union-Setint f[maxn];inline int getfar(int x) {    return x == f[x] ? x : f[x] = getfar(f[x]);}// Treap;struct Node {    int val, rank, sum;    Node* cid[2];    Node (int val);    void maintain();    int cmp(int x);};Node* root[maxn];void insert(Node* &o, int x);void rotate(Node* &o, int d);void remove(Node* &o, int x);// Rank Tree;void add_edge (int i);void remove_tree(Node* &o);void merge_tree(Node* &src, Node* & dest);int rankth(Node* o, int k);// Command;struct Command {    char type;    int x, p;}command[maxc];bool flag[maxm];ll tot, cnt;int N, M, C, W[maxn], U[maxm], V[maxm];void build () {    for (int i = 1; i <= N; i++) {        if (root[i] != NULL)            remove_tree(root[i]);        root[i] = new Node(W[i]);    }    for (int i = 1; i <= M; i++) {        if (!flag[i])            add_edge(i);    }}void init () {    C = 0;    memset(flag, 0, sizeof(flag));    for (int i = 1; i <= N; i++) {        f[i] = i;        scanf("%d", &W[i]);    }    for (int i = 1; i <= M; i++)        scanf("%d%d", &U[i], &V[i]);    int x, p;    char str[5];    while (scanf("%s", str) == 1 && str[0] != 'E') {        scanf("%d", &x);        if (str[0] == 'D') flag[x] = 1;        else if (str[0] == 'Q') scanf("%d", &p);        else if (str[0] == 'C') {            scanf("%d", &p);            swap(p, W[x]);        }        command[C++] = (Command){ str[0], x, p};    }    build();}void query (int x, int k) {    cnt++;    tot += rankth(root[getfar(x)], k);}void change (int x, int v) {    int u = getfar(x);    remove(root[u], W[x]);    insert(root[u], v);    W[x] = v;}int main () {    int cas = 0;    while (scanf("%d%d", &N, &M) == 2 && N) {        init();        tot = cnt = 0;        for (int i = C - 1; i >= 0; i--) {            char type = command[i].type;            if (type == 'D')                add_edge(command[i].x);            else if (type == 'Q')                query(command[i].x, command[i].p);            else                change(command[i].x, command[i].p);        }        printf("Case %d: %.6lf\n", ++cas, tot / (double) cnt);    }    return 0;}// Rank Tree;int rankth(Node* o, int k) {    if (o == NULL || k <= 0 || k > o->sum)        return 0;    int s = (o->cid[1] == NULL ? 0 : o->cid[1]->sum);    if (k == s + 1) return o->val;    else if (k <= s) return rankth(o->cid[1], k);    else return rankth(o->cid[0], k - s - 1);}void remove_tree (Node* &o) {    for (int i = 0; i < 2; i++) {        if (o->cid[i] != NULL)            remove_tree(o->cid[i]);    }    delete o;    o = NULL;}void add_edge (int x) {    int u = getfar(U[x]), v = getfar(V[x]);    if (u != v) {        if (root[u]->sum < root[v]->sum)            swap(u, v);        f[v] = u;        merge_tree(root[v], root[u]);    }}void merge_tree (Node* &src, Node* &dest) {    for (int i = 0; i < 2; i++) {        if (src->cid[i] != NULL)            merge_tree(src->cid[i], dest);    }    insert(dest, src->val);    delete src;    src = NULL;}// TreapNode::Node (int val) {    sum = 1;    rank = rand();    this->val = val;    cid[0] = cid[1] = NULL;}void Node::maintain() {    sum = 1;    if (cid[0] != NULL) sum += cid[0]->sum;    if (cid[1] != NULL) sum += cid[1]->sum;}int Node::cmp(int x) {    if (val == x)        return -1;    return val < x ? 1 : 0;}void remove(Node* &o, int x) {    int d = o->cmp(x);    if (d == -1) {        Node* u = o;        if (o->cid[0] != NULL && o->cid[1] != NULL) {            int d2 = (o->cid[0]->rank > o->cid[1]->rank ? 1 : 0);            rotate(o, d2);            remove(o->cid[d2], x);        } else {            o = (o->cid[0] == NULL ? o->cid[1] : o->cid[0]);            delete u;        }    } else        remove(o->cid[d], x);    if (o != NULL)        o->maintain();}void rotate (Node* &o, int d) {    Node* k = o->cid[d^1];    o->cid[d^1] = k->cid[d];    k->cid[d] = o;    o->maintain();    k->maintain();    o = k;}void insert(Node* &o, int x) {    if (o == NULL)        o = new Node(x);    else {        int d = (x < o->val ? 0 : 1);        insert(o->cid[d], x);        if (o->cid[d]->rank > o->rank)            rotate(o, d^1);    }    o->maintain();}