#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <string>
#include <time.h>
#include <stack>
#include <queue>
#include <random>
#include <fstream>
#define endl '\n'
#define flush fflush(stdout), cout.flush()
#define fast ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define debug cout << "ok" << endl
#define finish(x) return cout << x << endl, 0
typedef long long ll;
typedef long double ldb;
const int md = 1e9 + 7, inf = 1e9 + 7;
const ll hs = 199;
const ldb eps = 1e-9, pi = acos(-1);
using namespace std;
// 1 for maximum, -1 for minimum
struct cht {
struct line {
ll m, b;
bool q;
ll nxtm, nxtb;
line(ll mm = 0, ll bb = 0, bool qq = false) {
m = mm;
b = bb;
q = qq;
nxtm = nxtb = 9e18;
}
bool operator < (const line &x) const {
if (!q && !x.q)
return m < x.m;
if (x.q) {
// cout << "comparison with line " << -m << " " << -b << endl;
if (nxtm == (ll)9e18) return false;
// cout << "has next slope as " << nxtm << endl;
// cout << (ldb)(b - nxtb) / (nxtm - m) << endl;
return (b - nxtb) < x.m * (nxtm - m);
}
return !(x < *this);
}
};
int sign;
set<line> h;
cht(int type = 1) {
sign = type;
}
void upd(set<line>::iterator &it) {
if (next(it) == h.end()) return;
line l1 = *it, l2 = *next(it);
h.erase(it);
l1.nxtm = l2.m, l1.nxtb = l2.b;
it = h.insert(l1).first;
}
bool ok(set<line>::iterator it) {
if (it == h.begin() || next(it) == h.end()) return true;
auto it1 = prev(it), it2 = next(it);
bool rtn = (it1->b - it->b) * (it2->m - it->m) < (it->b - it2->b) * (it->m - it1->m);
if (!rtn) {
// cout << "erasing " << sign * it->m << " " << sign * it->b << endl;
h.erase(it);
upd(it1);
}
return rtn;
}
void insert(ll constant, ll slope) {
line l(sign * slope, sign * constant);
auto it = h.insert(l).first;
if (!ok(it)) return;
upd(it);
if (it != h.begin()) upd(--it), ++it;
if (it != h.begin()) while (!ok(prev(it)));
if (next(it) != h.end()) while (!ok(next(it)));
}
ll query(ll x) {
// cout << "looking for optimum on x " << x << endl;
line l(x, 0, true);
auto it = h.lower_bound(l);
// cout << "optimum for x " << x << " is line ";
// cout << sign * it->m << " " << sign * it->b << endl;
return sign * (x * it->m + it->b);
}
};
int n;
vector<ll> h, w, sw, dp;
cht c(-1);
int main() {
fast;
cin >> n;
h.resize(n);
w.resize(n);
sw.resize(n);
dp.resize(n);
for (auto &i : h) cin >> i;
for (auto &i : w) cin >> i;
sw[0] = w[0];
for (int i = 1; i < n; i++) sw[i] = sw[i - 1] + w[i];
dp[0] = 0;
// cout << "for i " << 0 << " inserted " << dp[0] + h[0] * h[0] - sw[0] << " " << -2 * h[0] << endl;
c.insert(dp[0] + h[0] * h[0] - sw[0], -2 * h[0]);
for (int i = 1; i < n; i++) {
dp[i] = c.query(h[i]) + sw[i - 1] + h[i] * h[i];
// cout << "for i " << i << " inserted " << -2 * h[i] << " " << dp[i] + h[i] * h[i] - sw[i] << endl;
c.insert(dp[i] + h[i] * h[i] - sw[i], -2 * h[i]);
}
// for (int i = 0; i < n; i++) cout << dp[i] << " "; cout << endl;
cout << dp.back() << endl;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
488 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
504 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
117 ms |
3652 KB |
Output is correct |
| 2 |
Incorrect |
116 ms |
3820 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
488 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
504 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
