oj.uz

답안 #630175

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
630175 2022-08-15T20:04:03 Z vovamr 3D Histogram (COCI20_histogram) C++17
110 / 110
 539 ms 41212 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 + 5;
 
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, int border) {
	if (vl == vr) {
		if (vl <= border) return void(cht[v] = {line(mnb[vl], -vl * 1ll * mnb[vl])});
		else return void(cht[v] = {line(mnb[vl], vl * 1ll * mnb[vl])});
	}
	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 cle(int v, int vl, int vr) {
	ptr[v] = 0, cht[v].clear();
	if (vl==vr)return;
	int m = vl + vr >> 1;
	cle(2 * v + 1, vl, m);
	cle(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;
	solve(l, m), solve(m + 1, r);
 
	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 + 2; i <= r; ++i) mnb[i] = min(mnb[i - 1], b[i]);
 
	build(0, l, r, m);
 
	// min(a) in [m + 1, r], min(b) in [m + 1, r]
	for (int i = m + 1, p1 = m, p2 = m; i <= r; ++i) {
		while (p1 >= l && mna[p1] >= mna[i]) --p1;
		while (p2 >= l && mnb[p2] >= mnb[i]) --p2;
		int pos = max(p1, p2);
		chmax(ans, mna[i] * 1ll * mnb[i] * 1ll * (i - pos));
	}
	// min(a) in [l, m], min(b) in [l, m]
	for (int i = m, p1 = m + 1, p2 = m + 1; i >= l; --i) {
		while (p1 <= r && mna[p1] >= mna[i]) ++p1;
		while (p2 <= r && mnb[p2] >= mnb[i]) ++p2;
		int pos = min(p1, p2);
		chmax(ans, mna[i] * 1ll * mnb[i] * 1ll * (m - i + 1 + pos - (m + 1)));
	}
 
	// min(a) in [m + 1, r], min(b) in [l, m]
	for (int i = m + 1, p1 = m, p2 = m; i <= r; ++i) {
		while (p1 >= l && mna[p1] >= mna[i]) --p1;
		while (p2 >= l && mnb[p2] >= mnb[i]) --p2;
		// left > p1, left <= p2
		if (p1 + 1 <= p2) {
			// max ( mna[i] * (i - left + 1) * mnb[left] )
			// mna[i] * max((i + 1 - left) * mnb[left])
			// mna[i] * max( (i + 1) * mnb[left] - left * mnb[left] )
			// left in [p1 + 1, p2]
 
			ll C = get(0, l, r, p1 + 1, p2, i + 1);
			if (C == -inf) continue;
			chmax(ans, mna[i] * C);
		}
	}
 
	// min(a) in [l, m], min(b) in [m + 1, r]
	for (int i = m, p1 = m + 1, p2 = m + 1; i >= l; --i) {
		while (p1 <= r && mna[p1] >= mna[i]) ++p1;
		while (p2 <= r && mnb[p2] >= mnb[i]) ++p2;
		// right < p1, right >= p2
		if (p2 <= p1 - 1) {
			// max( mna[i] * (right - i + 1) * mnb[right])
			// mna[i] * max((right - (i - 1)) * mnb[right])
			// mna[i] * max( -(i-1) * mnb[right] + mnb[right] * right )
			// right in [p2, p1 - 1]
 
			ll C = get(0, l, r, p2, p1 - 1, -(i - 1));
			if (C == -inf) continue;
			chmax(ans, mna[i] * C);
		}
	}
	cle(0, l, 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, int)':
histogram.cpp:50:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   50 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'void cle(int, int, int)':
histogram.cpp:74:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   74 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'long long int get(int, int, int, int, int, long long int)':
histogram.cpp:84:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   84 |  int m = vl + vr >> 1;
      |          ~~~^~~~
histogram.cpp: In function 'void solve(int, int)':
histogram.cpp:92:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   92 |  int m = l + r >> 1;
      |          ~~^~~

Subtask #1
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 13 ms 19284 KB Output is correct
2 Correct 12 ms 19268 KB Output is correct
3 Correct 13 ms 19252 KB Output is correct
4 Correct 12 ms 19256 KB Output is correct
5 Correct 12 ms 19284 KB Output is correct
6 Correct 12 ms 19284 KB Output is correct
7 Correct 12 ms 19284 KB Output is correct
8 Correct 12 ms 19284 KB Output is correct
9 Correct 12 ms 19284 KB Output is correct
10 Correct 12 ms 19284 KB Output is correct
11 Correct 10 ms 19060 KB Output is correct
12 Correct 17 ms 19236 KB Output is correct

Subtask #2
90.0 / 90.0

# 결과 실행 시간 메모리 Grader output
1 Correct 13 ms 19284 KB Output is correct
2 Correct 12 ms 19268 KB Output is correct
3 Correct 13 ms 19252 KB Output is correct
4 Correct 12 ms 19256 KB Output is correct
5 Correct 12 ms 19284 KB Output is correct
6 Correct 12 ms 19284 KB Output is correct
7 Correct 12 ms 19284 KB Output is correct
8 Correct 12 ms 19284 KB Output is correct
9 Correct 12 ms 19284 KB Output is correct
10 Correct 12 ms 19284 KB Output is correct
11 Correct 10 ms 19060 KB Output is correct
12 Correct 17 ms 19236 KB Output is correct
13 Correct 488 ms 38700 KB Output is correct
14 Correct 484 ms 40840 KB Output is correct
15 Correct 419 ms 38796 KB Output is correct
16 Correct 456 ms 38736 KB Output is correct
17 Correct 526 ms 41164 KB Output is correct
18 Correct 507 ms 41164 KB Output is correct
19 Correct 474 ms 40584 KB Output is correct
20 Correct 494 ms 41212 KB Output is correct
21 Correct 464 ms 38976 KB Output is correct
22 Correct 539 ms 41188 KB Output is correct
23 Correct 49 ms 21208 KB Output is correct
24 Correct 343 ms 38604 KB Output is correct