結果

問題 No.856 増える演算
ユーザー 37zigen
提出日時 2019-07-27 10:59:51
言語 Java
(openjdk 23)
結果
AC  
実行時間 1,365 ms / 3,153 ms
コード長 3,625 bytes
コンパイル時間 3,161 ms
コンパイル使用メモリ 79,452 KB
実行使用メモリ 96,972 KB
最終ジャッジ日時 2024-07-02 10:57:21
合計ジャッジ時間 64,855 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 * 80
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 # 

import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	final long MOD = (long) 1e9 + 7;

	long inv(long a) {
		return pow(a, MOD - 2);
	}

	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;
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		for (int i = 0; i < N; ++i) {
			A[i] = sc.nextInt();
		}
		long ans = 1;
		long sum = A[N - 1];
		for (int i = N - 2; i >= 0; --i) {
			ans = ans * pow(A[i], sum) % MOD;
			sum += A[i];
			sum %= MOD - 1;
		}
		long[] cnt = new long[100000 + 1];
		for (int i = 0; i < N; ++i)
			cnt[A[i]]++;
		long[] cnt2 = mul(cnt, cnt);
		for (int i = 0; i < N; ++i) {
			cnt2[2 * A[i]]--;
		}
		for (int i = 0; i < cnt2.length; ++i) {
			cnt2[i] /= 2;
			ans = ans * pow(i, cnt2[i]) % MOD;
		}

		long coe = -1;
		double v = Double.MAX_VALUE / 3;
		long min = A[0];
		for (int i = 1; i < N; ++i) {
			if (v > Math.log(A[i] + min) + A[i] * Math.log(min)) {
				v = Math.log(A[i] + min) + A[i] * Math.log(min);
				coe = (A[i] + min) % MOD * pow(min, A[i]) % MOD;
			}
			min = Math.min(min, A[i]);
		}

		ans = ans * inv(coe) % MOD;
		System.out.println(ans);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

	static long[] mul(long[] a, long[] b) {
		int n = 1;
		while (n < a.length + b.length)
			n *= 2;
		Complex[] ac = new Complex[n];
		Complex[] bc = new Complex[n];
		for (int i = 0; i < n; ++i) {
			ac[i] = new Complex(0, 0);
			bc[i] = new Complex(0, 0);
		}
		for (int i = 0; i < a.length; ++i) {
			ac[i].re = a[i];
		}
		for (int i = 0; i < b.length; ++i) {
			bc[i].re = b[i];
		}
		ac = fft(ac, false);
		bc = fft(bc, false);
		for (int i = 0; i < ac.length; ++i) {
			ac[i] = ac[i].mul(bc[i]);
		}
		ac = fft(ac, true);
		for (int i = 0; i < ac.length; ++i) {
			ac[i].re /= n;
			ac[i].co /= n;
		}
		long[] ret = new long[ac.length];
		for (int i = 0; i < ret.length; ++i) {
			ret[i] = (long) Math.round(ac[i].re);
		}
		return ret;

	}

	static Complex[] fft(Complex[] a, boolean rev) {
		int n = a.length;
		if (n == 1)
			return a;
		int c = 0;
		for (int i = 1; i < n; ++i) {
			int j;
			for (j = n >> 1; j > (c ^= j); j >>= 1)
				;
			if (c > i) {
				Complex tmp = a[c];
				a[c] = a[i];
				a[i] = tmp;
			}
		}

		for (int d = 1; d < n; d <<= 1) {
			for (int j = 0; j < d; ++j) {
				double angle = 2 * Math.PI / (2 * d) * (rev ? -1 : 1) * j;
				Complex mul = new Complex(Math.cos(angle), Math.sin(angle));
				for (int pos = 0; pos < n; pos += 2 * d) {
					double ure = a[pos + j].re;
					double uco = a[pos + j].co;
					double vre = a[pos + j + d].re * mul.re - a[pos + j + d].co * mul.co;
					double vco = a[pos + j + d].co * mul.re + a[pos + j + d].re * mul.co;
					a[pos + j].re = ure + vre;
					a[pos + j].co = uco + vco;
					a[pos + j + d].re = ure - vre;
					a[pos + j + d].co = uco - vco;
				}
			}
		}
		return a;
	}

	Complex exp(double a) {
		return new Complex(Math.cos(a), Math.sin(a));
	}

	static class Complex {
		double re, co;

		public Complex(double re, double co) {
			this.re = re;
			this.co = co;
		}

		Complex add(Complex o) {
			return new Complex(re + o.re, co + o.co);
		}

		Complex subtract(Complex o) {
			return new Complex(re - o.re, co - o.co);
		}

		Complex mul(Complex o) {
			return new Complex(re * o.re - co * o.co, re * o.co + o.re * co);
		}
	}
}
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