結果

問題 No.907 Continuous Kadomatu
ユーザー 37zigen
提出日時 2019-04-23 18:59:09
言語 Java
(openjdk 23)
結果
AC  
実行時間 515 ms / 2,000 ms
コード長 3,039 bytes
コンパイル時間 2,176 ms
コンパイル使用メモリ 79,896 KB
実行使用メモリ 44,908 KB
最終ジャッジ日時 2024-10-13 12:57:12
合計ジャッジ時間 11,224 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 * 5
other AC * 25
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// O(N^3)の解
// 制約の侵害の有無を確認
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
class Main {
    public static void main(String[] args) {
        new Main().run();
    }
    final long MOD = 1_000_000_000 + 7;
    long[] karamatsu_prob = new long[400];
    long[] fac = new long[400];
    long[] ifac = new long[400];
    long pow(long a, long n) {
        long ret = 1;
        for (; n > 0; n >>= 1, a = a * a % MOD) {
            if (n % 2 == 1) {
                ret = ret * a % MOD;
            }
        }
        return ret;
    }
    long inv(long a) {
        return pow(a, MOD - 2);
    }
    {
        fac[0] = fac[1] = 1;
        ifac[0] = ifac[1] = 1;
        for (int i = 2; i < fac.length; ++i)
            fac[i] = fac[i - 1] * i % MOD;
        for (int i = 2; i < ifac.length; ++i) {
            ifac[i] = inv(fac[i]);
        }
    }
    long comb(int n, int k) {
        return fac[n] * ifac[k] % MOD * ifac[n - k] % MOD;
    }
    {
        karamatsu_prob[0] = 1;
        karamatsu_prob[1] = 1;
        for (int i = 2; i < karamatsu_prob.length; ++i) {
            for (int j = 0; j <= i - 1; j += 2) {
                karamatsu_prob[i] += karamatsu_prob[j] * karamatsu_prob[i - j - 1] % MOD * comb(i - 1, j) % MOD;
                karamatsu_prob[i] %= MOD;
            }
        }
        for (int i = 0; i < karamatsu_prob.length; ++i) {
            karamatsu_prob[i] = karamatsu_prob[i] * ifac[i] % MOD;
        }
    }
    void run() {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        if (!(3 <= N && N <= 200))
            throw new AssertionError();
        ++N;
        long[] l = new long[N];
        long[] r = new long[N];
        HashSet<Long> set = new HashSet<>();
        for (int i = 1; i < N; ++i) {
            l[i] = sc.nextLong();
            r[i] = sc.nextLong();
            if (!(1 <= l[i] && r[i] <= 1e9 && l[i] < r[i]))
                throw new AssertionError();
            set.add(l[i]);
            set.add(r[i]);
            // [l[i],r[i])
        }
        set.add((long) 1e9);
        set.add((long) 1e9 + 1);
        l[0] = (long) 1e9;
        r[0] = (long) 1e9 + 1;
        long[] a = new long[set.size()];
        int sz = 0;
        for (long v : set) {
            a[sz] = v;
            ++sz;
        }
        Arrays.sort(a);
        // [a[i],a[i+1]]
        long[][] p = new long[N][sz];
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j + 1 < sz; ++j) {
                if (!(l[i] <= a[j] && a[j + 1] <= r[i]))
                    continue;
                p[i][j] = (a[j + 1] - a[j]) * inv(r[i] - l[i]) % MOD;
            }
        }
        long[][] prob = new long[N][sz];
        long[][] pending = new long[N][sz];
        prob[0][sz - 2] = 1;
        for (int t = 0; t < N; ++t) {
            for (int src = 0; src + 1 < sz; ++src) {
                long prob_cur = pending[t][src];
                for (int i = 0; i + t < N; ++i) {
                    prob_cur = prob_cur * p[t + i][src] % MOD;
                    prob[t + i][src] += prob_cur * karamatsu_prob[i + 1] % MOD;
                    prob[t + i][src] %= MOD;
                }
                for (int dst = 0; dst + 1 < sz; ++dst) {
                    if ((t % 2 == 1 && src >= dst) || (t % 2 == 0 && src <= dst))
                        continue;
                    if (t + 1 < N) {
                        pending[t + 1][dst] += prob[t][src] % MOD;
                        pending[t + 1][dst] %= MOD;
                    }
                }
            }
        }
        long ans = 0;
        for (int i = 0; i < prob[N - 1].length; ++i)
            ans = (ans + prob[N - 1][i]) % MOD;
        System.out.println(ans);
    }
    void tr(Object... objects) {
        System.out.println(Arrays.deepToString(objects));
    }
}
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