test/CHT-Monotone.test.cpp

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• Last update: 2025-07-04 15:57:54+09:00
• Problem: https://yukicoder.me/problems/no/703

Depends on

• CHT-Monotone.cpp

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/703
#include "../CHT-Monotone.cpp"
using ll = long long;
void solve() {
    int n;
    cin >> n;
    vector<ll> a(n), x(n), y(n), dp(n + 1);
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) cin >> x[i];
    for (int i = 0; i < n; i++) cin >> y[i];
    dp[0] = 0;
    CHT_Monotone<ll> cht;
    for (int i = 0; i < n; i++) {
        cht.add(-2 * x[i], dp[i] + x[i] * x[i] + y[i] * y[i]);
        dp[i + 1] = a[i] * a[i] + cht.query(a[i]);
    }
    cout << dp[n] << endl;
}
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    solve();
}

#line 1 "test/CHT-Monotone.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/703
#line 1 "CHT-Monotone.cpp"
#include <bits/stdc++.h>
using namespace std;
template <class T, bool isMax = false>
struct CHT_Monotone {
    // 追加クエリの傾き：単調減少 xor isMax
    // 取得クエリのx座標：単調増加 xor isMax
    // (単調増加,単調減少)のとき：a,x -1倍
    struct Line {
        T a, b;
        T y(T x) { return a * x + b; }
    };
    deque<Line> q;
    bool noneed(Line a, Line b, Line c) { return (b.b - c.b) * (b.a - a.a) <= (a.b - b.b) * (c.a - b.a); }
    void add(T a, T b) {
        Line l = {a, b};
        while (q.size() > 1 && noneed(q[q.size() - 2], q[q.size() - 1], l)) {
            q.pop_back();
        }
        q.push_back(l);
    }
    T query(T x) {
        if (q.empty()) return numeric_limits<T>::max() / 2;
        while (q.size() > 1 && ((q[0].y(x) > q[1].y(x)) ^ isMax)) {
            q.pop_front();
        }
        return q[0].y(x);
    }
};
#line 3 "test/CHT-Monotone.test.cpp"
using ll = long long;
void solve() {
    int n;
    cin >> n;
    vector<ll> a(n), x(n), y(n), dp(n + 1);
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) cin >> x[i];
    for (int i = 0; i < n; i++) cin >> y[i];
    dp[0] = 0;
    CHT_Monotone<ll> cht;
    for (int i = 0; i < n; i++) {
        cht.add(-2 * x[i], dp[i] + x[i] * x[i] + y[i] * y[i]);
        dp[i + 1] = a[i] * a[i] + cht.query(a[i]);
    }
    cout << dp[n] << endl;
}
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    solve();
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample1.txt	AC	5 ms	3 MB
g++	00_sample2.txt	AC	4 ms	4 MB
g++	00_sample3.txt	AC	4 ms	4 MB
g++	00_sample4.txt	AC	4 ms	4 MB
g++	20_small1.txt	AC	4 ms	4 MB
g++	20_small10.txt	AC	4 ms	3 MB
g++	20_small2.txt	AC	4 ms	4 MB
g++	20_small3.txt	AC	4 ms	3 MB
g++	20_small4.txt	AC	4 ms	4 MB
g++	20_small5.txt	AC	4 ms	4 MB
g++	20_small6.txt	AC	4 ms	3 MB
g++	20_small7.txt	AC	4 ms	4 MB
g++	20_small8.txt	AC	4 ms	4 MB
g++	20_small9.txt	AC	4 ms	4 MB
g++	30_medium1.txt	AC	4 ms	4 MB
g++	30_medium10.txt	AC	4 ms	4 MB
g++	30_medium2.txt	AC	4 ms	4 MB
g++	30_medium3.txt	AC	4 ms	4 MB
g++	30_medium4.txt	AC	4 ms	4 MB
g++	30_medium5.txt	AC	4 ms	4 MB
g++	30_medium6.txt	AC	4 ms	4 MB
g++	30_medium7.txt	AC	4 ms	4 MB
g++	30_medium8.txt	AC	4 ms	4 MB
g++	30_medium9.txt	AC	4 ms	4 MB
g++	40_large1.txt	AC	52 ms	13 MB
g++	40_large10.txt	AC	53 ms	13 MB
g++	40_large2.txt	AC	53 ms	13 MB
g++	40_large3.txt	AC	54 ms	13 MB
g++	40_large4.txt	AC	54 ms	13 MB
g++	40_large5.txt	AC	54 ms	13 MB
g++	40_large6.txt	AC	54 ms	13 MB
g++	40_large7.txt	AC	54 ms	13 MB
g++	40_large8.txt	AC	53 ms	13 MB
g++	40_large9.txt	AC	54 ms	13 MB
g++	50_large_binary1.txt	AC	52 ms	13 MB
g++	50_large_binary10.txt	AC	57 ms	13 MB
g++	50_large_binary2.txt	AC	52 ms	13 MB
g++	50_large_binary3.txt	AC	53 ms	13 MB
g++	50_large_binary4.txt	AC	53 ms	13 MB
g++	50_large_binary5.txt	AC	53 ms	13 MB
g++	50_large_binary6.txt	AC	52 ms	13 MB
g++	50_large_binary7.txt	AC	51 ms	13 MB
g++	50_large_binary8.txt	AC	51 ms	13 MB
g++	50_large_binary9.txt	AC	51 ms	13 MB
g++	99_corner1.txt	AC	5 ms	4 MB
g++	99_corner2.txt	AC	4 ms	4 MB
g++	99_corner3.txt	AC	52 ms	13 MB
g++	99_corner4.txt	AC	54 ms	13 MB
g++	99_system_test1.txt	AC	5 ms	4 MB
g++	99_system_test2.txt	AC	5 ms	4 MB
clang++	00_sample1.txt	AC	5 ms	4 MB
clang++	00_sample2.txt	AC	5 ms	4 MB
clang++	00_sample3.txt	AC	5 ms	4 MB
clang++	00_sample4.txt	AC	4 ms	4 MB
clang++	20_small1.txt	AC	4 ms	4 MB
clang++	20_small10.txt	AC	4 ms	4 MB
clang++	20_small2.txt	AC	4 ms	4 MB
clang++	20_small3.txt	AC	4 ms	4 MB
clang++	20_small4.txt	AC	4 ms	4 MB
clang++	20_small5.txt	AC	4 ms	4 MB
clang++	20_small6.txt	AC	4 ms	4 MB
clang++	20_small7.txt	AC	4 ms	4 MB
clang++	20_small8.txt	AC	4 ms	4 MB
clang++	20_small9.txt	AC	4 ms	4 MB
clang++	30_medium1.txt	AC	5 ms	4 MB
clang++	30_medium10.txt	AC	5 ms	4 MB
clang++	30_medium2.txt	AC	5 ms	4 MB
clang++	30_medium3.txt	AC	4 ms	4 MB
clang++	30_medium4.txt	AC	4 ms	4 MB
clang++	30_medium5.txt	AC	5 ms	4 MB
clang++	30_medium6.txt	AC	5 ms	4 MB
clang++	30_medium7.txt	AC	5 ms	4 MB
clang++	30_medium8.txt	AC	5 ms	4 MB
clang++	30_medium9.txt	AC	4 ms	4 MB
clang++	40_large1.txt	AC	53 ms	13 MB
clang++	40_large10.txt	AC	54 ms	13 MB
clang++	40_large2.txt	AC	54 ms	13 MB
clang++	40_large3.txt	AC	54 ms	13 MB
clang++	40_large4.txt	AC	54 ms	13 MB
clang++	40_large5.txt	AC	53 ms	13 MB
clang++	40_large6.txt	AC	53 ms	13 MB
clang++	40_large7.txt	AC	53 ms	13 MB
clang++	40_large8.txt	AC	53 ms	13 MB
clang++	40_large9.txt	AC	53 ms	13 MB
clang++	50_large_binary1.txt	AC	52 ms	13 MB
clang++	50_large_binary10.txt	AC	52 ms	13 MB
clang++	50_large_binary2.txt	AC	52 ms	13 MB
clang++	50_large_binary3.txt	AC	53 ms	13 MB
clang++	50_large_binary4.txt	AC	52 ms	13 MB
clang++	50_large_binary5.txt	AC	52 ms	13 MB
clang++	50_large_binary6.txt	AC	53 ms	13 MB
clang++	50_large_binary7.txt	AC	53 ms	13 MB
clang++	50_large_binary8.txt	AC	52 ms	13 MB
clang++	50_large_binary9.txt	AC	52 ms	13 MB
clang++	99_corner1.txt	AC	5 ms	4 MB
clang++	99_corner2.txt	AC	4 ms	4 MB
clang++	99_corner3.txt	AC	53 ms	13 MB
clang++	99_corner4.txt	AC	54 ms	13 MB
clang++	99_system_test1.txt	AC	5 ms	4 MB
clang++	99_system_test2.txt	AC	5 ms	4 MB

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