Submission #900356

#	Time	Username	Problem	Language	Result	Execution time	Memory
900356		gaga999	Aliens (IOI16_aliens)	C++17	100 / 100	152 ms	8652 KiB

aliens

#include <cstdio>
#include <stdio.h>
#include <iostream>
#include <math.h>
#include <vector>
#include <queue>
#include <stack>
#include <deque>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
#include <stdlib.h>
#include <cstring>
#include <string.h>
#include <string>
#include <sstream>
#include <assert.h>
#include <climits>
#include <sstream>
#include <numeric>
#include <time.h>
#include <limits.h>
#include <list>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <iomanip>
#include <complex>
#include <chrono>
#include <fstream>
#include <functional>
#include <unistd.h>
// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx,avx2,bmi,bmi2,lzcnt,popcnt")
#define lowbit(x) ((x) & -(x))
#define ml(a, b) ((1ll * (a) * (b)) % M)
#define tml(a, b) (a) = ((1ll * (a) * (b)) % M)
#define ad(a, b) ((0ll + (a) + (b)) % M)
#define tad(a, b) (a) = ((0ll + (a) + (b)) % M)
#define mi(a, b) ((0ll + M + (a) - (b)) % M)
#define tmi(a, b) (a) = ((0ll + M + (a) - (b)) % M)
#define tmin(a, b) (a) = min((a), (b))
#define tmax(a, b) (a) = max((a), (b))
#define iter(a) (a).begin(), (a).end()
#define riter(a) (a).rbegin(), (a).rend()
#define init(a, b) memset((a), (b), sizeof(a))
#define cpy(a, b) memcpy((a), (b), sizeof(a))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define pb emplace_back
#define mpr make_pair
#define ls(i) ((i) << 1)
#define rs(i) ((i) << 1 | 1)
#define INF 0x3f3f3f3f
#define NIF 0xc0c0c0c0
#define eps 1e-9
#define F first
#define S second
#define AC cin.tie(0)->sync_with_stdio(0)
using namespace std;
typedef long long llt;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef pair<llt, llt> pll;
typedef complex<double> cd;
// const int M = 998244353;

// random_device rm;
// mt19937 rg(rm());
// default_random_engine rg(rm());
// uniform_int_distribution<int> rd(INT_MIN, INT_MAX);
// uniform_real_distribution<double> rd(0, M_PI);

void db() { cerr << "\n"; }
template <class T, class... U>
void db(T a, U... b) { cerr << a << " ", db(b...); }

inline char gc()
{
    const static int SZ = 1 << 16;
    static char buf[SZ], *p1, *p2;
    if (p1 == p2 && (p2 = buf + fread(p1 = buf, 1, SZ, stdin), p1 == p2))
        return -1;
    return *p1++;
}
void rd() {}
template <typename T, typename... U>
void rd(T &x, U &...y)
{
    x = 0;
    bool f = 0;
    char c = gc();
    while (!isdigit(c))
        f ^= !(c ^ 45), c = gc();
    while (isdigit(c))
        x = (x << 1) + (x << 3) + (c ^ 48), c = gc();
    f && (x = -x), rd(y...);
}

template <typename T>
void prt(T x)
{
    if (x < 0)
        putchar('-'), x = -x;
    if (x > 9)
        prt(x / 10);
    putchar((x % 10) ^ 48);
}

struct L
{
    llt a, b;
    inline llt operator()(llt x) { return a * x + b; }
};

inline llt itp(const L &l1, const L &l2)
{
    return (l1.b - l2.b) / (l2.a - l1.a);
}

inline bool ck(const L &l1, const L &l2, const L &l3)
{
    return itp(l2, l3) <= itp(l1, l2);
}

const int N = 1e5 + 5;
pll pt[N];
vector<pll> ar(1, mpr(-1, -1));
llt dp[N], vv;
int fr[N];

void slv(int n)
{
    deque<pair<L, int>> q;
    q.pb(mpr(L{-2 * ar[1].F, ar[1].F * ar[1].F}, 0));
    for (int i = 1; i <= n; i++)
    {
        while (q.size() > 1 && q[1].F(ar[i].S) <= q[0].F(ar[i].S))
            q.pop_front();
        fr[i] = q[0].S + 1, dp[i] = q[0].F(ar[i].S) + ar[i].S * ar[i].S + vv;
        if (i == n)
            return;
        L tp = {-2 * ar[i + 1].F, dp[i] + ar[i + 1].F * ar[i + 1].F};
        if (ar[i].S > ar[i + 1].F)
            tp.b -= (ar[i].S - ar[i + 1].F) * (ar[i].S - ar[i + 1].F);
        while (q.size() > 1 && ck(q[q.size() - 2].F, q.back().F, tp))
            q.pop_back();
        q.pb(mpr(tp, fr[i]));
    }
}

llt take_photos(int n, int m, int k, vector<int> xr, vector<int> yr)
{
    for (int i = 0; i < n; i++)
    {
        pt[i].F = xr[i], pt[i].S = yr[i];
        if (pt[i].F > pt[i].S)
            swap(pt[i].F, pt[i].S);
        pt[i].S++;
    }
    sort(pt, pt + n);
    for (int i = 0; i < n; i++)
    {
        if (pt[i].F == ar.back().F)
            tmax(ar.back().S, pt[i].S);
        else if (pt[i].S > ar.back().S)
            ar.pb(pt[i]);
    }
    n = ar.size() - 1, tmin(k, n);
    llt l = 0ll, r = 100000000000ll;
    while (l < r - 1)
    {
        vv = (l + r) >> 1, slv(n);
        if (fr[n] == k)
            return dp[n] - vv * k;
        if (fr[n] > k)
            l = vv;
        else
            r = vv;
    }
    vv = l, slv(n);
    llt a1 = dp[n] - vv * fr[n], p1 = fr[n];
    vv = r, slv(n);
    llt a2 = dp[n] - vv * fr[n], p2 = fr[n];
    vv = l, slv(n);
    return a1 + (a1 - a2) / (p1 - p2) * (k - p1);
}

// signed main()
// {
//     int n, m, k;
//     rd(n, m, k);
//     vector<int> xr(n), yr(n);
//     for (int i = 0; i < n; i++)
//         rd(xr[i], yr[i]);
//     cerr << take_photos(n, m, k, xr, yr) << ' ';
// }

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40