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답안 #630172

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
630172 2022-08-15T20:00:13 Z vovamr 3D Histogram (COCI20_histogram) C++17
110 / 110
 544 ms 41712 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) 	(x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }

const int N = 2e5 + 100;

struct line {
	ll k, b;
	line() : k(0), b(0) {}
	line(ll k, ll b) : k(k), b(b) {}
	inline ll operator()(const ll &x) { return k * x + b; }
};
inline bool operator < (const line &a, const line &b) {
	if (a.k < b.k) return 1;
	else if (a.k > b.k) return 0;
	else return a.b > b.b;
}
inline bool bad(const line &a, const line &b, const line &c) {
	return (ld)(a.b - c.b) * (b.k - a.k) <= (ld)(c.k - a.k) * (a.b - b.b);
}

int a[N], b[N];
int mna[N], mnb[N];

int ptr[N];
ve<line> cht[4 * N];

inline void build(int v, int vl, int vr, const int &border) {
	if (vl == vr) {
		if (vl <= border)
			cht[v] = {line(mnb[vl], -vl * 1ll * mnb[vl])};
		else
			cht[v] = {line(mnb[vl], +vl * 1ll * mnb[vl])};
		return;
	}

	int m = vl + vr >> 1;
	build(2 * v + 1, vl, m, border);
	build(2 * v + 2, m + 1, vr, border);
	merge(all(cht[2 * v + 1]), all(cht[2 * v + 2]), back_inserter(cht[v]));

	ve<line> s;
	for (auto &c : cht[v]) {
		if (!sz(s)) s.pb(c);
		else {
			if (s.back().k == c.k) continue;
			while (sz(s) >= 2) {
				const line &a = s[sz(s) - 2];
				const line &b = s[sz(s) - 1];
				if (bad(a, b, c)) s.pop_back();
				else break;
			} s.pb(c);
		}
	} cht[v] = s;
}
inline void clear(int v, int vl, int vr) {
	cht[v].clear();
	ptr[v] = 0;
	if (vl == vr) return;
	int m = vl + vr >> 1;
	clear(2 * v + 1, vl, m);
	clear(2 * v + 2, m + 1, vr);
}

inline ll get(int v, int vl, int vr, int l, int r, ll x) {
	if (l > r || !sz(cht[v])) return -inf;
	else if (vl == l && vr == r) {
		while (ptr[v] + 1 < sz(cht[v]) && cht[v][ptr[v]](x) < cht[v][ptr[v] + 1](x)) ++ptr[v];
		return cht[v][ptr[v]](x);
	}
	int m = vl + vr >> 1;
	return max(get(2*v+1,vl,m,l,min(r,m),x),get(2*v+2,m+1,vr,max(l,m+1),r,x));
}

ll ans = 0;

inline void solve(int l, int r) {
	if (l == r) return void(chmax(ans, a[l] * 1ll * b[l]));

	int m = l + r >> 1;

	mna[m] = a[m], mna[m + 1] = a[m + 1];
	for (int i = m - 1; i >= l; --i) mna[i] = min(mna[i + 1], a[i]);
	for (int i = m + 2; i <= r; ++i) mna[i] = min(mna[i - 1], a[i]);

	mnb[m] = b[m], mnb[m + 1] = b[m + 1];
	for (int i = m - 1; i >= l; --i) mnb[i] = min(mnb[i + 1], b[i]);
	for (int i = m + 1; i <= r; ++i) mnb[i] = min(mnb[i - 1], b[i]);

	int p1, p2;

	p1 = p2 = m;
	for (int i = m + 1; i <= r; ++i) {
		while (p1 >= l && mna[p1] >= mna[i]) --p1;
		while (p2 >= l && mnb[p2] >= mnb[i]) --p2;
		int pos = max(p1, p2) + 1;
		if (pos <= m) {
			assert(min(mna[pos], mna[i]) == mna[i]);
			assert(min(mnb[pos], mnb[i]) == mnb[i]);
			chmax(ans, mna[i] * 1ll * mnb[i] * 1ll * (i - pos + 1));
		}
	}

	p1 = p2 = m + 1;
	for (int i = m; i >= l; --i) {
		while (p1 <= r && mna[p1] >= mna[i]) ++p1;
		while (p2 <= r && mnb[p2] >= mnb[i]) ++p2;
		int pos = min(p1, p2) - 1;
		if (pos >= m + 1) {
			assert(min(mna[pos], mna[i]) == mna[i]);
			assert(min(mnb[pos], mnb[i]) == mnb[i]);
			chmax(ans, mna[i] * 1ll * mnb[i] * 1ll * (pos - i + 1));
		}
	}

	build(0, l, r, m);

	p1 = p2 = m;
	for (int i = m + 1; i <= r; ++i) {
		while (p1 >= l && mna[p1] >= mna[i]) --p1;
		while (p2 >= l && mnb[p2] >= mnb[i]) --p2;
		if (p1 + 1 <= p2) {
			ll C = get(0, l, r, p1 + 1, p2, i + 1);
			chmax(ans, mna[i] * 1ll * C);
		}
	}

	p1 = p2 = m + 1;
	for (int i = m; i >= l; --i) {
		while (p1 <= r && mna[p1] >= mna[i]) ++p1;
		while (p2 <= r && mnb[p2] >= mnb[i]) ++p2;
		if (p2 <= p1 - 1) {
			ll C = get(0, l, r, p2, p1 - 1, -(i - 1));
			chmax(ans, mna[i] * 1ll * C);
		}
	}

	clear(0, l, r);

	solve(l, m);
	solve(m + 1, r);
}

inline void solve() {
	int n;
	cin >> n;
	for (int i = 0; i < n; ++i) cin >> a[i] >> b[i];

	solve(0, n - 1);
	cout << ans;
}

signed main() {
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	int q = 1; // cin >> q;
	while (q--) solve();
	cerr << fixed << setprecision(3) << "Time execution: " << (double)clock() / CLOCKS_PER_SEC << endl;
}

Compilation message

histogram.cpp: In function 'void build(int, int, int, const int&)':
histogram.cpp:55:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   55 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'void clear(int, int, int)':
histogram.cpp:78:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   78 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'long long int get(int, int, int, int, int, long long int)':
histogram.cpp:89:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   89 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'void solve(int, int)':
histogram.cpp:98:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   98 |  int m = l + r >> 1;
      |          ~~^~~

Subtask #1
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 13 ms 19288 KB Output is correct
2 Correct 13 ms 19364 KB Output is correct
3 Correct 12 ms 19288 KB Output is correct
4 Correct 12 ms 19268 KB Output is correct
5 Correct 12 ms 19240 KB Output is correct
6 Correct 13 ms 19288 KB Output is correct
7 Correct 13 ms 19368 KB Output is correct
8 Correct 12 ms 19296 KB Output is correct
9 Correct 12 ms 19288 KB Output is correct
10 Correct 12 ms 19284 KB Output is correct
11 Correct 9 ms 19156 KB Output is correct
12 Correct 12 ms 19284 KB Output is correct

Subtask #2
90.0 / 90.0

# 결과 실행 시간 메모리 Grader output
1 Correct 13 ms 19288 KB Output is correct
2 Correct 13 ms 19364 KB Output is correct
3 Correct 12 ms 19288 KB Output is correct
4 Correct 12 ms 19268 KB Output is correct
5 Correct 12 ms 19240 KB Output is correct
6 Correct 13 ms 19288 KB Output is correct
7 Correct 13 ms 19368 KB Output is correct
8 Correct 12 ms 19296 KB Output is correct
9 Correct 12 ms 19288 KB Output is correct
10 Correct 12 ms 19284 KB Output is correct
11 Correct 9 ms 19156 KB Output is correct
12 Correct 12 ms 19284 KB Output is correct
13 Correct 511 ms 38724 KB Output is correct
14 Correct 482 ms 41444 KB Output is correct
15 Correct 437 ms 38732 KB Output is correct
16 Correct 488 ms 38884 KB Output is correct
17 Correct 514 ms 40648 KB Output is correct
18 Correct 521 ms 41560 KB Output is correct
19 Correct 487 ms 40724 KB Output is correct
20 Correct 514 ms 41568 KB Output is correct
21 Correct 485 ms 38888 KB Output is correct
22 Correct 544 ms 41256 KB Output is correct
23 Correct 62 ms 21204 KB Output is correct
24 Correct 369 ms 41712 KB Output is correct