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HYSBZ 1588 营业额统计
题目链接:http://www.lydsy.com/JudgeOnline/problem.php?id=1588
题意:详见题面,中文
思路:平衡树的模板题。 可用Treap,Splay,Scapegoat Tree。
【替罪羊树代码】
#define _CRT_SECURE_NO_DEPRECATE#include<stdio.h> #include<string.h> #include<cstring>#include<algorithm> #include<queue> #include<math.h> #include<time.h>#include<vector>#include<iostream>using namespace std;typedef long long int LL;const int INF = 0x3f3f3f3f;typedef long long LL;namespace Scapegoat_Tree {#define MAXN (1000000 + 10) const double alpha = 0.75; struct Node { Node * ch[2]; int key, size, cover; // size为有效节点的数量,cover为节点总数量 bool exist; // 是否存在(即是否被删除) void PushUp(void) { size = ch[0]->size + ch[1]->size + (int)exist; cover = ch[0]->cover + ch[1]->cover + 1; } bool isBad(void) { // 判断是否需要重构 return ((ch[0]->cover > cover * alpha + 5) || (ch[1]->cover > cover * alpha + 5)); } }; struct STree { protected: Node mem_poor[MAXN]; //内存池,直接分配好避免动态分配内存占用时间 Node *tail, *root, *null; // 用null表示NULL的指针更方便,tail为内存分配指针,root为根 Node *bc[MAXN]; int bc_top; // 储存被删除的节点的内存地址,分配时可以再利用这些地址 Node * NewNode(int key) { Node * p = bc_top ? bc[--bc_top] : tail++; p->ch[0] = p->ch[1] = null; p->size = p->cover = 1; p->exist = true; p->key = key; return p; } void Travel(Node * p, vector<Node *>&v) { if (p == null) return; Travel(p->ch[0], v); if (p->exist) v.push_back(p); // 构建序列 else bc[bc_top++] = p; // 回收 Travel(p->ch[1], v); } Node * Divide(vector<Node *>&v, int l, int r) { if (l >= r) return null; int mid = (l + r) >> 1; Node * p = v[mid]; p->ch[0] = Divide(v, l, mid); p->ch[1] = Divide(v, mid + 1, r); p->PushUp(); // 自底向上维护,先维护子树 return p; } void Rebuild(Node * &p) { static vector<Node *>v; v.clear(); Travel(p, v); p = Divide(v, 0, v.size()); } Node ** Insert(Node *&p, int val) { if (p == null) { p = NewNode(val); return &null; } else { p->size++; p->cover++; // 返回值储存需要重构的位置,若子树也需要重构,本节点开始也需要重构,以本节点为根重构 Node ** res = Insert(p->ch[val >= p->key], val); if (p->isBad()) res = &p; return res; } } void Erase(Node *p, int id) { p->size--; int offset = p->ch[0]->size + p->exist; if (p->exist && id == offset) { p->exist = false; return; } else { if (id <= offset) Erase(p->ch[0], id); else Erase(p->ch[1], id - offset); } } public: void Init(void) { tail = mem_poor; null = tail++; null->ch[0] = null->ch[1] = null; null->cover = null->size = null->key = 0; root = null; bc_top = 0; } STree(void) { Init(); } void Insert(int val) { Node ** p = Insert(root, val); if (*p != null) Rebuild(*p); } int Rank(int val) { //相同值取最小的排名 Node * now = root; int ans = 1; while (now != null) { // 非递归求排名 if (now->key >= val) now = now->ch[0]; else { ans += now->ch[0]->size + now->exist; now = now->ch[1]; } } return ans; } int Kth(int k) { //支持相同值 Node * now = root; while (now != null) { // 非递归求第K大 if (now->ch[0]->size + 1 == k && now->exist) return now->key; else if (now->ch[0]->size >= k) now = now->ch[0]; else k -= now->ch[0]->size + now->exist, now = now->ch[1]; } } void Erase(int k) { Erase(root, Rank(k)); if (root->size < alpha * root->cover) Rebuild(root); } void Erase_kth(int k) { Erase(root, k); if (root->size < alpha * root->cover) Rebuild(root); } };#undef MAXN}using namespace Scapegoat_Tree;STree Scapegoat;int main(){ #ifdef kirito freopen("in.txt","r",stdin); freopen("out.txt","w",stdout); #endif // int start = clock(); int n,val; while (~scanf("%d", &n)){ LL sum=0; for (int i = 1; i <= n; i++){ scanf("%d", &val); if (i == 1){ sum += val; } else{ int valRank = Scapegoat.Rank(val); int a = abs(Scapegoat.Kth(valRank) - val); int b = abs(Scapegoat.Kth(valRank - 1) - val); int c = abs(Scapegoat.Kth(val + 1) - val); sum += min(a, min(b, c)); } Scapegoat.Insert(val); } printf("%d\n", sum); /* DEBUG INFO vector<Node *> xx; _t.Travel(_t.root, xx); cout << "::"; for(int i = 0; i < xx.size(); i++) cout << xx[i]->key << ‘ ‘; cout << endl; */ } //#ifdef LOCAL_TIME // cout << "[Finished in " << clock() - start << " ms]" << endl; //#endif return 0;}
【Splay代码】
#define _CRT_SECURE_NO_DEPRECATE#include<stdio.h> #include<string.h> #include<cstring>#include<algorithm> #include<queue> #include<math.h> #include<time.h>#include<vector>#include<iostream>using namespace std;typedef long long int LL;const int MAXN = 1e6 + 5;const int INF = 0x3f3f3f3f;int cnt, rt;struct Tree{ int key, size, fa, son[2]; void set(int _key, int _size, int _fa) { key = _key; size = _size; fa = _fa; son[0] = son[1] = 0; }}T[MAXN];inline void PushUp(int x){ T[x].size = T[T[x].son[0]].size + T[T[x].son[1]].size + 1;}inline void Rotate(int x, int p) { int y = T[x].fa; T[y].son[!p] = T[x].son[p]; T[T[x].son[p]].fa = y; T[x].fa = T[y].fa; if (T[x].fa) T[T[x].fa].son[T[T[x].fa].son[1] == y] = x; T[x].son[p] = y; T[y].fa = x; PushUp(y); PushUp(x);}void Splay(int x, int To) { while (T[x].fa != To) { if (T[T[x].fa].fa == To) Rotate(x, T[T[x].fa].son[0] == x); else { int y = T[x].fa, z = T[y].fa; int p = (T[z].son[0] == y); if (T[y].son[p] == x) Rotate(x, !p), Rotate(x, p); else Rotate(y, p), Rotate(x, p); } } if (To == 0) rt = x;}int find(int key) { int x = rt; while (x && T[x].key != key) x = T[x].son[key > T[x].key]; if (x) Splay(x, 0); return x;}int prev() { int x = T[rt].son[0]; if (!x) return 0; while (T[x].son[1]) x = T[x].son[1]; //Splay(x, 0); return x;}int succ() { int x = T[rt].son[1]; if (!x) return 0; while (T[x].son[0]) x = T[x].son[0]; //Splay(x, 0); return x;}void Insert(int key) { if (!rt) T[rt = cnt++].set(key, 1, 0); else { int x = rt, y = 0; while (x) { y = x; x = T[x].son[key > T[x].key]; } T[x = cnt++].set(key, 1, y); T[y].son[key > T[y].key] = x; Splay(x, 0); }}void Delete(int key) { int x = find(key); if (!x) return; int y = T[x].son[0]; while (T[y].son[1]) y = T[y].son[1]; int z = T[x].son[1]; while (T[z].son[0]) z = T[z].son[0]; if (!y && !z) { rt = 0; return; } if (!y) { Splay(z, 0); T[z].son[0] = 0; PushUp(z); return; } if (!z) { Splay(y, 0); T[y].son[1] = 0; PushUp(y); return; } Splay(y, 0); Splay(z, y); T[z].son[0] = 0; PushUp(z); PushUp(y);}int GetPth(int p) { if (!rt) return 0; int x = rt, ret = 0; while (x) { if (p == T[T[x].son[0]].size + 1) break; if (p>T[T[x].son[0]].size + 1) { p -= T[T[x].son[0]].size + 1; x = T[x].son[1]; } else x = T[x].son[0]; } Splay(x, 0); return x;}int GetRank(int key) { if (!rt) return 0; int x = rt, ret = 0, y; while (x) { y = x; if (T[x].key <= key) { ret += T[T[x].son[0]].size + 1; x = T[x].son[1]; } else x = T[x].son[0]; } Splay(y, 0); return ret;}int main(){ //#ifdef kirito // freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); //#endif // int start = clock(); int n; while (~scanf("%d", &n)){ LL ans = 0; rt = 0; cnt = 1; T[0].set(INF, 1, 0); for (int i = 1; i <= n; i++){ int val; scanf("%d", &val); Insert(val); if (i == 1){ ans = val; } else{ ans += min(abs(val - T[succ()].key), abs(val - T[prev()].key)); } } printf("%lld\n", ans); } //#ifdef LOCAL_TIME // cout << "[Finished in " << clock() - start << " ms]" << endl; //#endif return 0;}
HYSBZ 1588 营业额统计
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