#include <bits/stdc++.h>
using namespace std;
typedef double db;
typedef long long ll;
typedef long double ld;
#define int ll
typedef pair<int, int> pii;
#define lx (id << 1)
#define rx (lx | 1)
#define gcd __gcd
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define bit(i, mask) ((mask) >> (i) & 1)
#define reset(x, val) memset(x, val, sizeof(x))
#define foru(i,a,b) for(int i = (a); i <= (b); ++i)
#define ford(i,a,b) for(int i = (a); i >= (b); --i)
#define FastIO ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
template<typename T> bool maximize(T &res, const T &val) { if (res < val) { res = val; return true; } return false; }
template<typename T> bool minimize(T &res, const T &val) { if (val < res) { res = val; return true; } return false; }
const ll Linf = 0x3f3f3f3f3f3f3f3f;
const int Inf = 0x3f3f3f3f;
const ll Mod = 1e9 + 7;
const ll Mod2 = ll(1e9) + 9;
const int Lim = 1e6 + 5;
const int inv6 = 166666668;
// #define Sieve
#ifdef Sieve
vector<int> pr;
vector<int> lpf;
void Linear_sieve(int n = Lim) {
pr.assign(1, 2);
lpf.assign(n + 1, 2);
for (int x = 3; x <= n; x += 2) {
if (lpf[x] == 2) pr.push_back(lpf[x] = x);
for (int i = 1; i < pr.size() && pr[i] <= lpf[x] && pr[i] * x <= n; ++i)
lpf[pr[i] * x] = pr[i];
}
}
#endif
// #define Ckn_calc
#ifdef Ckn_calc
const int LIM = 1e6 + 16;
int fact[LIM + 10]; /// factorial: fact[n] = n!
int invs[LIM + 10]; /// inverse modular: invs[n] = n^(-1)
int tcaf[LIM + 10]; /// inverse factorial: tcaf[n] = (n!)^(-1)
void precal_nck(int n = LIM)
{
fact[0] = fact[1] = 1;
invs[0] = invs[1] = 1;
tcaf[0] = tcaf[1] = 1;
for (int i = 2; i <= n; ++i)
{
fact[i] = (1LL * fact[i - 1] * i) % Mod;
invs[i] = Mod - 1LL * (Mod / i) * invs[Mod % i] % Mod;
tcaf[i] = (1LL * tcaf[i - 1] * invs[i]) % Mod;
}
}
ll C(int n, int k) {
if (n < k || k < 0) return 0;
ll res = fact[n];
res *= tcaf[k], res %= Mod;
res *= tcaf[n - k], res %= Mod;
return res;
}
ll P(int n, int k) {
ll res = fact[n];
res *= tcaf[n - k], res %= Mod;
return res;
}
#endif
/// ====*====*====*====*====*====*====*====*====*====*====*====*====*====*====*====*====
const int base = 3;
const int N = 1e6 + 5;
const int K = log2(N) + 1;
const int dx[] = {+1, -1, 0, 0};
const int dy[] = {0, 0, +1, -1};
const int block_size = sqrt(2e9) + 2;
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b);
}
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
int n;
int a[N];
int w[N];
int dp[N];
void solve() {
cin >> n;
foru(i, 1, n) cin >> a[i];
foru(i, 1, n) cin >> w[i];
foru(i, 1, n) w[i] += w[i - 1];
LineContainer cht;
foru(i, 2, n) {
int j = i - 1;
cht.add(2LL * a[j], -(a[j] * a[j] + dp[j] - w[j]));
dp[i] = -cht.query(a[i]) + a[i] * a[i] + w[i - 1];
}
cout << dp[n];
}
signed main() {
FastIO;
#define task "test"
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
#ifdef Sieve
Linear_sieve();
#endif
#ifdef Ckn_calc
precal_nck();
#endif
int ntest = 1;
// cin >> ntest;
while (ntest--) {
//cout << "Case " << q << ": " << "\n";
solve();
cout << "\n";
}
return 0;
}
/** /\_/\
* (= ._.)
* / >TL \>AC
**/
Compilation message
building.cpp: In function 'int main()':
building.cpp:155:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
155 | freopen(task".inp", "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
building.cpp:156:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
156 | freopen(task".out", "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 2 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 3 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 4 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 5 |
Correct |
2 ms |
4444 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
33 ms |
9808 KB |
Output is correct |
| 2 |
Correct |
31 ms |
9816 KB |
Output is correct |
| 3 |
Correct |
34 ms |
9812 KB |
Output is correct |
| 4 |
Correct |
29 ms |
9552 KB |
Output is correct |
| 5 |
Correct |
27 ms |
10832 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 2 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 3 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 4 |
Correct |
1 ms |
4444 KB |
Output is correct |
| 5 |
Correct |
2 ms |
4444 KB |
Output is correct |
| 6 |
Correct |
33 ms |
9808 KB |
Output is correct |
| 7 |
Correct |
31 ms |
9816 KB |
Output is correct |
| 8 |
Correct |
34 ms |
9812 KB |
Output is correct |
| 9 |
Correct |
29 ms |
9552 KB |
Output is correct |
| 10 |
Correct |
27 ms |
10832 KB |
Output is correct |
| 11 |
Correct |
33 ms |
9844 KB |
Output is correct |
| 12 |
Correct |
33 ms |
9784 KB |
Output is correct |
| 13 |
Correct |
25 ms |
9816 KB |
Output is correct |
| 14 |
Correct |
31 ms |
10076 KB |
Output is correct |
| 15 |
Correct |
42 ms |
15952 KB |
Output is correct |
| 16 |
Correct |
31 ms |
10784 KB |
Output is correct |
| 17 |
Correct |
24 ms |
10324 KB |
Output is correct |
| 18 |
Correct |
17 ms |
9972 KB |
Output is correct |
