結果

問題 No.2988 Min-Plus Convolution Query
ユーザー tko919
提出日時 2024-12-20 09:54:43
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,466 ms / 2,000 ms
コード長 12,308 bytes
コンパイル時間 7,725 ms
コンパイル使用メモリ 322,384 KB
実行使用メモリ 126,608 KB
最終ジャッジ日時 2024-12-20 09:55:27
合計ジャッジ時間 38,248 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 2
other AC * 40
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ソースコード

diff #
プレゼンテーションモードにする

#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;
inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}
inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}
void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}
void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}
template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}
template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}
void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}
template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}
template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}
void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}
void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}
template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}
template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}
void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}
template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
    print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}
/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"
#line 2 "library/Algorithm/monotoneminima.hpp"
template<typename F>vector<int> MonotoneMinima(int R,int C,F cmp){
    // cmp(i,j,k) := compare A[i,j] and A[i,k] (A[i,j] -> false, A[i,k] -> true)
    vector<int> ret(R);
    auto rec=[&](auto& f,vector<int> target)->void{
        int m=target.size();
        if(m==0)return;
        vector<int> even;
        for(int i=1;i<m;i+=2)even.push_back(target[i]);
        f(f,even);
        int cur=0;
        for(int i=0;i<m;i+=2){
            ret[target[i]]=cur;
            int end=C-1;
            if(i!=m-1)end=ret[even[i/2]];
            while(cur<end){
                cur++;
                if(cmp(target[i],ret[target[i]],cur))ret[target[i]]=cur;
            }
        }
    };
    vector<int> tmp(R);
    iota(ALL(tmp),0);
    rec(rec,tmp);
    return ret;
}
/**
 * @brief Monotone Minima
 * @docs docs/monotoneminima.md
 */
#line 5 "sol.cpp"
int main() {
    int n, Q;
    read(n, Q);
    vector<int> a(n), b(n);
    read(a, b);
    int M = 1;
    while (M < Q)
        M <<= 1;
    using P = pair<int, int>;
    vector<vector<P>> seg(n);
    vector<vector<P>> qs(M * 2); // {k, index of query}
    rep(i, 0, n) {
        seg[i].push_back({0, a[i]});
    }
    rep(i, 0, Q) {
        int p, x, k;
        read(p, x, k);
        p--, k -= 2;
        seg[p].push_back({i, x});
        qs[i + M].push_back({k, i});
    }
    rrep(i, 1, M) {
        qs[i] = qs[i * 2];
        qs[i].insert(qs[i].end(), ALL(qs[i * 2 + 1]));
    }
    vector<vector<P>> vs(M * 2); // {index of A,value of A}
    auto add = [&](auto &add, int a, int b, P x, int cur = 1, int L = 0,
                   int R = -1) -> void {
        if (R == -1)
            R = M;
        if (R <= a or b <= L)
            return;
        if (a <= L and R <= b) {
            vs[cur].push_back(x);
            return;
        }
        int mid = (L + R) >> 1;
        add(add, a, b, x, cur * 2, L, mid);
        add(add, a, b, x, cur * 2 + 1, mid, R);
    };
    rep(i, 0, n) {
        seg[i].push_back({Q, -1});
        rep(j, 0, SZ(seg[i]) - 1) {
            int L = seg[i][j].first, R = seg[i][j + 1].first;
            if (L >= R)
                continue;
            int x = seg[i][j].second;
            add(add, L, R, P{i, x});
        }
    }
    vector<ll> ret(Q, INF);
    rep(node, 1, M * 2) {
        if (vs[node].empty() or qs[node].empty())
            continue;
        sort(ALL(vs[node]));
        sort(ALL(qs[node]));
        show(vs[node], qs[node]);
        auto get = [&](int i, int j) -> ll {
            int diff = qs[node][i].first - vs[node][j].first;
            if (diff < 0)
                return INF - diff;
            if (diff >= n)
                return INF + diff;
            return vs[node][j].second + b[diff];
        };
        auto ch = [&](int i, int j, int k) -> bool {
            return get(i, j) >= get(i, k);
        };
        int R = SZ(qs[node]), C = SZ(vs[node]);
        auto ids = MonotoneMinima(R, C, ch);
        show(node, ids);
        rep(i, 0, R) chmin(ret[qs[node][i].second], get(i, ids[i]));
    }
    rep(i, 0, Q) print(ret[i]);
    return 0;
}
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