oj.uz

답안 #630174

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
630174 2022-08-15T20:02:53 Z vovamr 3D Histogram (COCI20_histogram) C++17
20 / 110
 539 ms 83484 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) 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 12 ms 19284 KB Output is correct
2 Correct 12 ms 19284 KB Output is correct
3 Correct 14 ms 19288 KB Output is correct
4 Correct 12 ms 19284 KB Output is correct
5 Correct 12 ms 19284 KB Output is correct
6 Correct 16 ms 19296 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 9 ms 19028 KB Output is correct
12 Correct 12 ms 19284 KB Output is correct

Subtask #2
0 / 90.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 19284 KB Output is correct
2 Correct 12 ms 19284 KB Output is correct
3 Correct 14 ms 19288 KB Output is correct
4 Correct 12 ms 19284 KB Output is correct
5 Correct 12 ms 19284 KB Output is correct
6 Correct 16 ms 19296 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 9 ms 19028 KB Output is correct
12 Correct 12 ms 19284 KB Output is correct
13 Correct 503 ms 38536 KB Output is correct
14 Correct 469 ms 40792 KB Output is correct
15 Correct 423 ms 38728 KB Output is correct
16 Correct 468 ms 38836 KB Output is correct
17 Correct 539 ms 41304 KB Output is correct
18 Runtime error 522 ms 83484 KB Execution killed with signal 11
19 Halted 0 ms 0 KB -