#include<bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<pl> vpl;
typedef vector<ld> vld;
typedef pair<ld, ld> pld;
//typedef tree<ll, null_type, less_equal<ll>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
template<typename T>
ostream &operator<<(ostream &os, vector<T> &a) {
os << "[";
for (int i = 0; i < ll(a.size()); i++) { os << a[i] << ((i != ll(a.size() - 1) ? " " : "")); }
os << "]\n";
return os;
}
#define all(x) x.begin(),x.end()
#define YES out("YES")
#define NO out("NO")
#define out(x){cout << x << "\n"; return;}
#define GLHF ios_base::sync_with_stdio(false); cin.tie(NULL)
#define print(x){for(auto ait:x) cout << ait << " "; cout << "\n";}
#define pb push_back
#define umap unordered_map
template<typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> &p) {
os << "" << p.first << " " << p.second << "";
return os;
}
void usaco(string taskname) {
string fin = taskname + ".in";
string fout = taskname + ".out";
const char *FIN = fin.c_str();
const char *FOUT = fout.c_str();
freopen(FIN, "r", stdin);
freopen(FOUT, "w", stdout);
}
template<typename T>
void read(vector<T> &v) {
int n = v.size();
for (int i = 0; i < n; i++)
cin >> v[i];
}
template<typename T>
vector<T> UNQ(vector<T> a) {
vector<T> ans;
for (T t: a)
if (ans.empty() || t != ans.back())
ans.push_back(t);
return ans;
}
ll ceil(ll a, ll b) {
ll ans = a / b;
if (a % b)ans++;
return ans;
}
ld log(ld a, ld b) { return log(b) / log(a); }
ll power(ll base, ll exp, ll M = 1e18) {//(base^exp)%M
ll ans = 1;
while (exp) {
if (exp % 2 == 1)ans = ((ans % M) * (base % M)) % M;
base = ((base % M) * (base % M)) % M;
exp /= 2;
}
return ans;
}
string to_base(int n, int new_base) {
string s;
int nn = n;
while (nn) {
s += to_string(nn % new_base);
nn /= new_base;
}
reverse(all(s));
return s;
}
ll gcd(ll a, ll b) {
if (a < b)swap(a, b);
if (b == 0)return a;
return gcd(b, a % b);
}
ll lcm(ll a, ll b) {
ll x = (a / gcd(a, b));
return b * x;
}
vl generate_array(ll n, ll mn = 1, ll mx = 1e18 + 1) {
if (mx == 1e18 + 1)
mx = n;
vl ans(n);
for (int i = 0; i < n; i++)
ans[i] = (mn + rand() % (mx - mn + 1));
return ans;
}
string substr(string s, int l, int r) {
string ans;
for (int i = l; i <= r; i++)
ans += s[i];
return ans;
}
void solve();
int main() {
GLHF;
int t = 1;
//cin >> t;
while (t--)
solve();
}
struct line{
ll m,b;
line ():m(0),b(1e18){}
line (ll m,ll b):m(m),b(b){}
ll get(ll x){
return m*x+b;
}
};
struct Seg{
ll l,r,m;
line L;
Seg *lp=0,*rp=0;
Seg(ll l,ll r):l(l),r(r),m((l+r)/2){}
void expand(){
if(l+1==r)return;
if(!lp)lp=new Seg(l,m);
if(!rp)rp=new Seg(m,r);
}
void insert(line x){
expand();
bool lef=x.get(l)<L.get(l);
bool mid=x.get(m)<L.get(m);
if(mid)
swap(x,L);
if(l+1==r)return;
else if(lef!=mid)
lp->insert(x);
else
rp->insert(x);
}
ll query(ll x){
expand();
if(l+1==r)
return L.get(x);
else if(x<m)
return min(L.get(x),lp->query(x));
else
return min(L.get(x),rp->query(x));
}
};
void solve() {
ll n;
cin >> n;
vl a(n),w(n);
read(a);
read(w);
vl dp(n,1e18);
dp[0]=0;
vl pref(n);
for(int i=0; i<n; i++)
pref[i]=(i?pref[i-1]:0)+w[i];
vl A(n),B(n);
A[0]=a[0]*a[0]-pref[0];
for(int i=0; i<n; i++)
B[i]=a[i];
Seg s(0,1e6+1);
s.insert(line(-2*B[0],A[0]));
for(int i=1; i<n; i++){
ll mn=s.query(a[i]);
//for(int j=0; j<i; j++)
// mn=min(mn,A[j]-(2*a[i]*B[j]));
dp[i]=mn+pref[i-1]+a[i]*a[i];
A[i]=dp[i]+a[i]*a[i]-pref[i];
s.insert( line(-2*B[i],A[i]));
}
//print(dp)
out(dp[n-1])
}
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
Compilation message
building.cpp: In function 'void usaco(std::string)':
building.cpp:56:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
56 | freopen(FIN, "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~
building.cpp:57:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
57 | freopen(FOUT, "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
1 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
332 KB |
Output is correct |
| 4 |
Correct |
1 ms |
460 KB |
Output is correct |
| 5 |
Correct |
1 ms |
460 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
62 ms |
5984 KB |
Output is correct |
| 2 |
Correct |
63 ms |
6108 KB |
Output is correct |
| 3 |
Correct |
61 ms |
5960 KB |
Output is correct |
| 4 |
Correct |
55 ms |
5300 KB |
Output is correct |
| 5 |
Correct |
71 ms |
22388 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
1 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
332 KB |
Output is correct |
| 4 |
Correct |
1 ms |
460 KB |
Output is correct |
| 5 |
Correct |
1 ms |
460 KB |
Output is correct |
| 6 |
Correct |
62 ms |
5984 KB |
Output is correct |
| 7 |
Correct |
63 ms |
6108 KB |
Output is correct |
| 8 |
Correct |
61 ms |
5960 KB |
Output is correct |
| 9 |
Correct |
55 ms |
5300 KB |
Output is correct |
| 10 |
Correct |
71 ms |
22388 KB |
Output is correct |
| 11 |
Correct |
101 ms |
18000 KB |
Output is correct |
| 12 |
Correct |
108 ms |
17856 KB |
Output is correct |
| 13 |
Correct |
60 ms |
6504 KB |
Output is correct |
| 14 |
Correct |
109 ms |
18000 KB |
Output is correct |
| 15 |
Correct |
75 ms |
30916 KB |
Output is correct |
| 16 |
Correct |
69 ms |
23356 KB |
Output is correct |
| 17 |
Correct |
46 ms |
6100 KB |
Output is correct |
| 18 |
Correct |
47 ms |
6096 KB |
Output is correct |
