#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
int fstTrue(function<bool(int)> f, int lo, int hi) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
int mid = (lo+hi)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: LineContainer; add lines of the form $kx+m$,
* compute greatest $y$-coordinate for any $x$.
* Time: O(\log N)
* Source: KACTL
* https://github.com/kth-competitive-programming/kactl/commit/165807e28402c9be906f6e6a09452431787bb70d?diff=unified
* Verification:
* CSA Squared Ends not working :(
* https://codeforces.com/contest/1083/problem/E
* https://atcoder.jp/contests/arc066/tasks/arc066_d
*/
bool Q;
struct Line {
mutable ll k, m, p; // slope, y-intercept, last optimal x
ll eval (ll x) { return k*x+m; }
bool operator<(const Line& o) const { return Q?p<o.p:k<o.k; }
};
// for doubles, use inf = 1/.0, divi(a,b) = a/b
const ll inf = LLONG_MAX;
// floored div
ll divi(ll a, ll b) { return a/b-((a^b) < 0 && a%b); }
// last x such that first line is better
ll bet(const Line& x, const Line& y) {
if (x.k == y.k) return x.m >= y.m ? inf : -inf;
return divi(y.m-x.m,x.k-y.k); }
struct LC : multiset<Line> {
// updates x->p, determines if y is unneeded
bool isect(iterator x, iterator y) {
if (y == end()) { x->p = inf; return 0; }
x->p = bet(*x,*y); return x->p >= y->p; }
void add(ll k, ll m) {
k = -k;
m = -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());
Q = 1; auto l = *lb({0,0,x}); Q = 0;
return -(l.k*x+l.m);
}
};
const int mx = 100005;
ll h[mx];
ll w[mx];
LC lin;
ll dp[mx];
int main() {
setIO();
int n;
cin >> n;
for(int i = 1; i <= n; i++){
cin >> h[i];
}
ll ians = 0;
for(int i = 1; i <= n; i++){
cin >> w[i];
ians+=w[i];
w[i] = -w[i];
}
dp[1] = w[1];
lin.add(-2*h[1], dp[1]+h[1]*h[1]);
for(int i = 2; i <= n; i++){
dp[i] = lin.query(h[i]);
dp[i]+=h[i]*h[i]+w[i];
lin.add(-2*h[i], dp[i]+h[i]*h[i]);
}
ll fans = ians+dp[n];
ps(fans);
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
*/
Compilation message
building.cpp: In function 'void setIn(std::__cxx11::string)':
building.cpp:128:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
building.cpp: In function 'void setOut(std::__cxx11::string)':
building.cpp:129:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
256 KB |
Output is correct |
| 2 |
Correct |
5 ms |
384 KB |
Output is correct |
| 3 |
Correct |
5 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
416 KB |
Output is correct |
| 5 |
Correct |
6 ms |
384 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
55 ms |
3832 KB |
Output is correct |
| 2 |
Correct |
54 ms |
3832 KB |
Output is correct |
| 3 |
Correct |
54 ms |
3832 KB |
Output is correct |
| 4 |
Correct |
48 ms |
3664 KB |
Output is correct |
| 5 |
Correct |
46 ms |
4856 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
256 KB |
Output is correct |
| 2 |
Correct |
5 ms |
384 KB |
Output is correct |
| 3 |
Correct |
5 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
416 KB |
Output is correct |
| 5 |
Correct |
6 ms |
384 KB |
Output is correct |
| 6 |
Correct |
55 ms |
3832 KB |
Output is correct |
| 7 |
Correct |
54 ms |
3832 KB |
Output is correct |
| 8 |
Correct |
54 ms |
3832 KB |
Output is correct |
| 9 |
Correct |
48 ms |
3664 KB |
Output is correct |
| 10 |
Correct |
46 ms |
4856 KB |
Output is correct |
| 11 |
Correct |
54 ms |
3960 KB |
Output is correct |
| 12 |
Correct |
54 ms |
3704 KB |
Output is correct |
| 13 |
Correct |
43 ms |
3832 KB |
Output is correct |
| 14 |
Correct |
53 ms |
3960 KB |
Output is correct |
| 15 |
Correct |
63 ms |
9848 KB |
Output is correct |
| 16 |
Correct |
44 ms |
4984 KB |
Output is correct |
| 17 |
Correct |
30 ms |
3704 KB |
Output is correct |
| 18 |
Correct |
32 ms |
3704 KB |
Output is correct |
