結果

問題 No.737 PopCount
コンテスト
ユーザー ゆにぽけ
提出日時 2024-03-06 06:12:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 1,000 ms
コード長 3,849 bytes
コンパイル時間 1,292 ms
コンパイル使用メモリ 131,948 KB
最終ジャッジ日時 2025-02-20 01:13:58
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 * 3
other AC * 15
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 # 

#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <iterator>
#include <string>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
template<int m> struct modint
{
	private:
	unsigned int value;
	static constexpr int mod() {return m;}

	public:
	constexpr modint(const long long x = 0) noexcept
	{
		long long y = x;
		if(y < 0 || y >= mod())
		{
			y %= mod();
			if(y < 0) y += mod();
		}
		value = (unsigned int)y;
	}
	static constexpr int get_mod() noexcept {return m;}
	static constexpr int primitive_root() noexcept
	{
		assert(m == 998244353);
		return 3;
	}
	constexpr unsigned int val() noexcept {return value;}
	constexpr modint &operator+=(const modint &other) noexcept
	{
		value += other.value;
		if(value >= mod()) value -= mod();
		return *this;
	}
	constexpr modint &operator-=(const modint &other) noexcept
	{
		unsigned int x = value;
		if(x < other.value) x += mod();
		x -= other.value;
		value = x;
		return *this;
	}
	constexpr modint &operator*=(const modint &other) noexcept
	{
		unsigned long long x = value;
		x *= other.value;
		value = (unsigned int) (x % mod());
		return *this;
	}
	constexpr modint &operator/=(const modint &other) noexcept
	{
		return *this *= other.inverse();
	}
	constexpr modint inverse() const noexcept
	{
		assert(value);
		long long a = value,b = mod(),x = 1,y = 0;
		while(b)
		{
			long long q = a/b;
			a -= q*b; swap(a,b);
			x -= q*y; swap(x,y);
		}
		return modint(x);
	}
	constexpr modint power(long long N) const noexcept
	{
		assert(N >= 0);
		modint p = *this,ret = 1;
		while(N)
		{
			if(N & 1) ret *= p;
			p *= p;
			N >>= 1;
		}
		return ret;
	}
	constexpr modint operator+() {return *this;}
	constexpr modint operator-() {return modint() - *this;}
	constexpr modint &operator++(int) noexcept {return *this += 1;}
	constexpr modint &operator--(int) noexcept {return *this -= 1;}
	friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
	friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
	friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
	friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
	friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
/* using mint = modint<998244353>; */
using mint = modint<1000000007>;
void Main()
{
	long long N;
	cin >> N;
	string S;
	while(N)
	{
		S += char('0' + (N & 1));
		N >>= 1;
	}
	reverse(S.begin(),S.end());
	N = (int)S.size();
	vector<vector<mint>> dp(2,vector<mint>(N + 1));
	vector<vector<mint>> way(2,vector<mint>(N + 1));
	mint t = mint(2).power(N);
	const mint inv2 = mint(2).inverse();
	for(int i = 0;i < N;i++)
	{
		t *= inv2;
		int D = S[i] - '0';
		vector<vector<mint>> n_dp(2,vector<mint>(N + 1));
		vector<vector<mint>> n_way(2,vector<mint>(N + 1));
		for(int j = 0;j < 2;j++)
		{
			for(int k = 0;k <= i;k++)
			{
				for(int d = 0;d <= (j ? 1 : D);d++)
				{
					int nj = j || d < D;
					int nk = k + d;
					n_dp[nj][nk] += dp[j][k] + d * t * way[j][k];
					n_way[nj][nk] += way[j][k];
				}
			}
		}
		for(int d = 1;d <= (i > 0 ? 1 : D);d++)
		{
			int j = i > 0 || d < D;
			int k = 1;
			n_dp[j][k] += t;
			n_way[j][k]++;
		}
		swap(dp,n_dp);
		swap(way,n_way);
	}
	mint ans = 0;
	for(int k = 1;k <= N;k++)
	{
		ans += k * (dp[0][k] + dp[1][k]);
	}
	cout << ans << "\n";
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int tt = 1;
	/* cin >> tt; */
	while(tt--) Main();
}
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