結果

問題 No.3127 Multiple of Twin Prime
コンテスト
ユーザー InTheBloom
提出日時 2025-04-25 21:45:04
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 574 ms / 2,500 ms
コード長 7,127 bytes
コンパイル時間 4,116 ms
コンパイル使用メモリ 213,628 KB
実行使用メモリ 129,372 KB
最終ジャッジ日時 2025-04-25 21:45:31
合計ジャッジ時間 13,123 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 1
other AC * 12
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ソースコード

diff # 

import std;

void main () {
    int T = readln.chomp.to!int;
    // 先に列挙 -> 二分探索で解けるには解けるが、計算量がかなり怪しい

    alias ls = LinearSieve;
    ls.build(10 ^^ 7);

    auto candi = new long[](0);
    foreach (i; 2 .. 10 ^^ 7) {
        if (ls.is_prime(i) && ls.is_prime(i + 2)) {
            candi ~= 1L * i * (i + 2);
        }
    }

    auto ans = new long[](T);
    foreach (caseid; 0 .. T) {
        long N = readln.chomp.to!long;
        auto ret = bsearch!((int id) => candi[id] <= N)(0, candi.length.to!int - 1);
        if (ret.empty) {
            ans[caseid] = -1;
        }
        else {
            ans[caseid] = candi[ret.value];
        }
    }

    writefln("%(%s\n%)", ans);
}

void read (T...) (string S, ref T args) {
    import std.conv : to;
    import std.array : split;
    auto buf = S.split;
    foreach (i, ref arg; args) {
        arg = buf[i].to!(typeof(arg));
    }
}

import std.typecons : Tuple, tuple;

class LinearSieve {
    /// methods
    /// - void build (ulong N_)
    /// - Tuple!(long, long)[] prime_factors (ulong N_)
    /// - bool is_prime (ulong N_)
    /// - long[] divisors (ulong N_)

    private:
        static int N = 0;
        static int[] lpf;
        static int[] primes;
        static int[] lpf_ord;
        static int[] lpf_pow;

    import std.conv : to;
    import std.format : format;

    public:
        @disable this () {}

        static void build (ulong N_)
        in {
            assert(2 <= N_ && N_ <= int.max, format("Argument N_ = %s does not meet condition.", N_));
        }
        do {
            // Linear sieve.
            if (N+1 <= lpf.length) return;
            N = N_.to!int;

            primes.length = 0;
            lpf.length = N+1;

            lpf[0] = lpf[1] = 1;

            for (int i = 2; i <= N; i++) {
                if (lpf[i] == 0) {
                    lpf[i] = i;
                    primes ~= i;
                }

                foreach (p; primes) {
                    if (lpf[i] < p) break;
                    if (N < 1L * i * p) break;
                    lpf[i * p] = p;
                }
            }

            // Precomputation of prime factorization.
            lpf_ord.length = lpf_pow.length = N+1;
            lpf_pow[] = 1;

            for (int i = 2; i <= N; i++) {
                int prev = i / lpf[i];

                if (lpf[i] == lpf[prev]) {
                    lpf_ord[i] = lpf_ord[prev] + 1;
                    lpf_pow[i] = lpf_pow[prev] * lpf[i];
                }
                else {
                    lpf_ord[i] = 1;
                    lpf_pow[i] = lpf[i];
                }
            }
        }

        static Tuple!(long, long)[] prime_factors (ulong N_)
        in {
            assert(2 <= N_ && N_ <= N, format("Argument N_ = %s is not out of range. The valid range is [2, %s].", N_, N));
        }
        do {
            int n = N_.to!int;
            Tuple!(long, long)[] res;

            while (1 < n) {
                res ~= tuple(1L*lpf[n], 1L*lpf_ord[n]);
                n /= lpf_pow[n];
            }

            return res;
        }

        static bool is_prime (ulong N_)
        in {
            assert(2 <= N_ && N_ <= N, format("Argument N_ = %s is not out of range. The valid range is [2, %s].", N_, N));
        }
        do {
            int N = N_.to!int;
            return lpf[N] == N;
        }

        static long[] divisors (ulong N_)
        in {
            assert(N_ <= N, format("Argument N_ = %s is not out of range. The valid range is [2, %s].", N_, N));
        }
        do {
            if (N_ == 1) return [1L];

            import std.container : SList;
            import std.algorithm : sort;

            auto fac = prime_factors(N_);

            static SList!(Tuple!(int, long)) Q;
            Q.insertFront(tuple(0, 1L)); // (処理済み階層, 値)

            long[] res;
            while (!Q.empty) {
                auto h = Q.front; Q.removeFront;
                if (h[0] == fac.length) {
                    res ~= h[1];
                    continue;
                }

                auto p = fac[h[0]];
                long prod = 1;
                foreach (i; 0..p[1] + 1) {
                    Q.insertFront(tuple(h[0] + 1, h[1] * prod));
                    prod *= p[0];
                }
            }

            res.sort;
            return res;
        }
}

import std.traits : isIntegral;
import std.int128 : Int128;

class NoTrueRangeException: Exception {
    import std.exception: basicExceptionCtors;
    mixin basicExceptionCtors;
}

class BsearchException: Exception {
    import std.exception: basicExceptionCtors;
    mixin basicExceptionCtors;
}

struct BsearchResult (T) {
    import std.format: format;

    private bool has_value = true;
    private T l, r;
    private T _value;

    this (T _l, T _r) {
        this.l = _l;
        this.r = _r;
        this.has_value = false;
    }
    this (T _l, T _r, T _value) {
        this.l = _l;
        this.r = _r;
        this._value = _value;
    }

    bool empty () {
        return !this.has_value;
    }

    T value () {
        if (this.empty()) {
            throw new NoTrueRangeException(
                    format("No true condition found in the range [%s, %s].", l, r));
        }

        return _value;
    };
}

BsearchResult!T bsearch (alias func, T) (T l, T r)
if ((isIntegral!(T) || is(T == Int128)) &&
        !is(T == byte) &&
        !is(T == ubyte) &&
        !is(T == short) &&
        !is(T == ushort))
{
    import std.traits : isCallable, ReturnType, Parameters;
    import std.meta : AliasSeq;

    static assert(isCallable!(func));
    static assert(is(ReturnType!(func) == bool));
    static assert(is(Parameters!(func) == AliasSeq!(T)));

    import std.algorithm.comparison : min, max;
    T L = l, R = r;

    if (l == r) {
        if (func(l)) return BsearchResult!(T)(L, R, l);
        return BsearchResult!(T)(L, R);
    }

    while (min(l, r) + 1 < max(l, r)) {
        T m = midpoint(l, r);

        if (func(m)) {
            l = m;
        }
        else {
            r = m;
        }
    }

    bool lb = func(l);
    if (!lb) return BsearchResult!(T)(L, R);

    bool rb = func(r);
    if (rb) return BsearchResult!(T)(L, R, r);
    if (!rb) return BsearchResult!(T)(L, R, l);

    throw new BsearchException(format("This code path should never be reached. l: %s, r: %s.", L, R));
}

T midpoint (T) (T a, T b)
if (isIntegral!(T) || is(T == Int128))
{
    static if (is(T == short) || is(T == ushort) || is(T == byte) || is(T == ubyte)) {
        import std.conv : to;
        int x = a, y = b;
        return midpoint(x, y).to!(T);
    }
    else {
        import std.math.algebraic : abs;
        import std.algorithm.comparison : min, max;
        
        int as = (0 <= a) ? 1 : -1, bs = (0 <= b) ? 1 : -1;
        if (as == bs) {
            if (as == 1) {
                return min(a, b) + (max(a, b) - min(a, b)) / 2;
            }
            return max(a, b) + (min(a, b) - max(a, b)) / 2;
        }

        return (a + b) / 2;
    }
}
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