#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;
| ~~^~~
| # |
Verdict |
Execution time |
Memory |
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 |
| # |
Verdict |
Execution time |
Memory |
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 |
