/*
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 orderedset = 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];
struct chulldynamic
{
vector<pll> hull, brutes;
ll f(ll m, ll b, ll x)
{
return m * x + b;
}
ll overpass(pll a, pll b)
{
//when does line a pass line b?
//m1x+b1<m2x+b2 -> (m2-m1)x>(b1-b2) -> x>(b1-b2)/(m2-m1)
if (b.fi == a.fi)
{
if (a.se < b.se)
{
return -LLINF;
}
else
{
return LLINF;
}
}
return (a.se - b.se)/(b.fi - a.fi);
}
void rebuild()
{
sort(brutes.begin(), brutes.end());
reverse(hull.begin(), hull.end());
vector<pll> temp;
if (hull.back().fi > brutes.back().fi)
{
temp.PB(hull.back());
hull.pop_back();
}
else
{
temp.PB(brutes.back());
brutes.pop_back();
}
while(!hull.empty() || !brutes.empty())
{
pll cur;
if (hull.empty() || (!hull.empty() && !brutes.empty() && brutes.back().fi > hull.back().fi))
{
cur = brutes.back();
brutes.pop_back();
}
else
{
cur = hull.back();
hull.pop_back();
}
while(temp.size() >= 2)
{
pll l0 = temp[temp.size() - 2], l1 = temp[temp.size() - 1];
if (overpass(l1, l0) <= overpass(cur, l1))
{
break;
}
temp.pop_back();
}
temp.PB(cur);
}
hull = temp;
}
void insert(pll x)
{
if (hull.empty())
{
hull.PB(x);
return;
}
brutes.PB(x);
if (brutes.size() == MAGIC)
{
rebuild();
}
}
ll query(ll x)
{
ll res = LLINF;
int lo = 0, hi = hull.size() - 1;
while(hi > lo)
{
int mid = (hi + lo + 1)/2;
if (overpass(hull[mid], hull[mid - 1]) >= x)
{
hi = mid - 1;
}
else
{
lo = mid;
}
}
res = f(hull[lo].fi, hull[lo].se, x);
for (int i = 0; i < brutes.size(); i++)
{
res = min(res, f(brutes[i].fi, brutes[i].se, x));
}
return res;
}
};
chulldynamic cht;
int32_t main()
{
ios_base::sync_with_stdio(0);
srand(time(0));
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
if (fopen("input.in", "r"))
{
freopen ("input.in", "r", stdin);
freopen ("output.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 << ' ' << cht.query(-2 * arr[i].fi) << endl;
dp[i] = cht.query(-2 * arr[i].fi) + (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 << cur.fi << "x + " << cur.se << endl;
cht.insert(cur);
// cerr << dp[i] << endl;
}
cout << dp[N - 1] << '\n';
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
Compilation message
building.cpp: In member function 'll chulldynamic::query(ll)':
building.cpp:243:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < brutes.size(); i++)
~~^~~~~~~~~~~~~~~
building.cpp: In function 'int32_t main()':
building.cpp:261:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
freopen ("input.in", "r", stdin);
~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
building.cpp:262:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
freopen ("output.out", "w", stdout);
~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
376 KB |
Output is correct |
| 2 |
Correct |
3 ms |
496 KB |
Output is correct |
| 3 |
Correct |
2 ms |
496 KB |
Output is correct |
| 4 |
Correct |
3 ms |
496 KB |
Output is correct |
| 5 |
Correct |
3 ms |
500 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
117 ms |
3700 KB |
Output is correct |
| 2 |
Correct |
112 ms |
4772 KB |
Output is correct |
| 3 |
Correct |
112 ms |
6040 KB |
Output is correct |
| 4 |
Correct |
92 ms |
6648 KB |
Output is correct |
| 5 |
Correct |
241 ms |
8860 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
376 KB |
Output is correct |
| 2 |
Correct |
3 ms |
496 KB |
Output is correct |
| 3 |
Correct |
2 ms |
496 KB |
Output is correct |
| 4 |
Correct |
3 ms |
496 KB |
Output is correct |
| 5 |
Correct |
3 ms |
500 KB |
Output is correct |
| 6 |
Correct |
117 ms |
3700 KB |
Output is correct |
| 7 |
Correct |
112 ms |
4772 KB |
Output is correct |
| 8 |
Correct |
112 ms |
6040 KB |
Output is correct |
| 9 |
Correct |
92 ms |
6648 KB |
Output is correct |
| 10 |
Correct |
241 ms |
8860 KB |
Output is correct |
| 11 |
Correct |
128 ms |
8860 KB |
Output is correct |
| 12 |
Correct |
120 ms |
10000 KB |
Output is correct |
| 13 |
Correct |
86 ms |
11092 KB |
Output is correct |
| 14 |
Correct |
94 ms |
12284 KB |
Output is correct |
| 15 |
Correct |
784 ms |
20452 KB |
Output is correct |
| 16 |
Correct |
331 ms |
20452 KB |
Output is correct |
| 17 |
Correct |
556 ms |
22508 KB |
Output is correct |
| 18 |
Correct |
138 ms |
22508 KB |
Output is correct |
