제출 #64585

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
64585		qkxwsm	Building Bridges (CEOI17_building)	C++17	100 / 100	784 ms	22508 KiB

building

/*
PROG: source
LANG: C++11
_____
.'     '.
/  0   0  \
|     ^     |
|  \     /  |
\  '---'  /
'._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

struct chash
{
        int operator()(int x) const
        {
                x ^= (x >> 20) ^ (x >> 12);
                return x ^ (x >> 7) ^ (x >> 4);
        }
        int operator()(long long x) const
        {
                return x ^ (x >> 32);
        }
};

template<typename T> using orderedset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using hashtable = gp_hash_table<T, U, chash>;

template<class T>
void readi(T &x)
{
        T input = 0;
        bool negative = false;
        char c = ' ';
        while (c < '-')
        {
                c = getchar();
        }
        if (c == '-')
        {
                negative = true;
                c = getchar();
        }
        while (c >= '0')
        {
                input = input * 10 + (c - '0');
                c = getchar();
        }
        if (negative)
        {
                input = -input;
        }
        x = input;
}
template<class T>
void printi(T output)
{
        if (output == 0)
        {
                putchar('0');
                return;
        }
        if (output < 0)
        {
                putchar('-');
                output = -output;
        }
        int aout[20];
        int ilen = 0;
        while(output)
        {
                aout[ilen] = ((output % 10));
                output /= 10;
                ilen++;
        }
        for (int i = ilen - 1; i >= 0; i--)
        {
                putchar(aout[i] + '0');
        }
        return;
}
template<class T>
void ckmin(T &a, T b)
{
        a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
        a = max(a, b);
}
template<class T, class U>
T normalize(T x, U mod = 1000000007)
{
        return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
        return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
        return ((1ll << 15) * rand() + rand()) % mod;
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;

int N;
pll arr[MAXN];
ll dp[MAXN];
ll pref[MAXN];

struct chulldynamic
{
	vector<pll> hull, brutes;
	ll f(ll m, ll b, ll x)
	{
		return m * x + b;
	}
	ll overpass(pll a, pll b)
	{
		//when does line a pass line b?
		//m1x+b1<m2x+b2 -> (m2-m1)x>(b1-b2) -> x>(b1-b2)/(m2-m1)
		if (b.fi == a.fi)
		{
			if (a.se < b.se)
			{
				return -LLINF;
			}
			else
			{
				return LLINF;
			}
		}
		return (a.se - b.se)/(b.fi - a.fi);
	}
	void rebuild()
	{
		sort(brutes.begin(), brutes.end());
		reverse(hull.begin(), hull.end());
		vector<pll> temp;
		if (hull.back().fi > brutes.back().fi)
		{
			temp.PB(hull.back());
			hull.pop_back();
		}
		else
		{
			temp.PB(brutes.back());
			brutes.pop_back();
		}
		while(!hull.empty() || !brutes.empty())
		{
			pll cur;
			if (hull.empty() || (!hull.empty() && !brutes.empty() && brutes.back().fi > hull.back().fi))
			{
				cur = brutes.back();
				brutes.pop_back();
			}
			else
			{
				cur = hull.back();
				hull.pop_back();
			}
			while(temp.size() >= 2)
			{
				pll l0 = temp[temp.size() - 2], l1 = temp[temp.size() - 1];
				if (overpass(l1, l0) <= overpass(cur, l1))
				{
					break;
				}
				temp.pop_back();
			}
			temp.PB(cur);
		}
		hull = temp;
	}
	void insert(pll x)
	{
		if (hull.empty())
		{
			hull.PB(x);
			return;
		}
		brutes.PB(x);
		if (brutes.size() == MAGIC)
		{
			rebuild();
		}
	}
	ll query(ll x)
	{
		ll res = LLINF;
		int lo = 0, hi = hull.size() - 1;
		while(hi > lo)
		{
			int mid = (hi + lo + 1)/2;
			if (overpass(hull[mid], hull[mid - 1]) >= x)
			{
				hi = mid - 1;
			}
			else
			{
				lo = mid;
			}
		}
		res = f(hull[lo].fi, hull[lo].se, x);
		for (int i = 0; i < brutes.size(); i++)
		{
			res = min(res, f(brutes[i].fi, brutes[i].se, x));
		}
		return res;
	}
};

chulldynamic cht;

int32_t main()
{
        ios_base::sync_with_stdio(0);
        srand(time(0));
        //	cout << fixed << setprecision(10);
        //	cerr << fixed << setprecision(10);
        if (fopen("input.in", "r"))
        {
                freopen ("input.in", "r", stdin);
                freopen ("output.out", "w", stdout);
        }
        cin >> N;
        for (int i = 0; i < N; i++)
        {
                cin >> arr[i].fi;
        }
        for (int i = 0; i < N; i++)
        {
                cin >> arr[i].se;
        }
        for (int i = 0; i < N; i++)
        {
                pref[i + 1] = pref[i] + arr[i].se;
        }
        dp[0] = 0;
        for (int i = 0; i < N; i++)
        {
                if (i)
                {
                        // cerr << "query " << -2 * arr[i].fi << ' ' << cht.query(-2 * arr[i].fi) << endl;
                        dp[i] = cht.query(-2 * arr[i].fi) + (arr[i].fi * arr[i].fi + pref[i]);
                        // for (int j = 0; j < i; j++)
                        // {
                        //         //(arr[i] - arr[j])^2 = (arr[j]^2) - 2 * arr[i] * arr[j] + arr[i]^2
                        //         ckmin(dp[i], -2 * arr[i].fi * arr[j].fi + dp[j] + arr[j].fi * arr[j].fi - pref[j + 1]);
                        // }
                }
                pll cur = {arr[i].fi, dp[i] + arr[i].fi * arr[i].fi - pref[i + 1]};
                // cerr << cur.fi << "x + " << cur.se << endl;
                cht.insert(cur);
                // cerr << dp[i] << endl;
        }
        cout << dp[N - 1] << '\n';
        //	cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
        return 0;
}

컴파일 시 표준 에러 (stderr) 메시지

building.cpp: In member function 'll chulldynamic::query(ll)':
building.cpp:243:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for (int i = 0; i < brutes.size(); i++)
                   ~~^~~~~~~~~~~~~~~
building.cpp: In function 'int32_t main()':
building.cpp:261:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
                 freopen ("input.in", "r", stdin);
                 ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
building.cpp:262:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
                 freopen ("output.out", "w", stdout);
                 ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40