#782817 (C++17) No.2026 Yet Another Knapsack Problem

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問題	No.2026 Yet Another Knapsack Problem
コンテスト
ユーザー	haruki_K
提出日時	2022-07-30 08:28:49
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	1,824 ms / 10,000 ms
コード長	14,877 bytes
コンパイル時間	3,062 ms
コンパイル使用メモリ	216,832 KB
最終ジャッジ日時	2025-01-30 16:34:09
ジャッジサーバーID （参考情報）	judge2 / judge5
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 3
other	AC * 42
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ソースコード

raw source code
// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t)
{ bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; }
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
auto four_nbd(int n, int m) {
    static vector<pair<int, int>> v;
    return [n, m](int i, int j) {
        const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 };
        v.clear();
        rep (dir, 4) {
            int ni = i+dx[dir], nj = j+dy[dir];
            if (0 <= ni and ni < n and 0 <= nj and nj < m) {
                v.emplace_back(ni, nj);
            }
        }
        return v;
    };
};
template <class Comp> vector<int> iota(int n, Comp comp) {
    vector<int> idx(n);
    iota(begin(idx), end(idx), 0);
    stable_sort(begin(idx), end(idx), comp);
    return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class vec> int sort_unique(vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
// <<<
// >>> DST
template <class Handler>
struct DST : Handler {
    using Value = typename Handler::Value;
    using Handler::unit_value; // () -> Value
    using Handler::merge; // (Value, Value) -> Value
    static constexpr int bsr(int32_t x) { return x ? 31-__builtin_clz(x) : -1; }

    vector<vector<Value>> v;
    DST() {}
    template <class... T> DST(T&&... x) { build(forward<T>(x)...); }
    void build(int n) { build(n, unit_value()); }
    void build(int n, Value const& x) { build(n, [&](int) { return x; }); }
    void build(vector<Value> const& v) { build(v.size(), [&](int i) { return v[i]; }); }
    template <class F, class = decltype(declval<F>()(0))>
    void build(int n, F gen)  {
        assert(n >= 0);
        v.resize(1);
        v[0].resize(n, unit_value());
        for (int i = 0; i < n; i++) v[0][i] = gen(i);
        if (n <= 1) return;
        const int lg = __lg(2*n-1);
        v.resize(lg, vector<Value>(n, unit_value()));
        for (int h = 1; h < lg; ++h) {
            const int w = 1<<h;
            for (int b = w; b < n; b += (w<<1)) {
                Value x = unit_value();
                for (int j = b-1; j >= b-w; --j) {
                    v[h][j] = x = merge(v[0][j], x);
                }
                x = unit_value();
                for (int j = b; j < min(n, b+w); ++j) {
                    v[h][j] = x = merge(x, v[0][j]);
                }
            }
        }
    }
    int size() const { return v.empty() ? 0 : v[0].size(); }
    Value get(int l, int r) const {
        assert(0 <= l); assert(l <= r); assert(r <= size());
        if (l == r) return unit_value();
        --r;
        if (l == r) return v[0][l];
        const int h = bsr(l^r);
        return merge(v[h][l], v[h][r]);
    }
    Value operator[](int idx) const {
        assert(0 <= idx); assert(idx < size());
        return v[0][idx];
    }
};
// <<<
// >>> segment tree

template <class Handler> struct Segtree : Handler {
    using Value = typename Handler::Value;
    using Handler::unit_value;  // () -> Value
    using Handler::merge; // (Value, Value) -> Value

    vector<Value> v;
    int n;

    Segtree() {}
    template <class... T> Segtree(T&&... x) { init(forward<T>(x)...); }

    template <class F, class = decltype(declval<F>()(0))>
    void init(int n, F gen)  {
        assert(n >= 0);
        this->n = n;
        v.resize(2*n, unit_value());
        for (int i = 0; i < n; i++) v[n+i] = gen(i);
        for (int i = n-1; i >= 1; i--) v[i] = merge(v[i<<1], v[i<<1|1]);
    }
    void init(int n) { init(n, [&](int) { return unit_value(); }); }
    void init(int n, Value const& x) { init(n, [&](int) { return x; }); }
    void init(vector<Value> const& v) { init(v.size(), [&](int i) { return v[i]; }); }
    int size() const { return n; }

    void set(int i, Value const& x) {
        assert(0 <= i); assert(i < size());
        i += n; v[i] = x;
        while (i >>= 1) v[i] = merge(v[i<<1], v[i<<1|1]);
    }
    Value operator[](int i) const { return get(i); }
    Value get(int i) const {
        assert(0 <= i); assert(i < size());
        return v[n + i];
    }
    // [l, r)
    Value get(int l, int r) const {
        assert(0 <= l); assert(l <= r); assert(r <= size());
        Value x = unit_value(), y = unit_value();
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l&1) x = merge(x, v[l++]);
            if (r&1) y = merge(v[--r], y);
        }
        return merge(x, y);
    }
    Value get_all() const { return get(0, size()); }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l); assert(l <= size());
        assert(f(unit_value()));
        l += n;
        const int r = size() << 1;
        Value x = unit_value();
        while (true) {
            if (l == r) return size();
            int k = __builtin_ctz(l | 1 << __lg(r - l));
            auto y = merge(x, v[l >> k]);
            if (not f(y)) { l >>= k; break; }
            x = y, l += 1 << k;
        }
        while (l < size()) {
            auto y = merge(x, v[l <<= 1]);
            if (f(y)) x = y, l++;
        }
        return l - size();
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r); assert(r <= size());
        assert(f(unit_value()));
        r += n;
        const int l = size();
        Value x = unit_value();
        while (true) {
            if (l == r) return 0;
            int k = __builtin_ctz(r | 1 << __lg(r - l));
            auto y = merge(v[(r >> k) - 1], x);
            if (not f(y)) { r >>= k; --r; break; }
            x = y, r -= 1 << k;
        }
        while (r < size()) {
            r = r << 1 | 1;
            auto y = merge(v[r], x);
            if (f(y)) x = y, r--;
        }
        return r + 1 - size();
    }
    vector<Value> dat() const {
        vector<Value> ret(size());
        for (int i = 0; i < size(); i++) ret[i] = get(i);
        return ret;
    }
};

// <<<

struct Min {
    using Value = int;
    constexpr static Value unit_value() { return INF; }
    constexpr static Value merge(Value const& x, Value const& y) {
        return min(x, y);
    }
};
struct Max {
    using Value = int;
    constexpr static Value unit_value() { return -INF; }
    constexpr static Value merge(Value const& x, Value const& y) {
        return max(x, y);
    }
};

int32_t main() {
    int n; cin >> n;
    vector<int> c(n+1), v(n+1);
    rep1 (i, n) cin >> c[i] >> v[i];

    auto dp = make_v<int, 2>(n+1, n+1, -INF);
    dp[0][0] = 0;
    rep1R (k, n) {
        const int m = n/k;
        auto a = [&](int i, int w) { return dp[i][w] - i*v[k]; };
        debug {
            auto DP = dp;
            DP.resize(n/(k+1)+1);
            dump(k, m, n/(k+1), as_mat(DP));
        }
        repR (i, m+1) rep (w, n+1) if (not (i+1 < m+1 and w+k < n+1)) {
            static vector<int> dat(n+1);
            static DST<Max> dst(n+1);
            dat.clear();
            for (int pi = i, pw = w; pi >= 0 and pw >= 0; pi--, pw -= k) {
                dat.eb(a(pi, pw));
            }
            dst.build(dat);
            for (int pi = i, pw = w; pi >= 0 and pw >= 0; pi--, pw -= k) {
                int l = i-pi, r = min(dst.size(), l+c[k]+1);
                chmax(dp[pi][pw], dst.get(l, r) + pi*v[k]);
            }
        }
    }

    rep1 (i, n) cout << max(dp[i]) << '\n';

}
yukicoder

結果

ソースコード
