結果

問題 No.856 増える演算
ユーザー 👑 hos.lyrichos.lyric
提出日時 2019-07-26 22:50:33
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 526 ms / 3,153 ms
コード長 9,447 bytes
コンパイル時間 1,540 ms
コンパイル使用メモリ 159,356 KB
実行使用メモリ 32,736 KB
最終ジャッジ日時 2024-06-22 02:07:25
合計ジャッジ時間 32,196 ms
ジャッジサーバーID
(参考情報)
judge4 / 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 * 3
other AC * 80
権限があれば一括ダウンロードができます
コンパイルメッセージ
Main.d(332): Deprecation: function `std.math.exponential.log` is deprecated - `std.math.exponential.log` called with argument types `(long)` matches both `log(real)`, `log(double)`, and `log(float)`. Cast argument to floating point type instead.
Main.d(332): Deprecation: function `std.math.exponential.log` is deprecated - `std.math.exponential.log` called with argument types `(long)` matches both `log(real)`, `log(double)`, and `log(float)`. Cast argument to floating point type instead.

ソースコード

diff #
プレゼンテーションモードにする

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.regex, std.typecons;
import core.bitop;
class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens
    .popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }
bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }
int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1;
    (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }
struct ModInt(long M) {
long x;
this(in ModInt a) { x = a.x; }
this(in long a) { x = a % M; if (x < 0) x += M; }
ref ModInt opAssign(in long a) { return this = ModInt(a); }
ref ModInt opOpAssign(string op)(in ModInt a) {
static if (op == "+") { x += a.x; if (x >= M) x -= M; }
else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
else static if (op == "*") { x *= a.x; x %= M; }
else static assert(false);
return this;
}
ref ModInt opOpAssign(string op)(in long a) { return mixin("this " ~ op ~ "= ModInt(a)"); }
ModInt opUnary(string op)() const if (op == "-") { return ModInt(-x); }
ModInt opBinary(string op, T)(in T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
ModInt opBinaryRight(string op)(in long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
string toString() const { return x.to!string; }
}
// a^-1 (mod 2^64)
long modInv(long a)
in {
assert(a & 1, "modInv: a must be odd");
}
do {
long b = ((a << 1) + a) ^ 2;
b *= 2 - a * b;
b *= 2 - a * b;
b *= 2 - a * b;
b *= 2 - a * b;
return b;
}
// a^-1 (mod m)
long modInv(long a, long m)
in {
assert(m > 0, "modInv: m > 0 must hold");
}
do {
long b = m, x = 1, y = 0, t;
for (; ; ) {
t = a / b;
a -= t * b;
if (a == 0) {
assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
if (b == -1) {
y = -y;
}
return (y < 0) ? (y + m) : y;
}
x -= t * y;
t = b / a;
b -= t * a;
if (b == 0) {
assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
if (a == -1) {
x = -x;
}
return (x < 0) ? (x + m) : x;
}
y -= t * x;
}
}
// 2^-31 a (mod M)
long montgomery(long M)(long a) if (1 <= M && M <= 0x7fffffff && (M & 1))
in {
assert(0 <= a && a < (M << 31), "montgomery: 0 <= a < 2^31 M must hold");
}
do {
enum negInvM = -modInv(M) & 0x7fffffff;
const b = (a + ((a * negInvM) & 0x7fffffff) * M) >> 31;
return (b >= M) ? (b - M) : b;
}
// FFT on Z / M Z with Montgomery multiplication (x -> 2^31 x)
// G: primitive 2^K-th root of unity
class FFT(long M, int K, long G)
if (is(typeof(montgomery!(M)(0))) && K >= 0 && 0 < G && G < M) {
import std.algorithm : swap;
import core.bitop : bsf;
int n, invN;
long[] g;
this(int n)
in {
assert(!(n & (n - 1)), "FFT.this: n must be a power of 2");
assert(4 <= n && n <= 1 << K, "FFT.this: 4 <= n <= 2^K must hold");
}
do {
this.n = n;
this.invN = ((1L << 31) / n) % M;
g.length = n + 1;
g[0] = (1L << 31) % M;
g[1] = (G << 31) % M;
foreach (_; 0 .. K - bsf(n)) {
g[1] = montgomery!(M)(g[1] * g[1]);
}
foreach (i; 2 .. n + 1) {
g[i] = montgomery!(M)(g[i - 1] * g[1]);
}
assert(g[0] != g[n >> 1] && g[0] == g[n],
"FFT.this: G must be a primitive 2^K-th root of unity");
for (int i = 0, j = 0; i < n >> 1; ++i) {
if (i < j) {
swap(g[i], g[j]);
swap(g[n - i], g[n - j]);
}
for (int m = n >> 1; (m >>= 1) && !((j ^= m) & m); ) {}
}
}
void fftMontgomery(long[] x, bool inv)
in {
assert(x.length == n, "FFT.fftMontgomery: |x| = n must hold");
}
do {
foreach_reverse (h; 0 .. bsf(n)) {
const l = 1 << h;
foreach (i; 0 .. n >> 1 >> h) {
const gI = g[inv ? (n - i) : i];
foreach (j; i << 1 << h .. ((i << 1) + 1) << h) {
const t = montgomery!(M)(gI * x[j + l]);
if ((x[j + l] = x[j] - t) < 0) {
x[j + l] += M;
}
if ((x[j] += t) >= M) {
x[j] -= M;
}
}
}
}
for (int i = 0, j = 0; i < n; ++i) {
if (i < j) {
swap(x[i], x[j]);
}
for (int m = n; (m >>= 1) && !((j ^= m) & m); ) {}
}
if (inv) {
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(invN * x[i]);
}
}
}
long[] convolution(long[] a, long[] b)
in {
assert(a.length <= n, "FFT.convolution: |a| <= n must hold");
assert(b.length <= n, "FFT.convolution: |b| <= n must hold");
}
do {
auto x = new long[n], y = new long[n];
foreach (i; 0 .. a.length) {
const t = a[i] % M;
x[i] = (((t < 0) ? (t + M) : t) << 31) % M;
}
foreach (i; 0 .. b.length) {
const t = b[i] % M;
y[i] = (((t < 0) ? (t + M) : t) << 31) % M;
}
fftMontgomery(x, false);
fftMontgomery(y, false);
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(x[i] * y[i]);
}
fftMontgomery(x, true);
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(x[i]);
}
return x;
}
}
// P0 P1 P2 > 2^90, P0 + P1 + P2 = 2^32 + 3
enum FFT_P0 = 2013265921L; // 2^27 15 + 1
enum FFT_P1 = 1811939329L; // 2^26 27 + 1
enum FFT_P2 = 469762049L; // 2^26 7 + 1
alias FFT0 = FFT!(FFT_P0, 27, 440564289L); // 31^15
alias FFT1 = FFT!(FFT_P1, 26, 72705542L); // 13^27
alias FFT2 = FFT!(FFT_P2, 26, 2187L); // 3^ 7
// Convolution of a and b (indices mod fft0.n)
// modify a and b so that 0 <= a[i] < m, 0 <= b[i] < m
long[] convolution(FFT0 fft0, FFT1 fft1, FFT2 fft2, long[] a, long[] b, long m)
in {
assert(fft0.n == fft1.n && fft0.n == fft2.n, "convolution: fft0.n = fft1.n = fft2.n must hold");
assert(1 <= m && m <= 0x7fffffff, "convolution: 1 <= m < 2^31 must hold");
}
do {
enum FFT_INV01 = modInv(FFT_P0, FFT_P1);
enum FFT_INV012 = modInv(FFT_P0 * FFT_P1, FFT_P2);
foreach (i; 0 .. a.length) {
if ((a[i] %= m) < 0) {
a[i] += m;
}
}
foreach (i; 0 .. b.length) {
if ((b[i] %= m) < 0) {
b[i] += m;
}
}
const x0 = fft0.convolution(a, b);
const x1 = fft1.convolution(a, b);
const x2 = fft2.convolution(a, b);
auto x = new long[fft0.n];
foreach (i; 0 .. fft0.n) {
auto y0 = x0[i] % FFT_P0;
auto y1 = (FFT_INV01 * (x1[i] - y0)) % FFT_P1;
if (y1 < 0) {
y1 += FFT_P1;
}
auto y2 = (FFT_INV012 * ((x2[i] - y0 - FFT_P0 * y1) % FFT_P2)) % FFT_P2;
if (y2 < 0) {
y2 += FFT_P2;
}
x[i] = (y0 + FFT_P0 * y1 + ((FFT_P0 * FFT_P1) % m) * y2) % m;
}
return x;
}
enum long MO = 1000000007;
alias Mint = ModInt!MO;
Mint power(Mint a, long e) {
Mint x = a, y = 1;
for (; e; e >>= 1) {
if (e & 1) y *= x;
x *= x;
}
return y;
}
enum L = 2^^18;
int N;
long[] A;
void main() {
auto fft = new Fft(L);
auto fft0 = new FFT0(L);
auto fft1 = new FFT1(L);
auto fft2 = new FFT2(L);
try {
for (; ; ) {
N = readInt();
A = new long[N];
foreach (i; 0 .. N) {
A[i] = readInt();
}
// auto f = new real[L];
// f[] = 0.0;
// foreach (i; 0 .. N) {
// f[cast(int)(A[i])] += 1;
// }
// auto ff = fft.fft!real(f);
// foreach (l; 0 .. L) {
// ff[l] = ff[l] * ff[l];
// }
// auto g = fft.inverseFft!real(ff);
// pragma(msg,typeof(g));
// foreach (i; 0 .. N) {
// g[cast(int)(2 * A[i])] -= 1.0;
// }
// auto cnt = new long[L];
// foreach (l; 0 .. L) {
// cnt[l] = cast(long)(round(g[l].re / 2.0));
// }
// debug {
// writeln("cnt = ", cnt[0 .. 20]);
// }
auto f = new long[L];
foreach (i; 0 .. N) {
++f[cast(int)(A[i])];
}
auto g = convolution(fft0, fft1, fft2, f, f, 2 * (MO - 1));
foreach (i; 0 .. N) {
const l = cast(int)(2 * A[i]);
--g[l];
if (g[l] < 0) {
g[l] += 2 * (MO - 1);
}
}
foreach (l; 0 .. L) {
assert(g[l] % 2 == 0);
g[l] /= 2;
}
debug {
writeln("g = ", g[0 .. 20]);
}
Mint ans = 1;
foreach (l; 0 .. L) {
ans *= power(Mint(l), g[l]);
}
long ASum;
foreach_reverse (i; 0 .. N) {
ans *= power(Mint(A[i]), ASum);
ASum += A[i];
}
long AMin = long.max;
auto opt = tuple(real.infinity, 0L, 0L);
foreach_reverse (i; 0 .. N) {
if (i < N - 1) {
chmin(opt, tuple(log(A[i] + AMin) + log(A[i]) * AMin, A[i], AMin));
}
chmin(AMin, A[i]);
}
debug {
writeln("opt = ", opt);
}
Mint dnm = (opt[1] + opt[2]) * power(Mint(opt[1]), opt[2]);
ans *= modInv(dnm.x, MO);
writeln(ans);
}
} catch (EOFException e) {
}
}
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