test/yukicoder/1297.test.cpp

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• Last update: 2021-12-30 18:51:46+09:00
• Problem: https://yukicoder.me/problems/no/1297

Depends on

• cpp_src/other/LineContainer.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1297"
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

#define call_from_test
#include "../../cpp_src/other/LineContainer.hpp"
#undef call_from_test

const ll INF = TEN(18);

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int N;
    ll C;
    cin >> N >> C;
    V<ll> a(N), b(N);
    rep(i, N) cin >> a[i] >> b[i];

    V<ll> dp(N + 1, INF), sub(N + 1, INF);
    dp[0] = 0;

    LineContainer<false> ls, ld;

    rep(i, N) {
        ls.add(-i, C * i * i + dp[i] * 2);
        sub[i + 1] = ls.query((2 * i + 1) * C + 2 * a[i]);

        if (i) {
            ld.add(-i * C + a[i - 1],
                   -(i - 1) * a[i - 1] + C * i * (i - 3) / 2 + sub[i]);
            dp[i + 1] = ld.query(i) + C * (i + 1) * (i + 2) / 2;
        }

        sub[i + 1] =
            sub[i + 1] / 2 + b[i] + a[i] * (i + 1) + C * i * (i + 1) / 2;
        chmin(dp[i + 1], sub[i + 1]);
    }

    cout << dp[N] << endl;

    return 0;
}

#line 1 "test/yukicoder/1297.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1297"
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

#define call_from_test
#line 1 "cpp_src/other/LineContainer.hpp"
// modified
// https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h
// lines : y = kx + m
// find maximum at x

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; }
};

template <bool maximum>
struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const ll inf = numeric_limits<ll>::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) {
        if (!maximum) 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());
        auto l = *lower_bound(x);
        auto res = l.k * x + l.m;
        if (!maximum) res = -res;
        return res;
    }
};
#line 69 "test/yukicoder/1297.test.cpp"
#undef call_from_test

const ll INF = TEN(18);

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int N;
    ll C;
    cin >> N >> C;
    V<ll> a(N), b(N);
    rep(i, N) cin >> a[i] >> b[i];

    V<ll> dp(N + 1, INF), sub(N + 1, INF);
    dp[0] = 0;

    LineContainer<false> ls, ld;

    rep(i, N) {
        ls.add(-i, C * i * i + dp[i] * 2);
        sub[i + 1] = ls.query((2 * i + 1) * C + 2 * a[i]);

        if (i) {
            ld.add(-i * C + a[i - 1],
                   -(i - 1) * a[i - 1] + C * i * (i - 3) / 2 + sub[i]);
            dp[i + 1] = ld.query(i) + C * (i + 1) * (i + 2) / 2;
        }

        sub[i + 1] =
            sub[i + 1] / 2 + b[i] + a[i] * (i + 1) + C * i * (i + 1) / 2;
        chmin(dp[i + 1], sub[i + 1]);
    }

    cout << dp[N] << endl;

    return 0;
}

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