都说 Splay 不仅仅是平衡树那么简单,由于它可以任意旋转,它还可以高效完成一些在区间上的操作,于是就做了几道 Splay 的题目。虽然不是很难,但很巧妙,也确实很烦,所以就取了 "Boring Sequence Manipulation" 这个标题,呵呵~ 下面进入正题。
其实 Splay 高效做区间操作的原理和线段树几乎一样,都是标记延迟,都是从根到叶,在维护的时候,也都是从叶到根的维护。只是 Splay 可以改变根和叶的关系,而线段树的根叶关系则不能改变。因而Splay 可以实现任意插入和删除结点,更为轻松地实现旋转(rotate)、翻转(reverse) 等操作。然而,这不是没有代价的,因为每次做 splay/rotate 操作时都会要求立即还原被延迟的标记,使被旋转结点能够正确地被维护,所以这样会有更大的常数。而且 Splay 的码量也较线段树大。
然而实际做题的时候,问题最大的还是标记延迟的实现,这也是写线段树的关键点。鉴于以往线段树的实践,与线段树一样,我的做法是,父结点的标记都是给儿子结点做的。也就是说,父结点的标记表示的确切意义是,父结点的信息已维护,子结点的信息未维护。这就很好地对应了 rotate 的意图,push_down 为的就是使子结点的信息得到更正,而不是父结点自己的信息得到更正。相应地,从 splay/rotate 的实现中可以看出,update 总是假定父结点的标记已传给子结点,即假定 update 之前一定做过 push_down 。于是两者结合,就可以保证正确性了。
更详细地,所有结点的信息有三类,标记信息、固有信息、子结点相关信息。其中,第一个和第三个是和线段树一致的,第三个由于经常和要求的答案有直接关系,所以也被称为答案信息。由于 splay 的结点,其本身是序列中的一个元素,所以,较线段树来说,又多了一个固有信息,即与子结点无关的信息。push_down 的作用就是维护子结点固有信息和答案信息,而 update 的作用就是根据固有信息和 新建立父子关系的子结点 的信息,维护其本身的答案信息。由于 splay 的结点,同一般的树一样,既可以看成是一个结点,也可以看成是一棵子树。因而,在从某个结点到树根路径的旋转过程中,可以到最后才 update 。因为在这条路径中,从父结点 push_down 保证了固有信息的正确性,虽然在 push_down 的过程中,答案信息是错误的,但是终将会在最后的 update 操作中得到更正。并且,对该结点的 push_down ,起到了一个传递信息的作用,保证了旋转过程中 其临时子结点 的信息的正确性,这点保证了路径上其他结点的 update 操作是正确的。又由于该结点的答案信息只与固有信息和 最后建立父子关系 的子结点的答案信息有关,所以可以省去中间过程中的 update 操作。再结合 push_down 保证了固有信息的正确性,而且 update 在 push_down 之后,满足 update 的假设,所以这样做是正确的,固有信息和答案信息的正确性都得到了保证。
最后就是 mark_xxx 函数,其作用是对于给定标记,维护某个结点的固有信息和答案信息,并做上标记。事实上 push_down 也是用它来实现的,在标记信息有多个的时候 push_down 实现对子结点做何种标记,即调用哪个 mark_xxx 函数。
另外,每次做完标记,或者单独更新(对于那些只更新单个结点的题目来说)的时候,最好把其父结点转到根的位置,保证整棵树的正确性(对于那些只更新单个结点的题目,还可以提高效率)。事实上,平常的带 _size 域实现的 Splay 平衡树的删除结点操作就是这样来完成的。
那么,了解原理之后,对于这些函数做出设定,其他的基本上就可以交给模板来完成了。
#include <cstdio> #include <cstring> #include <algorithm> using namespace std; #define MAXMEM 100010 template <class T> struct Splay { struct Node { Node *_fa, *_ch[2]; T _val; Node *_min_node; int _size; bool _rev; Node* get_end(int c) { // 0 表示左端 1 表示右端 Node* x = this; while (x->_ch[c]) { x->push_down(); // notice! x = x->_ch[c]; } return x; } Node* get_near(int c) { if (_ch[c]) return _ch[c]->get_end(1 - c); Node* x = this; while (x->_fa && x->_fa->_ch[c] == x) x = x->_fa; return x->_fa; } Node* get_succ() { return get_near(1); } Node* get_prev() { return get_near(0); } int get_size() { // 兼容 this == 0 if (this) return _size; else return 0; } void mark_node() { if (this) { _rev = !_rev; swap(_ch[0], _ch[1]); } } void push_down() { // 向下传标记 if (_rev) { _ch[0]->mark_node(); _ch[1]->mark_node(); _rev = false; } } void update() { // 向上更新,可以为空 _size = 1 + _ch[0]->get_size() + _ch[1]->get_size(); _min_node = this; if (_ch[0] && _ch[0]->_min_node->_val < _min_node->_val) _min_node = _ch[0]->_min_node; if (_ch[1] && _ch[1]->_min_node->_val < _min_node->_val) _min_node = _ch[1]->_min_node; } }; Node *_root; static Node *const _fa_root, _nodes[MAXMEM]; void rotate(Node* x, int c) { // 旋转操作,0 表示左旋,1 表示右旋 Node* y = x->_fa; y->push_down(); x->push_down(); // y 在 x 之上,故先 y 后 x y->_ch[1 - c] = x->_ch[c]; if (x->_ch[c]) x->_ch[c]->_fa = y; x->_fa = y->_fa; if (y->_fa != _fa_root) { if (y->_fa->_ch[0] == y) y->_fa->_ch[0] = x; else y->_fa->_ch[1] = x; } else _root = x; x->_ch[c] = y; y->_fa = x; y->update(); // 维护 y } void splay(Node* x, Node *f) { // 把结点 x 转到结点 f 下面 x->push_down(); while (x->_fa != f) { if (x->_fa->_fa == f) { if (x->_fa->_ch[0] == x) rotate(x, 1); else rotate(x, 0); } else { Node *y = x->_fa, *z = y->_fa; if (z->_ch[0] == y) { if (y->_ch[0] == x) rotate(y, 1), rotate(x, 1); else rotate(x, 0), rotate(x, 1); } else { if (y->_ch[1] == x) rotate(y, 0), rotate(x, 0); else rotate(x, 1), rotate(x, 0); } } } x->update(); } void build(int a, int b) { _root = make_tree(a, b); _root->_fa = _fa_root; } static Node* make_tree(int a, int b) { if (a > b) return 0; Node* root = _nodes + (a + b) / 2; root->_rev = false; root->_ch[0] = make_tree(a, root - _nodes - 1); if (root->_ch[0]) root->_ch[0]->_fa = root; root->_ch[1] = make_tree(root - _nodes + 1, b); if (root->_ch[1]) root->_ch[1]->_fa = root; root->update(); return root; } }; template <class T> typename Splay<T>::Node *const Splay<T>::_fa_root = 0; template <class T> typename Splay<T>::Node Splay<T>::_nodes[MAXMEM]; Splay<pair<int, int> > tree; int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); #endif int n; while (scanf("%d", &n) != EOF) { if (n == 0) break; for (int i = 1; i <= n; ++i) { scanf("%d", &tree._nodes[i]._val.first); tree._nodes[i]._val.second = i; } tree._nodes[n + 1]._val = make_pair(0x7fffffff, 0x7fffffff); tree.build(0, n + 1); Splay<pair<int, int> >::Node * min_node = tree._nodes, *min_succ; for (int i = 1; i < n; ++i) { tree.splay(min_node, tree._fa_root); min_node = tree._root->_ch[1]->_min_node; tree.splay(min_node, tree._root); min_succ = min_node->get_succ(); tree.splay(min_succ, tree._root); printf("%d ", i - 1 + min_succ->_ch[0]->get_size()); min_succ->_ch[0]->mark_node(); } printf("%d\n", n); } return 0; }
简单的不带删除的翻转,push_down 、mark_node(以后叫 mark_rev) 和 update 写完了以后,就可以把任务交给模板了,不过要注意,由于翻转,所以 get_succ 的时候,要在路径上做维护,也就是不断地 push_down ,来得到真正的后继。不过其实这是在 get_end 里面完成的,因为已经旋转到根的下面,而且根已经被更新,所以可以直接调 get_succ ,因为它一定会调用 get_end 。所以更加严谨一些的话应该写 get_end ,不过由于意义上 get_succ 更明了,所以就写 get_succ 了。而且,对于有 _rev 这种信息的树来说,get_end 就必须要通过 push_down 来保证正确性。
#include <cstdio> #include <cstring> #include <algorithm> using namespace std; #define MAXN 100000 const int MAXMEM = MAXN * 3 + 2; int ans[MAXMEM], tot; template <class T> struct Splay { struct Node { Node *_fa, *_ch[2]; T _val; int _size; bool _rev; Node* get_end(int c) { // 0 表示左端 1 表示右端 Node* x = this; x->push_down(); // notice! while (x->_ch[c]) { x = x->_ch[c]; x->push_down(); // notice! } return x; } Node* get_near(int c) { if (_ch[c]) return _ch[c]->get_end(1 - c); Node* x = this; while (x->_fa && x->_fa->_ch[c] == x) x = x->_fa; return x->_fa; } Node* get_succ() { return get_near(1); } Node* get_prev() { return get_near(0); } int get_size() { // 兼容 this == 0 if (this) return _size; else return 0; } void mark_node() { if (this) { _rev = !_rev; swap(_ch[0], _ch[1]); } } void push_down() { // 向下传标记 if (_rev) { _ch[0]->mark_node(); _ch[1]->mark_node(); _rev = false; } } void update() { // 向上更新,可以为空 _size = 1 + _ch[0]->get_size() + _ch[1]->get_size(); } void travel() { push_down(); if (_ch[0]) _ch[0]->travel(); ans[tot++] = _val; if (_ch[1]) _ch[1]->travel(); } }; Node *_root; static Node *const _fa_root, _nodes[MAXMEM]; void rotate(Node* x, int c) { // 旋转操作,0 表示左旋,1 表示右旋 Node* y = x->_fa; y->push_down(); x->push_down(); // y 在 x 之上,故先 y 后 x y->_ch[1 - c] = x->_ch[c]; if (x->_ch[c]) x->_ch[c]->_fa = y; x->_fa = y->_fa; if (y->_fa != _fa_root) { if (y->_fa->_ch[0] == y) y->_fa->_ch[0] = x; else y->_fa->_ch[1] = x; } else _root = x; x->_ch[c] = y; y->_fa = x; y->update(); // 维护 y } void splay(Node* x, Node *f) { // 把结点 x 转到结点 f 下面 x->push_down(); while (x->_fa != f) { if (x->_fa->_fa == f) { if (x->_fa->_ch[0] == x) rotate(x, 1); else rotate(x, 0); } else { Node *y = x->_fa, *z = y->_fa; if (z->_ch[0] == y) { if (y->_ch[0] == x) rotate(y, 1), rotate(x, 1); else rotate(x, 0), rotate(x, 1); } else { if (y->_ch[1] == x) rotate(y, 0), rotate(x, 0); else rotate(x, 1), rotate(x, 0); } } } x->update(); } Node* find_kth(int k) { Node* x = _root; x->push_down(); // notice! while (k != x->_ch[0]->get_size() + 1) { if (k <= x->_ch[0]->get_size()) { x = x->_ch[0]; } else { k -= x->_ch[0]->get_size() + 1; x = x->_ch[1]; } x->push_down(); // notice! } return x; } void build(int a, int b) { _root = make_tree(a, b); _root->_fa = _fa_root; } static Node* make_tree(int a, int b) { if (a > b) return 0; Node* root = _nodes + (a + b) / 2; root->_rev = false; root->_ch[0] = make_tree(a, root - _nodes - 1); if (root->_ch[0]) root->_ch[0]->_fa = root; root->_ch[1] = make_tree(root - _nodes + 1, b); if (root->_ch[1]) root->_ch[1]->_fa = root; root->update(); // notice! return root; } void dispaly() { tot = 0; _root->travel(); } }; template <class T> typename Splay<T>::Node *const Splay<T>::_fa_root = 0; template <class T> typename Splay<T>::Node Splay<T>::_nodes[MAXMEM]; Splay<int> tree; char buf[100]; int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); #endif int n, m; while (scanf("%d%d", &n, &m) != EOF) { if (n < 0 && m < 0) break; for (int i = 1; i <= n + 1; ++i) tree._nodes[i]._val = i; tree.build(0, n + 1); for (int i = 0; i < m; ++i) { scanf("%s", buf); int a, b, c; if (buf[0] == 'C') { scanf("%d%d%d", &a, &b, &c); tree.splay(tree.find_kth(a), tree._fa_root); tree.splay(tree.find_kth(b + 2), tree._root); Splay<int>::Node* handle = tree._root->_ch[1]->_ch[0]; tree._root->_ch[1]->_ch[0] = 0; tree.splay(tree._root->_ch[1], tree._fa_root); tree.splay(tree.find_kth(c + 1), tree._fa_root); tree.splay(tree._root->get_succ(), tree._root); tree._root->_ch[1]->_ch[0] = handle; handle->_fa = tree._root->_ch[1]; // notice; tree.splay(tree._root->_ch[1], tree._fa_root); } else { scanf("%d%d", &a, &b); tree.splay(tree.find_kth(a), tree._fa_root); tree.splay(tree.find_kth(b + 2), tree._root); tree._root->_ch[1]->_ch[0]->mark_node(); tree.splay(tree._root->_ch[1], tree._fa_root); } } tree.dispaly(); for (int i = 1; i <= n; ++i) { if (i != 1) putchar(' '); printf("%d", ans[i]); } putchar('\n'); } return 0; }
带删除和插入以及查询第 k 个结点的区间翻转,基本同上,find_kth 跟 get_end 一样,在 _rev 环境下需要 push_down 保证正确性。本机调试的时候忘记维护父指针了,结果爆栈。
#include <cstdio> #include <cstring> #include <algorithm> using namespace std; #define MAXN 100000 const int MAXMEM = MAXN * 2 + 1; int pick[MAXN + 1], tot; pair<int, int> seg[MAXN * 2 + 1]; int stot; template <class T> struct Splay { struct Node { Node *_fa, *_ch[2]; T _val; int _size; Node* get_end(int c) { // 0 表示左端 1 表示右端 Node* x = this; x->push_down(); // notice! while (x->_ch[c]) { x = x->_ch[c]; x->push_down(); // notice! } return x; } Node* get_near(int c) { if (_ch[c]) return _ch[c]->get_end(1 - c); Node* x = this; while (x->_fa && x->_fa->_ch[c] == x) x = x->_fa; return x->_fa; } Node* get_succ() { return get_near(1); } Node* get_prev() { return get_near(0); } int get_size() { // 兼容 this == 0 if (this) return _size; else return 0; } void push_down() {} // 向下传标记 void update() { // 向上更新,可以为空 _size = _val.second - _val.first + 1 + _ch[0]->get_size() + _ch[1]->get_size(); } }; Node *_root; static Node *const _fa_root, _nodes[MAXMEM]; void rotate(Node* x, int c) { // 旋转操作,0 表示左旋,1 表示右旋 Node* y = x->_fa; y->push_down(); x->push_down(); // y 在 x 之上,故先 y 后 x y->_ch[1 - c] = x->_ch[c]; if (x->_ch[c]) x->_ch[c]->_fa = y; x->_fa = y->_fa; if (y->_fa != _fa_root) { if (y->_fa->_ch[0] == y) y->_fa->_ch[0] = x; else y->_fa->_ch[1] = x; } else _root = x; x->_ch[c] = y; y->_fa = x; y->update(); // 维护 y } void splay(Node* x, Node *f) { // 把结点 x 转到结点 f 下面 x->push_down(); while (x->_fa != f) { if (x->_fa->_fa == f) { if (x->_fa->_ch[0] == x) rotate(x, 1); else rotate(x, 0); } else { Node *y = x->_fa, *z = y->_fa; if (z->_ch[0] == y) { if (y->_ch[0] == x) rotate(y, 1), rotate(x, 1); else rotate(x, 0), rotate(x, 1); } else { if (y->_ch[1] == x) rotate(y, 0), rotate(x, 0); else rotate(x, 1), rotate(x, 0); } } } x->update(); } Node* join(Node* r1, Node* r2) { if (r1 && r2) { Node *right_end = r1->get_end(1); splay(right_end, r1->_fa); right_end->_ch[1] = r2; r2->_fa = right_end; right_end->update(); // notice! return right_end; } if (r1) return r1; if (r2) return r2; return 0; } int find_kth_number(int k) { Node* x = _root; x->push_down(); // notice! while ( !(x->_ch[0]->get_size() < k && k <= x->_ch[0]->get_size() + x->_val.second - x->_val.first + 1) ) { if (k <= x->_ch[0]->get_size()) { x = x->_ch[0]; } else { k -= x->_ch[0]->get_size() + x->_val.second - x->_val.first + 1; x = x->_ch[1]; } x->push_down(); // notice! } int res = x->_val.first - 1 + k - x->_ch[0]->get_size(); splay(x, _fa_root); return res; } void delete_node(Node* nd) { Node* x = join(nd->_ch[0], nd->_ch[1]); if (nd->_fa == _fa_root) { _root = x; } else { if (nd->_fa->_ch[0] == nd) nd->_fa->_ch[0] = x; else nd->_fa->_ch[1] = x; } if (x) x->_fa = nd->_fa; if (nd->_fa) splay(nd->_fa, _fa_root); } void build(int a, int b) { _root = make_tree(a, b); _root->_fa = _fa_root; } static Node* make_tree(int a, int b) { if (a > b) return 0; Node* root = _nodes + (a + b) / 2; root->_val = seg[(a + b) / 2]; root->_ch[0] = make_tree(a, root - _nodes - 1); if (root->_ch[0]) root->_ch[0]->_fa = root; root->_ch[1] = make_tree(root - _nodes + 1, b); if (root->_ch[1]) root->_ch[1]->_fa = root; root->update(); // notice! return root; } }; template <class T> typename Splay<T>::Node *const Splay<T>::_fa_root = 0; template <class T> typename Splay<T>::Node Splay<T>::_nodes[MAXMEM]; Splay<pair<int, int> > tree; char buf[100]; int n, m; struct Query { char _c; int _x; } q[MAXN]; int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); #endif int test; scanf("%d", &test); for (int cas = 1; cas <= test; ++cas) { scanf("%d%d", &n, &m); tot = 0; for (int i = 0; i < m; ++i) { scanf("%s%d", buf, &q[i]._x); q[i]._c = buf[0]; if (q[i]._c != 'R') pick[tot++] = q[i]._x; } sort(pick, pick + tot); tot = unique(pick, pick + tot) - pick; pick[tot] = n + 1; stot = 0; if (pick[0] != 1) seg[stot++] = make_pair(1, pick[0] - 1); for (int i = 0; i < tot; ++i) { seg[stot++] = make_pair(pick[i], pick[i]); if (pick[i] + 1 != pick[i + 1]) seg[stot++] = make_pair(pick[i] + 1, pick[i + 1] - 1); } tree.build(0, stot - 1); printf("Case %d:\n", cas); for (int i = 0; i < m; ++i) { if (q[i]._c == 'T') { int pos = lower_bound(seg, seg + stot, make_pair(q[i]._x, q[i]._x)) - seg; Splay<pair<int, int> >::Node* nd = tree._nodes + pos; tree.delete_node(nd); nd->_fa = tree._fa_root; nd->_ch[0] = 0; nd->_ch[1] = tree._root; if (tree._root) // notice! tree._root->_fa = nd; tree._root = nd; nd->update(); } else if (q[i]._c == 'Q') { int pos = lower_bound(seg, seg + stot, make_pair(q[i]._x, q[i]._x)) - seg; Splay<pair<int, int> >::Node* nd = tree._nodes + pos; tree.splay(nd, tree._fa_root); printf("%d\n", tree._root->_ch[0]->get_size() + 1); } else { // 'R' printf("%d\n", tree.find_kth_number(q[i]._x)); } } } return 0; }
这题没有 push_down ,应该说更简单些吧。Splay 上的离线化操作,由于 Top 的特殊性,所以可以离散化后,根据内存的固定性,离线来做。如果 Top x 是说当前第 x 个人到前端,那么可以用动态新建结点,动态插入来实现。这题我刚开始忘记考虑删除之后,可能会得到空树了,结果 RE = =... 之前都是 1Y 的,没想到在这题上被打破了。
#include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> using namespace std; #define MAXMEM 500002 int arr[MAXMEM]; template <class T> struct Splay { struct Node { Node *_fa, *_ch[2]; T _val, _clear_val, _sum, _max_rsum, _max_lsum, _max_sum; int _size; // _size 可以不要,标记这里加 bool _rev, _clr; int get_size() { // 兼容 this == 0 if (this) return _size; else return 0; } int get_sum() { if (this) return _sum; else return 0; } int get_max_lsum() { if (this) return _max_lsum; else return 0; } int get_max_rsum() { if (this) return _max_rsum; else return 0; } Node() {} Node(const T& x) { set_value(x); } void *operator new(size_t) { if (_stop != 0) return _st[--_stop]; else return _nodes + _mtot++; } void operator delete(void* p, size_t) { _st[_stop++] = (Node*)p; } void recycle() { if (_ch[0]) _ch[0]->recycle(); if (_ch[1]) _ch[1]->recycle(); delete this; } void set_value(const T& x) { _val = x; _size = 1; _rev = _clr = false; _sum = _max_sum = x; _max_lsum = max(0, x); _max_rsum = max(0, x); _ch[0] = _ch[1] = 0; _fa = _fa_root; } void mark_rev() { if (this && !_clr) { _rev = !_rev; swap(_ch[0], _ch[1]); swap(_max_lsum, _max_rsum); } } void mark_clear(const T& v) { if (this) { _clr = true; _clear_val = _val = v; // notice! _sum = v * _size; _max_lsum = max(0, v * _size); _max_rsum = max(0, v * _size); _max_sum = max(v, v * _size); _rev = false; } } void push_down() { // 向下传标记 if (_rev) { _ch[0]->mark_rev(); _ch[1]->mark_rev(); _rev = false; } else if(_clr) { _ch[0]->mark_clear(_clear_val); _ch[1]->mark_clear(_clear_val); _clr = false; } } void update_size() { _size = 1 + _ch[0]->get_size() + _ch[1]->get_size(); } void update_sum() { _sum = _val + _ch[0]->get_sum() + _ch[1]->get_sum(); } void update_max_sum() { _max_sum = _ch[0]->get_max_rsum() + _val + _ch[1]->get_max_lsum(); if (_ch[0]) _max_sum = max(_max_sum, _ch[0]->_max_sum); if (_ch[1]) _max_sum = max(_max_sum, _ch[1]->_max_sum); } void update_max_lsum() { _max_lsum = max(_ch[0]->get_max_lsum(), _ch[0]->get_sum() + _val + _ch[1]->get_max_lsum()); } void update_max_rsum() { _max_rsum = max(_ch[1]->get_max_rsum(), _ch[1]->get_sum() + _val + _ch[0]->get_max_rsum()); } void update() { // 向上更新 update_size(); update_sum(); update_max_sum(); update_max_lsum(); update_max_rsum(); } }; Node *_root; static Node *const _fa_root, _nodes[MAXMEM], *_st[MAXMEM]; static int _mtot, _stop; void rotate(Node* x, int c) { // 旋转操作,0 表示左旋,1 表示右旋 Node* y = x->_fa; y->push_down(); x->push_down(); // y 在 x 之上,故先 y 后 x y->_ch[1 - c] = x->_ch[c]; if (x->_ch[c]) x->_ch[c]->_fa = y; x->_fa = y->_fa; if (y->_fa != _fa_root) { if (y->_fa->_ch[0] == y) y->_fa->_ch[0] = x; else y->_fa->_ch[1] = x; } else _root = x; x->_ch[c] = y; y->_fa = x; y->update(); // 维护 y } void splay(Node* x, Node *f) { // 把结点 x 转到结点 f 下面 x->push_down(); while (x->_fa != f) { if (x->_fa->_fa == f) { if (x->_fa->_ch[0] == x) rotate(x, 1); else rotate(x, 0); } else { Node *y = x->_fa, *z = y->_fa; if (z->_ch[0] == y) { if (y->_ch[0] == x) rotate(y, 1), rotate(x, 1); else rotate(x, 0), rotate(x, 1); } else { if (y->_ch[1] == x) rotate(y, 0), rotate(x, 0); else rotate(x, 1), rotate(x, 0); } } } x->update(); } Node* find_kth(int k) { Node* x = _root; x->push_down(); // notice! while (k != x->_ch[0]->get_size() + 1) { if (k <= x->_ch[0]->get_size()) { x = x->_ch[0]; } else { k -= x->_ch[0]->get_size() + 1; x = x->_ch[1]; } x->push_down(); // notice! } return x; } void build(int a, int b) { _root = make_tree(a, b); if (_root) _root->_fa = _fa_root; } static Node* make_tree(int a, int b) { if (a > b) return 0; int mid = (a + b) / 2; Node* root = new Node(arr[mid]); root->_ch[0] = make_tree(a, mid - 1); if (root->_ch[0]) root->_ch[0]->_fa = root; root->_ch[1] = make_tree(mid + 1, b); if (root->_ch[1]) root->_ch[1]->_fa = root; root->update(); // notice! return root; } void clear() { _root = 0; } static void mem_init() { _mtot = _stop = 0; } }; template <class T> typename Splay<T>::Node *const Splay<T>::_fa_root = 0; template <class T> typename Splay<T>::Node Splay<T>::_nodes[MAXMEM]; template <class T> typename Splay<T>::Node* Splay<T>::_st[MAXMEM]; template <class T> int Splay<T>::_stop = 0; template <class T> int Splay<T>::_mtot = 0; int n, m; Splay<int> tree; char buf[100]; inline void pre_operation(int s, int e) { Splay<int>::Node *pa = tree.find_kth(s), *pb = tree.find_kth(e); tree.splay(pa, tree._fa_root); tree.splay(pb, tree._root); } inline void post_operation() { tree.splay(tree._root->_ch[1], tree._fa_root); } int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); #endif int test; scanf("%d", &test); for (int cas = 1; cas <= test; ++cas) { tree.mem_init(); scanf("%d%d", &n, &m); for (int i = 1; i <= n; ++i) scanf("%d", arr + i); tree.build(0, n + 1); for (int i = 0; i < m; ++i) { scanf("%s", buf); int k, t, v; switch (buf[0]) { case 'M': if (buf[2] == 'K') { // MAKE-SAME scanf("%d%d%d", &k, &t, &v); pre_operation(k, k + t + 1); tree._root->_ch[1]->_ch[0]->mark_clear(v); post_operation(); } else { // MAX-SUM pre_operation(1, tree._root->get_size()); printf("%d\n", tree._root->_ch[1]->_ch[0]->_max_sum); } break; case 'I': { // INSERT scanf("%d%d", &k, &t); pre_operation(k + 1, k + 2); for (int i = 0; i < t; ++i) scanf("%d", arr + i); Splay<int>::Node* h = Splay<int>::make_tree(0, t - 1); tree._root->_ch[1]->_ch[0] = h; if (h) h->_fa = tree._root->_ch[1]; post_operation(); } break; case 'D': { // DELETE scanf("%d%d", &k, &t); pre_operation(k, k + t + 1); Splay<int>::Node* h = tree._root->_ch[1]->_ch[0]; tree._root->_ch[1]->_ch[0] = 0; if (h) h->recycle(); post_operation(); } break; case 'R': { // REVERSE scanf("%d%d", &k, &t); pre_operation(k, k + t + 1); tree._root->_ch[1]->_ch[0]->mark_rev(); post_operation(); } break; case 'G': { // GET-SUM scanf("%d%d", &k, &t); pre_operation(k, k + t + 1); printf("%d\n", tree._root->_ch[1]->_ch[0]->get_sum()); } break; } } } return 0; }
比较麻烦的题,两种标记,_clr 和 _rev 都有,然后还有插入删除,以及最最ws的 MAX-SUM 询问,最后加起来,结点内信息的个数就相当恐怖了。再加上是在十分疲劳的状态下写的,于是 RE 和 WA了 N 次之后,终于 AC 。首先,这题的数据里,有一个 GET-SUM 的 tot 是 0 ,会导致非法解引用,找出这个错误,花了大概 N/3 个 RE 。之后一直 WA ,最后发现,原来是 mark_clear 里面,_val 忘记更新了,囧~ 这个错误真是太水了。这题最麻烦的还是两个标记的处理,我的做法是延续线段树时代的做法,由于 _clr 的特殊性质,每次保证标记信息中 _clr 和 _rev 里面只有一个为 true ,然后就好处理了。还有就是在 DELETE 那个地方,我纠结了好久,终于决定的方式返还内存了。开始是想返还内存的,但是想到普通实现用 new 的时候就会 ,觉得得不偿失,最后没有采用。忽然想到一种 del 操作 new 操作 的实现,不过比较麻烦,那就以后实现吧。
最后有个小插曲,我发现,在 SPOJ 上 AC 的代码,在衡阳八中 OJ 上,居然 WA 了。一开始以为是数据错了,搞了半天发现,果然是数据问题,SPOJ 把数据合并了,开头有个 test ,而衡阳八中 OJ 是原始 NOI2005 数据,开头没有 test 。做到这里,我差点晕过去,果然状态不好的时候不应该碰这种繁琐题的 = =...
ps. 今天还有个插曲,我居然想不通如何维护乘法和加法的标记延迟了,囧~ 这什么状态,最后经大神提醒,终于知道怎么搞了。唉,看来今天是比较悲剧的。。。
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