2020 Petrozavodsk Winter Camp, Jagiellonian U Contest

目录

• Problem C. Bookface 保序回归
• AC Code2

dalao题解
题面和官方题解

Problem C. Bookface 保序回归

链接：点我点我

做法1：优先队列维护dp转折点
链接：点我点我

做法2：左偏树维护中位数
原题P4331my详细讲解
本题有一点麻烦的地方在于要保证\(c_i\)数组永远不为负数。所以对生成的序列要做一点修改。

AC Code2

/*
链接：
[点我点我](https://codeforces.com/gym/102576/problem/C)
题意：
n(2e5),d([1,1e6]),c_i([0,3e11])，每次操作可以把一个数加一或者减一，问最少操作次数使得对
任意(i < j)满足abs(c_j - c_i)大于等于d。
思路：
保序回归论文题
*/
#pragma comment(linker, "/STACK:102400000,102400000")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize(3,"Ofast","inline")
#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#define fi first
#define se second
#define o2(x) (x) * (x)
#define mk make_pair
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define clr(a, b) memset((a), (b), sizeof((a)))
#define rep(i,s,t) for(register int i=s;i<t;++i)
#define per(i,s,t) for(register int i=s;i>=t;--i)
#define GKD std::ios::sync_with_stdio(false);cin.tie(0)
#define my_unique(x) sort(all(x)), x.erase(unique(all(x)), x.end())
using namespace std;
typedef long long LL;
typedef long long int64;
typedef unsigned long long uint64;
typedef pair<int, int> pii;
// mt19937 rng(time(NULL));
// mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
// mt19937_64 generator(std::clock());
// shuffle(arr, arr + n, generator);
inline int64 read() {
    int64 x = 0;int f = 0;char ch = getchar();
    while (ch < '0' || ch > '9') f |= (ch == '-'), ch = getchar();
    while (ch >= '0' && ch <= '9') x = (x << 3) + (x << 1) + ch - '0', ch =
    getchar(); return x = f ? -x : x;
}
inline void write(int64 x, bool f = true) {
    if (x == 0) {putchar('0'); if(f)putchar('\n');else putchar(' ');return;}
    if (x < 0) {putchar('-');x = -x;}
    static char s[23];
    int l = 0;
    while (x != 0)s[l++] = x % 10 + 48, x /= 10;
    while (l)putchar(s[--l]);
    if(f)putchar('\n');else putchar(' ');
}
int lowbit(int x) { return x & (-x); }
template <class T>
T big(const T &a1, const T &a2) {return a1 > a2 ? a1 : a2;}
template <class T>
T sml(const T &a1, const T &a2) {return a1 < a2 ? a1 : a2;}
template <typename T, typename... R>
T big(const T &f, const R &... r) {return big(f, big(r...));}
template <typename T, typename... R>
T sml(const T &f, const R &... r) {return sml(f, sml(r...));}
void debug_out() { cout << '\n'; }
template <typename T, typename... R>
void debug_out(const T &f, const R &... r) {
    cout << f << " ";
    debug_out(r...);
}
#ifdef LH_LOCAL
#define debug(...) cout << "[" << #__VA_ARGS__ << "]: ", debug_out(__VA_ARGS__);
#else
#define debug(...) ;
#endif
/*================Header Template==============*/
const int INF = 0x3f3f3f3f;
const int mod = 998244353;// 998244353
const int MXN = 1e6 + 5;
const int MXE = 2e6 + 5;
int n, m;
int64 d, br[MXN];
class Stack {
public:
    int l, r, rt, sz;
    int64 val;
};
int top;
Stack stk[MXN];
class Node {
public:
    int l, r, d;
    int64 val;
    int fa;
}tr[MXE];
bool cmp(const Node&a, const Node&b) {
    return a.val < b.val;
}
void push_up(int x) {
    if(!x) return ;
    if(tr[x].d != tr[tr[x].r].d + 1) {
        tr[x].d = tr[tr[x].r].d + 1;
        push_up(tr[x].fa);
    }
}
int delx(int x, int y) {
    if(!x || !y) return x | y;
    if(tr[x].val < tr[y].val) swap(x, y);
    tr[x].r = delx(tr[x].r, y);
    tr[tr[x].r].fa = x;
    push_up(x);
    return x;
}
int merge(int x, int y) {
    if(!x || !y) return x | y;
    if(tr[x].val < tr[y].val) swap(x, y);
    tr[x].r = merge(tr[x].r, y);
    tr[tr[x].r].fa = x;
    if(tr[tr[x].r].d > tr[tr[x].l].d) swap(tr[x].l, tr[x].r);
    tr[x].d = tr[tr[x].r].d + 1;
    push_up(x);
    return x;
}

int main() {
#ifdef LH_LOCAL
    freopen("D:in.txt", "r", stdin);
    //freopen("D:out.txt", "w", stdout);
#endif
    int tim = read();
    while(tim --) {
        n = read();
        d = read();
        rep(i, 1, n + 1) tr[i].val = read();
        sort(tr + 1, tr + n + 1, cmp);
        rep(i, 1, n + 1) {
            tr[i].val = tr[i].val - d * (i - 1);
            if(i == 1) {
                stk[++ top] = {i, i, i, 1, tr[i].val};
                continue;
            }
            stk[++ top] = {i, i, i, 1, tr[i].val};
            while(top ^ 1 && stk[top].val < stk[top - 1].val) {
                -- top;
                stk[top].r = stk[top + 1].r;
                stk[top].rt = merge(stk[top].rt, stk[top + 1].rt);
                stk[top].sz += stk[top + 1].sz;
                while(stk[top].sz > (stk[top].r - stk[top].l + 1 + 1) / 2) {
                    -- stk[top].sz;
                    stk[top].rt = merge(tr[stk[top].rt].l, tr[stk[top].rt].r);
                }
                stk[top].val = tr[stk[top].rt].val;
            }
        }
        int p = 1;
        int64 ans = 0, add = 0;
        rep(i, 1, n + 1) {
            tr[i].val += d * (i - 1);
            while(p < top && i > stk[p].r) ++ p;
            br[i] = stk[p].val + d * (i - 1);
            if(br[i] < 0) add = 0 - br[i];
            br[i] += add;
            add = 0;
            if(i > 1 && br[i] - br[i - 1] < d) {
                add += br[i - 1] + d - br[i];
            }
            br[i] += add;
            add = 0;
            ans += abs(tr[i].val - br[i]);
            //printf("%lld%c", br[i], " \n"[i == n]);
        }
        printf("%lld\n", ans);
        //rep(i, 1, n + 1) printf("%lld%c", br[i], " \n"[i == n]);
        if(tim) rep(i, 1, n + 1) tr[i] = {0, 0, 0, 0, 0};
        top = 0;
    }
#ifdef LH_LOCAL
    cout << "time cost:" << 1.0 * clock() / CLOCKS_PER_SEC << "s" << endl;
    // system("pause");
#endif
    return 0;
}