/**
* Author: Anil Byar
**/
#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;
// template<class T>
// using ordered_set = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)(x).size()
#define uniq(v) v.erase(unique(all(v)), v.end())
#define ft first
#define sd second
#define pb push_back
#define eb emplace_back
// Source: https://codeforces.com/blog/entry/68809
// { start
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '"' << x << '"';}
void __print(const string &x) {cerr << '"' << x << '"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
// } end
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vii;
typedef vector<ll> vl;
typedef vector<pll> vll;
typedef vector<vi> vvi;
typedef vector<vii> vvii;
typedef vector<vl> vvl;
#define dbg if(0)
const ll MOD = 1e9+7;
const ll MOD9 = 998244353;
const ll INFLL = 1e18+5;
const int INF = 1e9;
void printbit(int x, int len) {string s="\n";while(len--){s=((x%2)?'1':'0')+s;x/=2;} cout<<s;}
ll power(ll x, ll y, ll mod){if (y==0) return 1;ll ret = power(x, y/2, mod);ret *= ret;ret%=mod;if (y&1) ret *= x;return ret%mod;}
ll modinv(ll x, ll mod = MOD) {return power(x, mod-2, mod);}
template<class T> bool chmin(T& a, T b){return (a>b?a=b,1:0);}
template<class T> bool chmax(T& a, T b){return (a<b?a=b,1:0);}
template<class T>
istream& operator>>(istream&in, vector<T>&v){
for (T& x:v) in>>x;
return in;
}
template<class T>
ostream& operator<<(ostream&out, vector<T>&v){
for (T& x:v) out<<x<<' ';
cout<<'\n';
return out;
}
// use ?: with brackets (?:)
// check for overflow
// think about dp
// Read the statement carefully
/**
* Author: Simon Lindholm
* Date: 2017-04-20
* License: CC0
* Source: own work
* Description: Container where you can add lines of the form kx+m, and query maximum values at points x.
* Useful for dynamic programming (``convex hull trick'').
* Time: O(\log N)
* Status: stress-tested
*/
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;
}
};
void solve(){
int n;cin>>n;
vl h(n), w(n);
vl pref(n);
cin>>h>>w;
pref[0] = w[0];
for (int i = 1;i<n;i++) pref[i] = pref[i-1] + w[i];
ll dp[n+1]{};
LineContainer chull;
dp[1] = 0;
chull.add(-2*h[0], dp[0] + h[0] * h[0] - pref[0]);
for (int i = 1;i<n;i++) {
dp[i] = h[i] * h[i] + pref[i-1] + chull.query(h[i]);
chull.add(-2*h[i], dp[i] + h[i] * h[i] - pref[i]);
}
cout<<dp[n-1];
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
#define ONLINE_JUDGE
#ifndef ONLINE_JUDGE
freopen("input.in", "r", stdin);
freopen("output.out", "w", stdout);
freopen("debug.dbg", "w", stderr);
int tt = clock();
#endif
int t=1, i = 1;
// cin>>t;
while(t--){
// cout<<"Case #"<<i++<<": ";
solve();
cout<<'\n';
}
#ifndef ONLINE_JUDGE
cerr << "TIME = " << (float)(clock() - tt)/CLOCKS_PER_SEC << endl;
tt = clock();
#endif
}
Compilation message
building.cpp: In function 'int main()':
building.cpp:173:11: warning: unused variable 'i' [-Wunused-variable]
173 | int t=1, i = 1;
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
1 ms |
340 KB |
Output is correct |
| 5 |
Correct |
1 ms |
340 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
30 ms |
3528 KB |
Output is correct |
| 2 |
Correct |
31 ms |
4436 KB |
Output is correct |
| 3 |
Correct |
30 ms |
4536 KB |
Output is correct |
| 4 |
Correct |
28 ms |
4308 KB |
Output is correct |
| 5 |
Correct |
26 ms |
5588 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
1 ms |
340 KB |
Output is correct |
| 5 |
Correct |
1 ms |
340 KB |
Output is correct |
| 6 |
Correct |
30 ms |
3528 KB |
Output is correct |
| 7 |
Correct |
31 ms |
4436 KB |
Output is correct |
| 8 |
Correct |
30 ms |
4536 KB |
Output is correct |
| 9 |
Correct |
28 ms |
4308 KB |
Output is correct |
| 10 |
Correct |
26 ms |
5588 KB |
Output is correct |
| 11 |
Correct |
36 ms |
4680 KB |
Output is correct |
| 12 |
Correct |
30 ms |
4436 KB |
Output is correct |
| 13 |
Correct |
25 ms |
4576 KB |
Output is correct |
| 14 |
Correct |
36 ms |
4692 KB |
Output is correct |
| 15 |
Correct |
42 ms |
10572 KB |
Output is correct |
| 16 |
Correct |
29 ms |
5580 KB |
Output is correct |
| 17 |
Correct |
17 ms |
4436 KB |
Output is correct |
| 18 |
Correct |
17 ms |
4436 KB |
Output is correct |
