#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#else
#define debug(...)
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
template<typename T> T gcd(T a, T b) { return (b == 0? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
#define FOS(i, r, l) for (int (i) = (r); (i) >= (l); --(i))
#define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
#define FSN(i, n) for (int (i) = (n) - 1; (i) >= 0; --(i))
#define EACH(i, x) for (auto &(i) : (x))
#define WHILE while
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
DIT ME CHUYEN BAO LOC
----------------------------------------------------------------
*/
const ll oo = 1e18;
const int N = 1e5 + 1;
const int T = 4e6 + 15;
int n, h[N], w[N];
ll f[N], d[N];
pll tr[T];
ll f1(pll &func, int &x) { return x * func.st + func.nd; }
void upd(int i, int l, int r, pll v) {
int mid = l + (r - l) / 2;
bool gt = f1(v, l) > f1(tr[i], l), gt1 = f1(v, mid) > f1(tr[i], mid);
if (!gt1) swap(v, tr[i]);
if (l == r) return;
if (gt == gt1) upd(i * 2 + 1, mid + 1, r, v);
else upd(i * 2, l, mid, v);
}
ll get(int i, int l, int r, int q) {
if (r < q || l > q) return oo;
ll ans = f1(tr[i], q);
if (l == r) return ans;
int mid = l + (r - l) / 2;
return min({ans, get(i * 2, l, mid, q), get(i * 2 + 1, mid + 1, r, q)});
}
signed main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
// freopen(file".inp", "r", stdin);
// freopen(file".out", "w", stdout);
cin >> n;
FOR(i, 1, n) cin >> h[i];
FOR(i, 1, n) cin >> w[i];
FOR(i, 1, n) f[i] = f[i - 1] + w[i];
FOR(i, 1, T - 1) tr[i] = {0, oo};
upd(1, 0, 1e6, {-2LL * h[1], 1LL * h[1] * h[1] - f[1]});
FOR(i, 2, n) {
d[i] = get(1, 0, 1e6, h[i]) + f[i - 1] + 1LL * h[i] * h[i];
upd(1, 0, 1e6, {-2LL * h[i], 1LL * h[i] * h[i] - f[i] + d[i]});
}
cout << d[n];
return 0;
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
Compilation message
building.cpp: In function 'int main()':
building.cpp:32:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
32 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
building.cpp:78:5: note: in expansion of macro 'FOR'
78 | FOR(i, 1, n) cin >> h[i];
| ^~~
building.cpp:32:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
32 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
building.cpp:79:5: note: in expansion of macro 'FOR'
79 | FOR(i, 1, n) cin >> w[i];
| ^~~
building.cpp:32:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
32 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
building.cpp:80:5: note: in expansion of macro 'FOR'
80 | FOR(i, 1, n) f[i] = f[i - 1] + w[i];
| ^~~
building.cpp:32:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
32 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
building.cpp:81:5: note: in expansion of macro 'FOR'
81 | FOR(i, 1, T - 1) tr[i] = {0, oo};
| ^~~
building.cpp:32:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
32 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
building.cpp:83:5: note: in expansion of macro 'FOR'
83 | FOR(i, 2, n) {
| ^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
27 ms |
62924 KB |
Output is correct |
| 2 |
Correct |
31 ms |
62880 KB |
Output is correct |
| 3 |
Correct |
26 ms |
62924 KB |
Output is correct |
| 4 |
Correct |
33 ms |
62884 KB |
Output is correct |
| 5 |
Correct |
27 ms |
62860 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
69 ms |
65224 KB |
Output is correct |
| 2 |
Correct |
67 ms |
66272 KB |
Output is correct |
| 3 |
Correct |
96 ms |
66224 KB |
Output is correct |
| 4 |
Correct |
69 ms |
66208 KB |
Output is correct |
| 5 |
Correct |
63 ms |
66164 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
27 ms |
62924 KB |
Output is correct |
| 2 |
Correct |
31 ms |
62880 KB |
Output is correct |
| 3 |
Correct |
26 ms |
62924 KB |
Output is correct |
| 4 |
Correct |
33 ms |
62884 KB |
Output is correct |
| 5 |
Correct |
27 ms |
62860 KB |
Output is correct |
| 6 |
Correct |
69 ms |
65224 KB |
Output is correct |
| 7 |
Correct |
67 ms |
66272 KB |
Output is correct |
| 8 |
Correct |
96 ms |
66224 KB |
Output is correct |
| 9 |
Correct |
69 ms |
66208 KB |
Output is correct |
| 10 |
Correct |
63 ms |
66164 KB |
Output is correct |
| 11 |
Correct |
75 ms |
66388 KB |
Output is correct |
| 12 |
Correct |
85 ms |
66304 KB |
Output is correct |
| 13 |
Correct |
68 ms |
66380 KB |
Output is correct |
| 14 |
Correct |
72 ms |
66380 KB |
Output is correct |
| 15 |
Correct |
65 ms |
66056 KB |
Output is correct |
| 16 |
Correct |
61 ms |
66244 KB |
Output is correct |
| 17 |
Correct |
57 ms |
66232 KB |
Output is correct |
| 18 |
Correct |
63 ms |
66280 KB |
Output is correct |
