結果
| 問題 | No.1510 Simple Integral |
| ユーザー |
 fairy_lettuce
|
| 提出日時 | 2021-05-22 07:48:49 |
| 言語 | C#(csc) (csc 3.9.0) |
| 結果 |
AC
|
| 実行時間 | 108 ms / 2,000 ms |
| コード長 | 13,593 bytes |
| コンパイル時間 | 1,310 ms |
| コンパイル使用メモリ | 119,308 KB |
| 実行使用メモリ | 33,848 KB |
| 最終ジャッジ日時 | 2024-10-10 10:48:12 |
| 合計ジャッジ時間 | 6,176 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 43 |
コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc) Copyright (C) Microsoft Corporation. All rights reserved.
ソースコード
using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Globalization;
using System.Threading;
using static System.Math;
namespace FertiLib.Contest.F
{
public class Solver
{
Scanner sr;
StreamWriter sw;
bool isMultipleTestCases = false;
ModInt one = 1;
ModInt[] factorial, finv;
public void Solve()
{
var n = sr.ReadInt();
var a = sr.ReadIntArray(n);
Init(n);
Array.Sort(a);
var s = a.Distinct().ToArray();
var v = s.Select((value, index) => (value, index))
.ToDictionary(p => p.value, p => p.index);
var dp = CreateArray(v.Count, n + 1, (i, j) => new ModInt(0));
dp[v[a[0]]][1] = 1;
for (int i = 1; i < n; i++)
{
var next = CreateArray(v.Count, n + 1, (i, j) => new ModInt(0));
for (int j = 0; j < dp.Length; j++)
{
if (s[j] == a[i])
{
for (int k = 0; k < n; k++)
{
if (dp[j][k] == 0) continue;
next[j][k + 1] += dp[j][k];
}
}
else
{
var f = (ModInt)s[j] * s[j] - (ModInt)a[i] * a[i];
for (int k = 0; k <= n; k++)
{
if (dp[j][k] == 0) continue;
next[v[a[i]]][1] += dp[j][k] / f.Pow(k);
for (int t = 0; t < k; t++)
{
next[j][k - t] += dp[j][k] * (-1) / f.Pow(t + 1);
}
}
}
}
dp = next;
}
var c = new ModInt[n + 1];
for (int i = 0; i < dp.Length; i++)
{
for (int j = 1; j <= n; j++)
{
c[j] += dp[i][j] / (new ModInt(2).Pow(j - 1) * new ModInt(s[i]).Pow(2 * j - 1));
}
}
//var table = Calc(n);
ModInt ans = 0;
for (int i = 1; i <= n; i++)
{
ModInt t = 0;
for (int j = 0; j < i; j += 2)
{
//t += Binom(i - 1, j) * table[j];
t += Binom(i - 1, j) * Binom(j, j / 2) / ModInt.Pow(2, j);
}
ans += c[i] * t;
}
Console.WriteLine(ans);
}
public ModInt Binom(int n, int r) => factorial[n] * finv[r] * finv[n - r];
public void Init(int n)
{
factorial = new ModInt[n + 1];
finv = new ModInt[n + 1];
factorial[0] = finv[0] = 1;
for (int i = 0; i < n; i++)
{
factorial[i + 1] = factorial[i] * (i + 1);
finv[i + 1] = factorial[i + 1].Inverse();
}
}
//public ModInt[] Calc(int n)
//{
// var ret = CreateArray(n + 1, n + 1, (i, j) => new ModInt(0));
// ret[0][0] = 1;
// // ret[i][j]: (cos^(2j) theta = \sum_i ret[i][j] cos 2*i*theta
// for (int j = 0; j < n; j++)
// {
// ret[1][j + 1] += ret[0][j];
// for (int i = 1; i <= n - 1; i++)
// {
// if (ret[i][j] == 0) continue;
// ret[i - 1][j + 1] += ret[i][j] / 2;
// ret[i + 1][j + 1] += ret[i][j] / 2;
// }
// ret[n - 1][j + 1] += ret[n][j] / 2;
// }
// return ret[0];
//}
public Solver(Scanner cin, StreamWriter cout)
{
this.sr = cin;
this.sw = cout;
}
public void Start()
{
int _t = 1;
if (isMultipleTestCases) _t = sr.ReadInt();
while (_t-- > 0) Solve();
}
public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO");
public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No");
public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no");
public static T SignOutput<T>(int x, T pos, T zero, T neg) => x == 0 ? zero : (x > 0 ? pos : neg);
public static T[] CreateArray<T>(int n, Func<int, T> func) => Enumerable.Range(0, n).Select(p => func(p)).ToArray();
public static T[][] CreateArray<T>(int h, int w, Func<int, int, T> func) => Enumerable.Range(0, h).Select(i => Enumerable.Range(0, w).Select(j => func(i, j)).ToArray()).ToArray();
}
public struct ModInt : IEquatable<ModInt>
{
public static long MOD = 998244353;
public static bool isModPrime { get; set; }
private readonly long num;
public ModInt(long n) { num = n; isModPrime = true; }
public override string ToString() => num.ToString();
public static ModInt operator +(ModInt l, ModInt r)
{
long x = l.num + r.num;
if (x >= MOD) x -= MOD;
return new ModInt(x);
}
public static ModInt operator -(ModInt l, ModInt r)
{
long x = l.num - r.num;
if (x < 0) x += MOD;
return new ModInt(x);
}
public static ModInt operator *(ModInt l, ModInt r) => new ModInt((l.num * r.num) % MOD);
public static ModInt operator /(ModInt l, ModInt r) => l * r.Inverse();
public static ModInt operator ++(ModInt x)
{
var tmp = x + new ModInt(1);
return tmp;
}
public static ModInt operator --(ModInt x)
{
var tmp = x - new ModInt(1);
return tmp;
}
public static bool operator ==(ModInt l, ModInt r) => l.Equals(r);
public static bool operator !=(ModInt l, ModInt r) => !l.Equals(r);
public static implicit operator long(ModInt x) => x.num;
public static implicit operator ModInt(long n)
{
n %= MOD;
if (n < 0) n += MOD;
return new ModInt(n);
}
public ModInt Inverse() => Inverse(this, MOD);
public static ModInt Inverse(ModInt x) => Inverse(x.num, MOD);
public static long Inverse(long x, long m)
{
if (x % m == 0) throw new DivideByZeroException();
long a = x, b = m, u = 1, v = 0;
while (b > 0)
{
long t = a / b;
a -= t * b;
long p = a; a = b; b = p; // swap(a, b);
u -= t * v;
p = u; u = v; v = p; // swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
public ModInt Pow(long n) => Pow(this, n);
public static ModInt Pow(long x, long n)
{
if (n < 0) return Pow(x, -n).Inverse();
x %= MOD;
long now = 1;
if (isModPrime) n %= MOD - 1;
for (; n > 0; n /= 2, x = x * x % MOD)
{
if (n % 2 == 1) now = now * x % MOD;
}
return new ModInt(now);
}
public bool Equals(ModInt x) => num == x.num;
public override bool Equals(object obj) => obj is ModInt m && num == m.num;
public override int GetHashCode()
{
return HashCode.Combine(num);
}
}
public static class Program
{
public static void Main(string[] args)
{
var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
Console.SetOut(sw);
var cin = new Scanner();
var solver = new Solver(cin, sw);
solver.Start();
Console.Out.Flush();
}
}
public static class Extention
{
public static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
public static int UpperBound<T>(this IList<T> list, T value) => list.BinarySearch(value, true, 0, list.Count, Comparer<T>.Default);
public static int LowerBound<T>(this IList<T> list, T value) => list.BinarySearch(value, false, 0, list.Count, Comparer<T>.Default);
public static int BinarySearch<T>(this IList<T> list, T value, bool isUpperBound, int index, int length, Comparer<T> comparer)
{
var ng = index - 1;
var ok = index + length;
while (ok - ng > 1)
{
var mid = ng + (ok - ng) / 2;
var res = comparer.Compare(list[mid], value);
if (res < 0 || (isUpperBound && res == 0)) ng = mid;
else ok = mid;
}
return ok;
}
public static bool Chmax<T>(ref this T a, T b) where T : struct, IComparable<T>
{
if (a.CompareTo(b) >= 0) return false;
a = b;
return true;
}
public static bool Chmin<T>(ref this T a, T b) where T : struct, IComparable<T>
{
if (a.CompareTo(b) <= 0) return false;
a = b;
return true;
}
}
public class Scanner
{
string[] s;
int i;
char[] separator = new char[] { ' ' };
public Scanner()
{
s = new string[0];
i = 0;
}
public string Read() => ReadString();
public string ReadString()
{
if (i < s.Length) return s[i++];
string st = Console.ReadLine();
while (st == "") st = Console.ReadLine();
s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries);
if (s.Length == 0) return ReadString();
i = 0;
return s[i++];
}
public string[] ReadStringArray(int N)
{
string[] Array = new string[N];
for (int i = 0; i < N; i++)
{
Array[i] = ReadString();
}
return Array;
}
public int ReadInt() => int.Parse(ReadString());
public int[] ReadIntArray(int N, int add = 0)
{
int[] Array = new int[N];
for (int i = 0; i < N; i++)
{
Array[i] = ReadInt() + add;
}
return Array;
}
public long ReadLong() => long.Parse(ReadString());
public long[] ReadLongArray(int N, long add = 0)
{
long[] Array = new long[N];
for (int i = 0; i < N; i++)
{
Array[i] = ReadLong() + add;
}
return Array;
}
public double ReadDouble() => double.Parse(ReadString());
public double[] ReadDoubleArray(int N, double add = 0)
{
double[] Array = new double[N];
for (int i = 0; i < N; i++)
{
Array[i] = ReadDouble() + add;
}
return Array;
}
public T1 ReadValue<T1>() => (T1)Convert.ChangeType(ReadString(), typeof(T1));
public (T1, T2) ReadValue<T1, T2>()
{
var inputs = ReadStringArray(2);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
return (v1, v2);
}
public (T1, T2, T3) ReadValue<T1, T2, T3>()
{
var inputs = ReadStringArray(3);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
return (v1, v2, v3);
}
public (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
{
var inputs = ReadStringArray(4);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
return (v1, v2, v3, v4);
}
public (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>()
{
var inputs = ReadStringArray(5);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
return (v1, v2, v3, v4, v5);
}
public (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>()
{
var inputs = ReadStringArray(6);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
return (v1, v2, v3, v4, v5, v6);
}
public (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>()
{
var inputs = ReadStringArray(7);
var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
return (v1, v2, v3, v4, v5, v6, v7);
}
public T1[] ReadValueArray<T1>(int N)
{
var v1 = new T1[N];
for (int i = 0; i < N; i++)
{
v1[i] = ReadValue<T1>();
}
return v1;
}
public (T1[], T2[]) ReadValueArray<T1, T2>(int N)
{
var (v1, v2) = (new T1[N], new T2[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2) = ReadValue<T1, T2>();
v1[i] = t1;
v2[i] = t2;
}
return (v1, v2);
}
public (T1[], T2[], T3[]) ReadValueArray<T1, T2, T3>(int N)
{
var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2, t3) = ReadValue<T1, T2, T3>();
v1[i] = t1;
v2[i] = t2;
v3[i] = t3;
}
return (v1, v2, v3);
}
public (T1[], T2[], T3[], T4[]) ReadValueArray<T1, T2, T3, T4>(int N)
{
var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2, t3, t4) = ReadValue<T1, T2, T3, T4>();
v1[i] = t1;
v2[i] = t2;
v3[i] = t3;
v4[i] = t4;
}
return (v1, v2, v3, v4);
}
public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray<T1, T2, T3, T4, T5>(int N)
{
var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2, t3, t4, t5) = ReadValue<T1, T2, T3, T4, T5>();
v1[i] = t1;
v2[i] = t2;
v3[i] = t3;
v4[i] = t4;
v5[i] = t5;
}
return (v1, v2, v3, v4, v5);
}
public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray<T1, T2, T3, T4, T5, T6>(int N)
{
var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2, t3, t4, t5, t6) = ReadValue<T1, T2, T3, T4, T5, T6>();
v1[i] = t1;
v2[i] = t2;
v3[i] = t3;
v4[i] = t4;
v5[i] = t5;
v6[i] = t6;
}
return (v1, v2, v3, v4, v5, v6);
}
public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray<T1, T2, T3, T4, T5, T6, T7>(int N)
{
var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]);
for (int i = 0; i < N; i++)
{
var (t1, t2, t3, t4, t5, t6, t7) = ReadValue<T1, T2, T3, T4, T5, T6, T7>();
v1[i] = t1;
v2[i] = t2;
v3[i] = t3;
v4[i] = t4;
v5[i] = t5;
v6[i] = t6;
v7[i] = t7;
}
return (v1, v2, v3, v4, v5, v6, v7);
}
}
}