#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#include <stack>
#include <map>
#include <queue>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cstring>
#include <cmath>
#include <functional>
#include <cassert>
#include <iomanip>
#include <numeric>
#include <bitset>
#include <sstream>
#include <chrono>
#include <random>
#define ff first
#define ss second
#define PB push_back
#define sz(x) int(x.size())
#define rsz resize
#define fch(xxx, yyy) for (auto xxx : yyy) // abusive notation
#define all(x) (x).begin(),(x).end()
#define eps 1e-9
// more abusive notation (use at your own risk):
// #define int ll
using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
// debugging
void __print(int x) {std::cerr << x;}
void __print(ll x) {std::cerr << x;} /* remember to uncomment this when not using THE MACRO */
void __print(unsigned x) {std::cerr << x;}
void __print(ull x) {std::cerr << x;}
void __print(float x) {std::cerr << x;}
void __print(double x) {std::cerr << x;}
void __print(ld x) {std::cerr << x;}
void __print(char x) {std::cerr << '\'' << x << '\'';}
void __print(const char *x) {std::cerr << '\"' << x << '\"';}
void __print(const string& x) {std::cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V> void __print(const pair<T, V> &x) {std::cerr << '{'; __print(x.ff); std::cerr << ", "; __print(x.ss); std::cerr << '}';}
template<typename T> void __print(const T& x) {int f = 0; std::cerr << '{'; for (auto &i: x) std::cerr << (f++ ? ", " : ""), __print(i); std::cerr << "}";}
void _print() {std::cerr << "]\n";}
template <typename T, typename... V> void _print(T t, V... v) {__print(t); if (sizeof...(v)) std::cerr << ", "; _print(v...);}
void println() {std::cerr << ">--------------------<" << endl;}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
// templates
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 b>a ? a = b, 1 : 0;}
template <class T> using gr = greater<T>;
template <class T> using vc = vector<T>;
template <class T> using p_q = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vc<T>, gr<T>>;
template <class T1, class T2> using pr = pair<T1, T2>;
mt19937_64 rng_ll(chrono::steady_clock::now().time_since_epoch().count());
int rng(int M) {return (int)(rng_ll()%M);} /*returns any random number in [0, M) */
// const variables
constexpr int INF = (int)2e9;
constexpr int MOD = 998244353;
constexpr long double EPS = (ld)1e-10, PI = 3.1415926535;
constexpr ll LL_INF = (ll)3e18;
constexpr int mod = (int)1e9 + 7;
constexpr ll inverse = 500000004LL; // inverse of 2 modulo 1e9 + 7
void setIO(const string& str) {// fast input/output
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
if (str.empty()) return;
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
const int MAXQ = int(1e6) + 5;
int N;
vll h, w, psum;
vll dp;
vc<pll> lines;
vi t, laz;
ll f(int index, ll x) {
return lines[index].ff * x + lines[index].ss;
}
int position(ll a1, ll b1, ll a2, ll b2, ll m) {
if (a1 == a2) return -1; // they will never intersect
if (a2 < a1) {
swap(a1, a2);
swap(b1, b2);
}
return b1 - b2 >= m * (a2 - a1); // if true, it is in the right half [m+1, tr]
}
bool check(int u, int index, int tl, int tr) {
int mid = (tl + tr)/2;
return f(t[u], mid) > f(index, mid);
}
void propagate(int u, int tl, int tr) {
if (laz[u] == -1) return;
int mid = (tl + tr)/2;
if (check(2 * u, laz[u], tl, mid)) {
t[2 * u] = laz[2 * u] = laz[u];
}
if (check(2 * u + 1, laz[u], mid+1, tr)) {
t[2 * u + 1] = laz[2 * u + 1] = laz[u];
}
laz[u] = -1;
}
ll query(int u, int tl, int tr, ll x) {
assert(t[u] != -1);
ll ans = f(t[u], x);
if (tl == tr) return ans;
int mid = (tl + tr)/2;
propagate(u, tl, tr);
if (x <= mid) return min(ans, query(2 * u, tl, mid, x));
else return min(ans, query(2 * u + 1, mid+1, tr, x));
}
void update(int u, int tl, int tr, int index) {
int mid = (tl + tr)/2;
int p = position(lines[t[u]].ff, lines[t[u]].ss, lines[index].ff, lines[index].ss, mid+1);
//debug(u, tl, tr, t[u], index);
if (f(t[u], mid) > f(index, mid)) { // t[u] is already the correct value
t[u] = index;
}
//debug(t[u], p);
if (p == -1) {
if (t[u] == index) laz[u] = index;
return;
}
if (tl == tr) return;
propagate(u, tl, tr);
if (p == 0) {
update(2 * u, tl, mid, index);
if (check(2 * u + 1, index, mid+1, tr)) {
t[2 * u + 1] = laz[2 * u + 1] = index;
}
} else {
update(2 * u + 1, mid+1, tr, index);
if (check(2 * u, index, tl, mid)) {
t[2 * u] = laz[2 * u] = index;
}
}
}
void add_line(ll m, ll b) {
int k = sz(lines);
lines.PB({m, b});
// debug("add_line");
// debug(m, b);
update(1, 0, MAXQ-1, k);
}
signed main() { // TIME YOURSELF !!!
setIO("");
cin >> N;
h.rsz(N), w.rsz(N), psum.rsz(N), dp.rsz(N, INF);
for (int i = 0; i < N; ++i) {
cin >> h[i];
}
for (int i = 0; i < N; ++i) {
cin >> w[i];
psum[i] = (i > 0 ? psum[i-1] : 0) + w[i];
}
t.rsz(4 * MAXQ, 0), laz.rsz(4 * MAXQ, -1);
// debug(-2LL * h[0], h[0] * h[0] - psum[0]);
lines.PB({-2LL * h[0], h[0] * h[0] - psum[0]});
dp[0] = 0;
for (int i = 1; i < N; ++i) {
ll q = query(1, 0, MAXQ-1, h[i]);
// debug(h[i], i, q);
dp[i] = q + h[i] * h[i] + psum[i-1];
// debug(dp[i]);
// debug(-2LL * h[i], dp[i] - psum[i] + h[i] * h[i]);
add_line(-2LL * h[i], dp[i] - psum[i] + h[i] * h[i]);
}
// debug(lines);
// debug(position(-24, 147, -14, 78, 2));
cout << dp[N-1];
return 0;
}
// TLE -> TRY NOT USING DEFINE INT LONG LONG
// CE -> CHECK LINE 45
// 5000 * 5000 size matrices are kinda big (potential mle)
// Do something, start simpler
Compilation message
building.cpp: In function 'void setIO(const string&)':
building.cpp:89:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
89 | freopen((str + ".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
building.cpp:90:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
90 | freopen((str + ".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
9 ms |
31568 KB |
Output is correct |
| 2 |
Incorrect |
9 ms |
31568 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
74 ms |
38852 KB |
Output is correct |
| 2 |
Correct |
74 ms |
38852 KB |
Output is correct |
| 3 |
Incorrect |
79 ms |
38856 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
9 ms |
31568 KB |
Output is correct |
| 2 |
Incorrect |
9 ms |
31568 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
