bzoj 1112 treap树

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<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define pii pair<int,int>
#define piii pair<int, pair<int,int> >

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("
"); }
    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
", ans);
    return 0;
}
/*
5 5
3 9 2 3 1
*/