Submission #75498

#	Time	Username	Problem	Language	Result	Execution time	Memory
75498		qkxwsm	Building Bridges (CEOI17_building)	C++17	0 / 100	6 ms	376 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 ordered_set = 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];
ordered_set<pll> chull;

ll overpass(pll x, pll y)
{
	ll m1 = x.fi, b1 = x.se, m2 = y.fi, b2 = y.se;
	//when does x beat y?
	if (m1 == m2)
	{
		if (b1 < b2) return -LLINF;
		else return LLINF;
	}
	//m1x + b1 <= m2x + b2
	//(m2 - m1) x >= (b1 - b2)
	//x >= (b1 - b2) / (m2 - m1)
	return (((b1 - b2) % (m2 - m1) || (b1 - b2) < 0) ? (b1 - b2) / (m2 - m1) : (b1 - b2) / (m2 - m1) + 1);
	// return (b1 - b2 + (m2 - m1 - 1)) / (m2 - m1);
}
void insert(ordered_set<pll> &a, pll x)
{
	if (a.empty())
	{
		a.insert(x);
		return;
	}
	auto it = a.LB(x);
	if (it == a.end())
	{
		if (a.rbegin() -> fi == x.fi)
		{
			return;
		}
		it--;
		while(it != a.begin() && overpass(*prev(it), *it) <= overpass(*it, x))
		{
			it = a.erase(it);
			it--;
		}
		a.insert(x);
		return;
	}
	else if (it == a.begin())
	{
		while(next(it) != a.end() && overpass(x, *it) <= overpass(*it, *next(it)))
		{
			it = a.erase(it);
		}
		a.insert(x);
		return;
	}
	bool change = false;
	do
	{
		change = false;
		while(next(it) != a.end() && overpass(x, *it) <= overpass(*it, *next(it)))
		{
			change = true;
			it = a.erase(it);
		}
		it--;
		while(it != a.begin() && overpass(*prev(it), *it) <= overpass(*it, x))
		{
			change = true;
			it = a.erase(it);
			it--;
		}
		it++;
	}
	while (change);
	it--;
	if (overpass(*it, x) > overpass(x, *next(it)))
	{
		a.insert(x);
	}
	return;
}
//take it to the left as
ll query(ll x, ordered_set<pll> &a)
{
	// ll res = LLINF;
	// for (pll p : a)
	// {
	// 	ckmin(res, p.fi * x + p.se);
	// }
	// return res;
	// cerr << "overpasses: ";
	// for (int i = 1; i < a.size() - 1; i++)
	// {
	// 	pll pr = *a.find_by_order(i - 1), pm = *a.find_by_order(i), pl = *a.find_by_order(i + 1);
	// 	// assert(overpass(pr, pm) > overpass(pm, pl));
	// 	// assert(pr.fi != pm.fi && pm.fi != pl.fi);
	// 	// cerr << overpass(pr, pm) << ' ';
	// }
	// cerr << overpass(*a.find_by_order(a.size() - 2), *a.find_by_order(a.size() - 1)) << endl;
	// debug(x);
	// cerr << endl;
	// if (a.empty())
	// {
	// 	return 0ll;
	// }
	//find p such that overpass(p, p + 1) <= x
	//it decreases, and you want first guy such that f(p, p + 1) to be <= x
	int lo = 0, hi = a.size() - 1;
	while(hi > lo)
	{
		int mid = (lo + hi) / 2;
		auto it = a.find_by_order(mid);
		pll pr = *it, pl = *next(it);
		if (overpass(pr, pl) <= x)
		{
			hi = mid;
		}
		else
		{
			lo = mid + 1;
		}
	}
	//find the biggest p such that overpass(p, p + 1) <= x
	auto it = a.find_by_order(lo);
	// assert(next(it) == a.end() || overpass(*it, *next(it)) <= x);
	// cerr << "contains: ";
	// for (pll x : a)
	// {
	// 	cerr << x.fi << "x + " << x.se << endl;
	// }
	// if (it != a.begin())
	// {
	// 	assert(overpass(*prev(it), *it) > x);
	// }
	// cerr << "query " << x << " just beat " << (next(it) == a.end() ? -LLINF : overpass(*it, *next(it)));
	// cerr << "query " << x << " get " << opt.fi * x + opt.se << endl;
	ll res = LLINF;
	for (pll p : a)
	{
		ckmin(res, p.fi * x + p.se);
		// cerr << p.fi * x + p.se << ' ';
	}
	// cerr << "send " << it -> fi * x + it -> se << endl;
	// return res;
	return it -> fi * x + it -> se;
}
int32_t main()
{
	ios_base::sync_with_stdio(0);
	srand(time(0));
	//	cout << fixed << setprecision(10);
	//	cerr << fixed << setprecision(10);
	freopen ("file.in", "r", stdin);
	freopen ("file.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 << ' ' << query(-2 * arr[i].fi, chull) << endl;
			dp[i] = query(-2 * arr[i].fi, chull) + (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 << "insert " << cur.fi << "x + " << cur.se << endl;
		insert(chull, cur);
		// cerr << "contents of chull:\n";
		// for (pll x : chull)
		// {
		// 	cerr << x.fi << "x + " << x.se << endl;
		// }
		// cerr << dp[i] << endl;
	}
	cout << dp[N - 1] << '\n';
	//	cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}

Compilation message (stderr)

building.cpp: In function 'int32_t main()':
building.cpp:293:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  freopen ("file.in", "r", stdin);
  ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
building.cpp:294:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  freopen ("file.out", "w", stdout);
  ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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• Subtask 2: 0 / 30
• Subtask 3: 0 / 40