思路:我们只要check一遍每个长度为k的区间就好啦,对于一个区间来说的最优值显然是中位数,我们显然要动态求
第k大,所以需要一个二叉搜索树,用treap就好啦。
#include#define LL long long#define fi first#define se second#define mk make_pair#define pii pair #define piii pair >using namespace std;const int N = 2e5 + 10;const int M = 10 + 7;const int inf = 0x3f3f3f3f;const LL INF = 0x3f3f3f3f3f3f3f3f;const int mod = 1e9 + 7;const double eps = 1e-6;int n, k, a[N];struct node { node* ch[2]; int key, fix, sz, cnt; LL sum; void update() { sz = ch[0]->sz + ch[1]->sz + cnt; sum = ch[0]->sum + ch[1]->sum + 1ll * cnt * key; }};typedef node* P_node;struct Treap { node base[N], nil; P_node root, null, len; Treap() { root = null = &nil; null->key = null->fix = 1e9; null->sz = null->cnt = null->sum = 0; null->ch[0] = null->ch[1] = null; len = base; } P_node newnode(int tkey) { len->key = tkey; len->fix = rand(); len->ch[0] = len->ch[1] = null; len->sz = len->cnt = 1; len->sum = tkey; return len++; } void rot(P_node &p, int d) { P_node k = p->ch[d ^ 1]; p->ch[d ^ 1] = k->ch[d]; k->ch[d] = p; p->update(); k->update(); p = k; } void _Insert(P_node &p, int tkey) { if(p == null) { p = newnode(tkey); } else if(p->key == tkey) { p->cnt++; } else { int d = tkey > p->key; _Insert(p->ch[d], tkey); if(p->ch[d]->fix > p->fix) { rot(p, d ^ 1); } } p->update(); } void _Delete(P_node &p, int tkey) { if(p == null) return; if(p->key == tkey) { if(p->cnt > 1) p->cnt--; else if(p->ch[0] == null) p = p->ch[1]; else if(p->ch[1] == null) p = p->ch[0]; else { int d = p->ch[0]->fix > p->ch[1]->fix; rot(p, d); _Delete(p->ch[d], tkey); } } else { _Delete(p->ch[tkey > p->key], tkey); } p->update(); } int _Kth(P_node p, int k) { if(p == null || k < 1 || k > p->sz) return 0; if(k < p->ch[0]->sz + 1) return _Kth(p->ch[0], k); if(k > p->ch[0]->sz + p->cnt) return _Kth(p->ch[1], k - p->ch[0]->sz - p->cnt); return p->key; } int _Rank(P_node p, int tkey, int res) { if(p == null) return -1; if(p->key == tkey) return p->ch[0]->sz + res + 1; if(tkey < p->key) return _Rank(p->ch[0], tkey, res); return _Rank(p->ch[1], tkey, res + p->ch[0]->sz + p->cnt); } int _Pred(P_node p, int tkey){ if(p == null) return -1e9; if(tkey <= p->key) return _Pred(p->ch[0], tkey); return max(p->key, _Pred(p->ch[1], tkey)); } int _Succ(P_node p, int tkey){ if(p == null) return 1e9; if(tkey >= p->key) return _Succ(p->ch[1], tkey); return min(p->key, _Succ(p->ch[0], tkey)); } void _Print(P_node p){ if(p == null) return; _Print(p -> ch[0]); for(int i = 1; i <= p->cnt; i++) printf("%d ",p->key); _Print(p->ch[1]); } LL _Query(P_node p, int tkey) { if(p == null) return 0; if(p->key == tkey) { return 1ll * tkey * p->ch[0]->sz - p->ch[0]->sum + p->ch[1]->sum - 1ll * tkey * p->ch[1]->sz; } else if(p->key < tkey) { return 1ll * tkey * (p->ch[0]->sz + p->cnt) - (p->ch[0]->sum + 1ll * p->cnt * p->key) + _Query(p->ch[1], tkey); } else { return (p->ch[1]->sum + 1ll * p->cnt * p->key) - 1ll * tkey * (p->ch[1]->sz + p->cnt) + _Query(p->ch[0], tkey); } } void Insert(int tkey){ _Insert(root,tkey); } void Delete(int tkey){ _Delete(root,tkey); } int Kth(int k){ return _Kth(root,k); } int Rank(int tkey){ return _Rank(root,tkey,0); } int Pred(int tkey){ return _Pred(root,tkey); } int Succ(int tkey){ return _Succ(root,tkey); } void Print(){ _Print(root); printf("\n"); } LL Query(int tkey) { return _Query(root, tkey); }}tp;int main() { scanf("%d%d", &n, &k); for(int i = 1; i <= n; i++) { scanf("%d", &a[i]); } for(int i = 1; i <= k; i++) { tp.Insert(a[i]); } int l = 1, r = k, mid = k / 2; if(k & 1) mid++; LL ans = INF; while(r <= n) { int num = tp.Kth(mid); ans = min(ans, tp.Query(num)); tp.Delete(a[l++]); tp.Insert(a[++r]); } printf("%lld\n", ans); return 0;}/*5 53 9 2 3 1*/