Submission #75500

# Submission time Handle Problem Language Result Execution time Memory
75500 2018-09-10T00:44:45 Z qkxwsm Building Bridges (CEOI17_building) C++17
100 / 100
494 ms 15560 KB
/*
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;
	// 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;
}
# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 452 KB Output is correct
3 Correct 2 ms 464 KB Output is correct
4 Correct 3 ms 464 KB Output is correct
5 Correct 3 ms 604 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 208 ms 3640 KB Output is correct
2 Correct 210 ms 3876 KB Output is correct
3 Correct 209 ms 3932 KB Output is correct
4 Correct 209 ms 3932 KB Output is correct
5 Correct 279 ms 4908 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 452 KB Output is correct
3 Correct 2 ms 464 KB Output is correct
4 Correct 3 ms 464 KB Output is correct
5 Correct 3 ms 604 KB Output is correct
6 Correct 208 ms 3640 KB Output is correct
7 Correct 210 ms 3876 KB Output is correct
8 Correct 209 ms 3932 KB Output is correct
9 Correct 209 ms 3932 KB Output is correct
10 Correct 279 ms 4908 KB Output is correct
11 Correct 166 ms 5040 KB Output is correct
12 Correct 228 ms 6044 KB Output is correct
13 Correct 89 ms 7008 KB Output is correct
14 Correct 196 ms 8380 KB Output is correct
15 Correct 494 ms 15560 KB Output is correct
16 Correct 278 ms 15560 KB Output is correct
17 Correct 35 ms 15560 KB Output is correct
18 Correct 32 ms 15560 KB Output is correct