Submission #64585

# Submission time Handle Problem Language Result Execution time Memory
64585 2018-08-05T00:37:33 Z qkxwsm Building Bridges (CEOI17_building) C++17
100 / 100
784 ms 22508 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 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;
}

Compilation message

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);
                 ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB Output is correct
2 Correct 3 ms 496 KB Output is correct
3 Correct 2 ms 496 KB Output is correct
4 Correct 3 ms 496 KB Output is correct
5 Correct 3 ms 500 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 117 ms 3700 KB Output is correct
2 Correct 112 ms 4772 KB Output is correct
3 Correct 112 ms 6040 KB Output is correct
4 Correct 92 ms 6648 KB Output is correct
5 Correct 241 ms 8860 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB Output is correct
2 Correct 3 ms 496 KB Output is correct
3 Correct 2 ms 496 KB Output is correct
4 Correct 3 ms 496 KB Output is correct
5 Correct 3 ms 500 KB Output is correct
6 Correct 117 ms 3700 KB Output is correct
7 Correct 112 ms 4772 KB Output is correct
8 Correct 112 ms 6040 KB Output is correct
9 Correct 92 ms 6648 KB Output is correct
10 Correct 241 ms 8860 KB Output is correct
11 Correct 128 ms 8860 KB Output is correct
12 Correct 120 ms 10000 KB Output is correct
13 Correct 86 ms 11092 KB Output is correct
14 Correct 94 ms 12284 KB Output is correct
15 Correct 784 ms 20452 KB Output is correct
16 Correct 331 ms 20452 KB Output is correct
17 Correct 556 ms 22508 KB Output is correct
18 Correct 138 ms 22508 KB Output is correct