BZOJ 1901: Zju2112 Dynamic Rankings 区间k大 带修改 在线 线段树套平衡树

之前写线段树套splay数组版。。写了6.2k。。然后弃疗了。现在发现还是很水的。。嘎嘎。。

zju过不了，超时。

　　upd:才发现zju是多组数据。。TLE一版才发现。然后改了，MLE。。。手写内存池。。尼玛终于过了。。附zju2112代码于后。

bzoj倒是过了，1A的感觉还是很爽的。。可是时间不好看。。这就是所谓\(O(nlog^3n)\)的复杂度的可怜之处么？

写挂的地方：

• insert一定要是传地址指针进去。
• delete时先把地址指针delete掉，最后把是地址指针指向左儿子or右儿子or NULL。
• 节点初始化时一定要把左右儿子指针指向NULL。
• 注意脑残，b打错变量名的问题。

做法：线段树约束区间，平衡树支持修改和查询，没了。

　　修改：每次在包含点的线段树节点所包含的平衡树中删除要改的节点值，在插入新的值，\(O(log^2n)\)。

　　查询：由于无法直接查询，所以二分答案，求得答案在区间內的排名，等于各区间小于该值的节点数量，select直接搞，总共\(O(log^3n)\)，具体可以先插入一个值节点，在求值节点的rank，最后删掉即可。

我是用线段树套treap。

然后树状数组套平衡树也可以过，常数小很多。。。

达成成就：AC树套树。

 #include <cstdio>
 #include <cstdlib>
 #include <ctime>
 #include <cstring>
 typedef long long LL;
 const int maxn =  + ;
 int n, m, sum, a[maxn], INF = 0x3f3f3f3f;
 struct treap_node {
     treap_node *ch[];
     int key, fix, cnt, size;
     treap_node() {
         ch[] = ch[] = NULL;
     }
     treap_node(int _key) {
         ch[] = ch[] = NULL;
         key = _key;
         size = cnt = ;
         fix = rand();
     }
 } *T[maxn << ];
 inline void maintain(treap_node *t) {
     t->size = t->cnt;
     if(t->ch[]) t->size += t->ch[]->size;
     if(t->ch[]) t->size += t->ch[]->size;
 }
 void rot(treap_node *&t, int d) {
     treap_node *p = t->ch[d ^ ];
     t->ch[d ^ ] = p->ch[d], p->ch[d] = t;
     maintain(t), maintain(p);
     t = p;
 }
 void insert(treap_node *&t, int val) {
     if(t == NULL) {
         t = new treap_node(val);
     } else {
         if(val < t->key) {
             insert(t->ch[], val);
             if(t->ch[]->fix < t->fix) rot(t, );
         } else if(t->key < val) {
             insert(t->ch[], val);
             if(t->ch[]->fix < t->fix) rot(t, );
         } else
             ++t->cnt;
     }
     maintain(t);
 }
 void del(treap_node *&t, int val) {
     if(t->key == val) {
         if(t->cnt == ) {
             if(!t->ch[] || !t->ch[]) {
                 treap_node *p = t;
                 if(!p->ch[]) p = t->ch[];
                 else p = t->ch[];
                 delete t;
                 t = p;
             } else {
                 int d = t->ch[]->fix < t->ch[]->fix;
                 rot(t, d);
                 del(t->ch[d], val);
             }
         } else --t->cnt;
     } else del(t->ch[t->key < val], val);
     if(t) maintain(t);
 }
 int select(treap_node *t, int val) {
     if(t == NULL) return ;
     if(val < t->key) return select(t->ch[], val);
     int p = (t->ch[]) ? t->ch[]->size + t->cnt : t->cnt;
     if(t->key < val) p += select(t->ch[], val);
     return p;
 }
 bool ok;
 void query(int l, int r, int rt, int ql, int qr, int val) {
     if(ql <= l && r <= qr) {
         sum += select(T[rt], val);
         return ;
     } else {
         int mid = (l + r) >> ;
         if(ql <= mid) query(l, mid, rt << , ql, qr, val);
         if(mid < qr) query(mid + , r, rt <<  | , ql, qr, val);
     }
 }
 void seg_del(int l, int r, int rt, int pos, int val) {
     del(T[rt], val);
     if(l == r) return ;
     int mid = (l + r) >> ;
     if(pos <= mid) seg_del(l, mid, rt << , pos, val);
     else if(mid < pos) seg_del(mid + , r, rt <<  | , pos, val);
 }
 void seg_insert(int l, int r, int rt, int pos, int val) {
     insert(T[rt], val);
     if(l == r) return ;
     int mid = (l + r) >> ;
     if(pos <= mid) seg_insert(l, mid, rt << , pos, val);
     else if(mid < pos) seg_insert(mid + , r, rt <<  | , pos, val);
 }

 char gchar() {
     char ret = getchar();
     for(; ret == '\n' || ret == '\r' || ret == ' '; ret = getchar());
     return ret;
 }
 int main() {
 #ifndef ONLINE_JUDGE
     freopen("data.in", "r", stdin), freopen("data.out", "w", stdout);
 #endif
     scanf("%d%d", &n, &m);
     srand(n * m + );
     for(int i = ; i <= n; ++i) {
         scanf("%d", &a[i]);
         seg_insert(, n, , i, a[i]);
     }
     ok = false;
     for(int i = , p, b, c, d; i <= m; ++i) {
         d = gchar();
         if(d == 'C') {
             scanf("%d%d", &p, &b);
             seg_del(, n, , p, a[p]);
             a[p] = b;
             seg_insert(, n, , p, a[p]);
         } else {
             scanf("%d%d%d", &b, &c, &p);
             LL l = , r = INF;
             while(l < r) {
                 LL mid = (l + r) >> ;
                 sum = ;
                 query(, n, , b, c, mid);
                 if(sum < p) {
                     l = mid + ;
                 } else {
                     r = mid;
                 }
             }
             printf("%lld\n", l);
         }
     }
     return ;
 }

 #include <cstdio>
 #include <cstdlib>
 #include <ctime>
 #include <cstring>
 typedef long long LL;
 const int maxn =  + ;
 int n, m, sum, a[maxn], INF = 0x3f3f3f3f;
 struct treap_node {
     treap_node *ch[];
     int key, fix, cnt, size;
     treap_node() {
         ch[] = ch[] = NULL;
     }
     treap_node(int _key) {
         ch[] = ch[] = NULL;
         key = _key;
         size = cnt = ;
         fix = rand();
     }
 } *T[maxn << ];
 treap_node null_thing;
 struct storage {
     treap_node free_node[maxn * ];
     int top, rec;
     void init() {
         rec = maxn * ;
         for(int i = ; i < rec; ++i) free_node[top++] = i;
     }
     treap_node _new(int val) {
         return free_node[--top] = treap_node(val);
     }
     void back_data() {
         for(int i = top; i < rec; ++i) free_node[top++] = i;
     }
 }S;

 inline void maintain(treap_node *t) {
     t->size = t->cnt;
     if(t->ch[]) t->size += t->ch[]->size;
     if(t->ch[]) t->size += t->ch[]->size;
 }
 void rot(treap_node *&t, int d) {
     treap_node *p = t->ch[d ^ ];
     t->ch[d ^ ] = p->ch[d], p->ch[d] = t;
     maintain(t), maintain(p);
     t = p;
 }
 void insert(treap_node *&t, int val) {
     if(t == NULL) {
         S._new(val);
         t = &S.free_node[S.top];
     } else {
         if(val < t->key) {
             insert(t->ch[], val);
             if(t->ch[]->fix < t->fix) rot(t, );
         } else if(t->key < val) {
             insert(t->ch[], val);
             if(t->ch[]->fix < t->fix) rot(t, );
         } else
             ++t->cnt;
     }
     maintain(t);
 }
 void del(treap_node *&t, int val) {
     if(t->key == val) {
         if(t->cnt == ) {
             if(!t->ch[] || !t->ch[]) {
                 treap_node *p = t;
                 if(!p->ch[]) p = t->ch[];
                 else p = t->ch[];
                 t = p;
             } else {
                 int d = t->ch[]->fix < t->ch[]->fix;
                 rot(t, d);
                 del(t->ch[d], val);
             }
         } else --t->cnt;
     } else del(t->ch[t->key < val], val);
     if(t) maintain(t);
 }
 int select(treap_node *t, int val) {
     if(t == NULL) return ;
     if(val < t->key) return select(t->ch[], val);
     int p = (t->ch[]) ? t->ch[]->size + t->cnt : t->cnt;
     if(t->key < val) p += select(t->ch[], val);
     return p;
 }
 bool ok;
 void query(int l, int r, int rt, int ql, int qr, int val) {
     if(ql <= l && r <= qr) {
         sum += select(T[rt], val);
         return ;
     } else {
         int mid = (l + r) >> ;
         if(ql <= mid) query(l, mid, rt << , ql, qr, val);
         if(mid < qr) query(mid + , r, rt <<  | , ql, qr, val);
     }
 }
 void seg_del(int l, int r, int rt, int pos, int val) {
     del(T[rt], val);
     if(l == r) return ;
     int mid = (l + r) >> ;
     if(pos <= mid) seg_del(l, mid, rt << , pos, val);
     else if(mid < pos) seg_del(mid + , r, rt <<  | , pos, val);
 }
 void seg_insert(int l, int r, int rt, int pos, int val) {
     insert(T[rt], val);
     if(l == r) return ;
     int mid = (l + r) >> ;
     if(pos <= mid) seg_insert(l, mid, rt << , pos, val);
     else if(mid < pos) seg_insert(mid + , r, rt <<  | , pos, val);
 }

 char gchar() {
     char ret = getchar();
     for(; ret == '\n' || ret == '\r' || ret == ' '; ret = getchar());
     return ret;
 }
 void del_tree(int l, int r, int rt) {
     T[rt] = NULL;
     if(l == r) return ;
     int mid = (l + r) >> ;
     del_tree(l, mid, rt << );
     del_tree(mid + , r, rt <<  | );
 }
 int main() {

     int test_num;
     scanf("%d", &test_num);
     S.init();
     while(test_num--) {
         S.back_data();
         scanf("%d%d", &n, &m);
         del_tree(, n, );
         srand(n * m + );
         for(int i = ; i <= n; ++i) {
             scanf("%d", &a[i]);
             seg_insert(, n, , i, a[i]);
         }
         ok = false;
         for(int i = , p, b, c, d; i <= m; ++i) {
             d = gchar();
             if(d == 'C') {
                 scanf("%d%d", &p, &b);
                 seg_del(, n, , p, a[p]);
                 a[p] = b;
                 seg_insert(, n, , p, a[p]);
             } else {
                 scanf("%d%d%d", &b, &c, &p);
                 LL l = , r = INF;
                 while(l < r) {
                     LL mid = (l + r) >> ;
                     sum = ;
                     query(, n, , b, c, mid);
                     if(sum < p) {
                         l = mid + ;
                     } else {
                         r = mid;
                     }
                 }
                 printf("%lld\n", l);
             }
         }
     }
     return ;
 }

zju 2112