/*
PROG: source
LANG: C++11
_____
.' '.
/ 0 0 \
| ^ |
| \ / |
\ '---' /
'._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
struct chash
{
int operator()(int x) const
{
x ^= (x >> 20) ^ (x >> 12);
return x ^ (x >> 7) ^ (x >> 4);
}
int operator()(long long x) const
{
return x ^ (x >> 32);
}
};
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using hashtable = gp_hash_table<T, U, chash>;
template<class T>
void readi(T &x)
{
T input = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
input = input * 10 + (c - '0');
c = getchar();
}
if (negative)
{
input = -input;
}
x = input;
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int aout[20];
int ilen = 0;
while(output)
{
aout[ilen] = ((output % 10));
output /= 10;
ilen++;
}
for (int i = ilen - 1; i >= 0; i--)
{
putchar(aout[i] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
template<class T, class U>
T normalize(T x, U mod = 1000000007)
{
return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
return ((1ll << 15) * rand() + rand()) % mod;
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
int N;
pll arr[MAXN];
ll dp[MAXN];
ll pref[MAXN];
ordered_set<pll> chull;
ll overpass(pll x, pll y)
{
ll m1 = x.fi, b1 = x.se, m2 = y.fi, b2 = y.se;
//when does x beat y?
if (m1 == m2)
{
if (b1 < b2) return -LLINF;
else return LLINF;
}
//m1x + b1 <= m2x + b2
//(m2 - m1) x >= (b1 - b2)
//x >= (b1 - b2) / (m2 - m1)
return (((b1 - b2) % (m2 - m1) || (b1 - b2) < 0) ? (b1 - b2) / (m2 - m1) : (b1 - b2) / (m2 - m1) + 1);
// return (b1 - b2 + (m2 - m1 - 1)) / (m2 - m1);
}
void insert(ordered_set<pll> &a, pll x)
{
if (a.empty())
{
a.insert(x);
return;
}
auto it = a.LB(x);
if (it == a.end())
{
if (a.rbegin() -> fi == x.fi)
{
return;
}
it--;
while(it != a.begin() && overpass(*prev(it), *it) <= overpass(*it, x))
{
it = a.erase(it);
it--;
}
a.insert(x);
return;
}
else if (it == a.begin())
{
while(next(it) != a.end() && overpass(x, *it) <= overpass(*it, *next(it)))
{
it = a.erase(it);
}
a.insert(x);
return;
}
bool change = false;
do
{
change = false;
while(next(it) != a.end() && overpass(x, *it) <= overpass(*it, *next(it)))
{
change = true;
it = a.erase(it);
}
it--;
while(it != a.begin() && overpass(*prev(it), *it) <= overpass(*it, x))
{
change = true;
it = a.erase(it);
it--;
}
it++;
}
while (change);
it--;
if (overpass(*it, x) > overpass(x, *next(it)))
{
a.insert(x);
}
return;
}
//take it to the left as
ll query(ll x, ordered_set<pll> &a)
{
// ll res = LLINF;
// for (pll p : a)
// {
// ckmin(res, p.fi * x + p.se);
// }
// return res;
// cerr << "overpasses: ";
// for (int i = 1; i < a.size() - 1; i++)
// {
// pll pr = *a.find_by_order(i - 1), pm = *a.find_by_order(i), pl = *a.find_by_order(i + 1);
// // assert(overpass(pr, pm) > overpass(pm, pl));
// // assert(pr.fi != pm.fi && pm.fi != pl.fi);
// // cerr << overpass(pr, pm) << ' ';
// }
// cerr << overpass(*a.find_by_order(a.size() - 2), *a.find_by_order(a.size() - 1)) << endl;
// debug(x);
// cerr << endl;
// if (a.empty())
// {
// return 0ll;
// }
//find p such that overpass(p, p + 1) <= x
//it decreases, and you want first guy such that f(p, p + 1) to be <= x
int lo = 0, hi = a.size() - 1;
while(hi > lo)
{
int mid = (lo + hi) / 2;
auto it = a.find_by_order(mid);
pll pr = *it, pl = *next(it);
if (overpass(pr, pl) <= x)
{
hi = mid;
}
else
{
lo = mid + 1;
}
}
//find the biggest p such that overpass(p, p + 1) <= x
auto it = a.find_by_order(lo);
// assert(next(it) == a.end() || overpass(*it, *next(it)) <= x);
// cerr << "contains: ";
// for (pll x : a)
// {
// cerr << x.fi << "x + " << x.se << endl;
// }
// if (it != a.begin())
// {
// assert(overpass(*prev(it), *it) > x);
// }
// cerr << "query " << x << " just beat " << (next(it) == a.end() ? -LLINF : overpass(*it, *next(it)));
// cerr << "query " << x << " get " << opt.fi * x + opt.se << endl;
ll res = LLINF;
for (pll p : a)
{
ckmin(res, p.fi * x + p.se);
// cerr << p.fi * x + p.se << ' ';
}
// cerr << "send " << it -> fi * x + it -> se << endl;
// return res;
return it -> fi * x + it -> se;
}
int32_t main()
{
ios_base::sync_with_stdio(0);
srand(time(0));
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
// freopen ("file.in", "r", stdin);
// freopen ("file.out", "w", stdout);
cin >> N;
for (int i = 0; i < N; i++)
{
cin >> arr[i].fi;
}
for (int i = 0; i < N; i++)
{
cin >> arr[i].se;
}
for (int i = 0; i < N; i++)
{
pref[i + 1] = pref[i] + arr[i].se;
}
dp[0] = 0;
for (int i = 0; i < N; i++)
{
if (i)
{
// cerr << "query " << -2 * arr[i].fi << ' ' << query(-2 * arr[i].fi, chull) << endl;
dp[i] = query(-2 * arr[i].fi, chull) + (arr[i].fi * arr[i].fi + pref[i]);
// for (int j = 0; j < i; j++)
// {
// //(arr[i] - arr[j])^2 = (arr[j]^2) - 2 * arr[i] * arr[j] + arr[i]^2
// ckmin(dp[i], -2 * arr[i].fi * arr[j].fi + dp[j] + arr[j].fi * arr[j].fi - pref[j + 1]);
// }
}
pll cur = {arr[i].fi, dp[i] + arr[i].fi * arr[i].fi - pref[i + 1]};
// cerr << "insert " << cur.fi << "x + " << cur.se << endl;
insert(chull, cur);
// cerr << "contents of chull:\n";
// for (pll x : chull)
// {
// cerr << x.fi << "x + " << x.se << endl;
// }
// cerr << dp[i] << endl;
}
cout << dp[N - 1] << '\n';
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
352 KB |
Output is correct |
| 2 |
Correct |
2 ms |
376 KB |
Output is correct |
| 3 |
Correct |
2 ms |
444 KB |
Output is correct |
| 4 |
Correct |
3 ms |
460 KB |
Output is correct |
| 5 |
Correct |
3 ms |
648 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
949 ms |
3876 KB |
Output is correct |
| 2 |
Correct |
930 ms |
4076 KB |
Output is correct |
| 3 |
Correct |
949 ms |
4076 KB |
Output is correct |
| 4 |
Correct |
367 ms |
4076 KB |
Output is correct |
| 5 |
Execution timed out |
3056 ms |
4376 KB |
Time limit exceeded |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
352 KB |
Output is correct |
| 2 |
Correct |
2 ms |
376 KB |
Output is correct |
| 3 |
Correct |
2 ms |
444 KB |
Output is correct |
| 4 |
Correct |
3 ms |
460 KB |
Output is correct |
| 5 |
Correct |
3 ms |
648 KB |
Output is correct |
| 6 |
Correct |
949 ms |
3876 KB |
Output is correct |
| 7 |
Correct |
930 ms |
4076 KB |
Output is correct |
| 8 |
Correct |
949 ms |
4076 KB |
Output is correct |
| 9 |
Correct |
367 ms |
4076 KB |
Output is correct |
| 10 |
Execution timed out |
3056 ms |
4376 KB |
Time limit exceeded |
