Submission #189435

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Source Code Expand

////////////////////
///   template   ///
////////////////////

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <functional>
#include <vector>
#include <queue>
#include <string>
#include <complex>
#include <stack>
#include <set>
#include <map>
#include <list>
#include <unordered_map>
using namespace std;

//// MACRO ////
#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (s); i < (n); i++)
#define allof(c) c.begin(), c.end()
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)
#define EPS 1e-10
#define INF 1000000000

#define countof(a) (sizeof(a)/sizeof(a[0]))
#define PREDIACTE(t,a) [](const t & a) -> bool
#define COMPARISON_T(t) bool(*)(const t &, const t &)
#define COMPARISON(t,a,b) [](const t & a, const t & b) -> bool

// start up //
void solve();
int main() { solve(); return 0; }

//// prime ////
vector<unsigned char> isPrime;
vector<int> primes;
void initPrimes(int n)
{
	isPrime = vector<unsigned char>(n + 1, true);
	isPrime[0] = isPrime[1] = false;
	FOR(i, 2, n + 1)
	{
		if (!isPrime[i]) continue;
		primes.push_back(i);
		for (int j = i * 2; j <= n; j += i)
			isPrime[j] = false;
	}
}

//// Probability ////

// パスカルの三角形(二項定理) 2種類の並べ替えにつかう。
vector<vector<double>> makePascalTriangle(int n, bool probability = false)
{
	typedef vector<double> VD;
	vector<VD> t;
	if (!t.size()) { t.push_back(VD(1, 1)); }
	FOR(i, t.size(), n + 1)
	{
		t.push_back(VD(i + 1));
		REP(j, i)
		{
			double x = t[i - 1][j] * (probability ? 0.5 : 1);
			t[i][j] += x;
			t[i][j + 1] += x;
		}
	}
	return t;
}


//// iota iterator ////
struct iotait
{
	int n;
	iotait(int n = 0) : n(n) { }
	iotait &operator ++() { ++n; return *this; }
	int operator *() { return n; }
};

//// geo ////
struct P3
{
	double x, y, z;
	P3(double x = 0, double y = 0, double z = 0) : x(x), y(y), z(z) { }
	P3 operator +() const { return *this; }
	P3 operator +(const P3 &_) const { return P3(x + _.x, y + _.y, z + _.z); }
	P3 operator -() const { return P3(-x, -y, -z); }
	P3 operator -(const P3 &_) const { return *this + -_; }
	P3 operator *(double _) const { return P3(x*_, y*_, z*_); }
	P3 operator /(double _) const { return P3(x / _, y / _, z / _); }
	double dot(const P3 &_) const { return x*_.x + y*_.y + z*_.z; } // 内積
	P3 cross(const P3 &_) const { return P3(y*_.z - z*_.y, z*_.x - x*_.z, x*_.y - y*_.x); } // 外積
	double sqlength() const { return x*x + y*y + z*z; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P3 direction() const { return *this / length(); } // 方向ベクトル
};

struct Sphere
{
	P3 c;
	double r;
	Sphere(double x, double y, double z, double r) : c(x, y, z), r(r) { }
	bool IntersectWith(const Sphere &rhs) { return (c - rhs.c).length() - (r + rhs.r) < EPS; } // 接してても真。
};

//// graph ////
struct Path
{
	int from;
	int to;
	double cost;
	Path(int from = 0, int to = 0, double cost = 0) : from(from), to(to), cost(cost) { }
	bool operator < (const Path &rhs) const { return cost < rhs.cost; }
	bool operator >(const Path &rhs) const { return cost > rhs.cost; }
};

// prim //
pair<double, vector<int>> prim(const vector<vector<double>> &costTable)
{
	int N = costTable.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(0, 0, 0));

	vector<int> parent(N, -1);
	double totalCost = 0;
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (parent[i] != -1) continue;
		parent[i] = cur.from;
		totalCost += cur.cost;
		REP(j, N) if (parent[j] == -1) q.push(Path(i, j, costTable[i][j]));
	}
	return make_pair(totalCost, parent);
}

// dijkstra //
pair<vector<double>, vector<int>> dijkstra(const vector<vector<Path>> &routes, int start = 0, int goal = -1)
{
	int N = routes.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(start, start, 0));

	vector<int> prev(N, -1);
	vector<double> cost(N, INF);
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (prev[i] != -1) continue;
		prev[i] = cur.from;
		cost[i] = cur.cost;
		if (i == goal) { break; }
		REP(j, routes[i].size())
		{
			Path next = Path(i, routes[i][j].to, cur.cost + routes[i][j].cost);
			if (prev[next.to] == -1)
				q.push(next);
		}
	}
	return make_pair(cost, prev);
}

//// i/o ////
template <class T>
class vevector : public vector<vector<T>>
{
public:
	vevector(int n = 0, int m = 0) : vector<vector<T>>(n, vector<T>(m)) { };
	vevector(int n, int m, const T &initial) : vector<vector<T>>(n, vector<T>(m, initial)) { };
};

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(read<T>(read<int>())); return v; }
template <class T> void write(const T &t) { cout << t << endl; }
template <class T> void write(const T &t, const T &t2) { cout << t << ' ' << t2 << endl; }
template <class T> void write(const vector<T> &v)
{
	ostringstream ss;
	for (auto x : v) ss << x << ' ';
	auto s = ss.str();
	cout << s.substr(0, s.length() - 1) << endl;
}

struct _Reader { template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
#define READ(t,...) t __VA_ARGS__; _Reader(), __VA_ARGS__

////////////////////
/// template end ///
////////////////////

void solve()
{
	READ(int, N, D, X, Y);
	
	// たどり着けぬ。。
	if (abs(X) % D != 0 || abs(Y) % D != 0)
	{
		printf("0.0\n");
		return;
	}

	// mp[x][y] = x回ジャンプしたときに y-Nに居る確率
	auto mp = vevector<double>(N + 1, N * 2 + 1); mp[0][N] = 1.0;
	REP(i, N) FOR(j, 1, mp[i].size() - 1)
	{
		mp[i + 1][j - 1] += mp[i][j] / 2.0;
		mp[i + 1][j + 1] += mp[i][j] / 2.0;
	}

	// 最終的にいるべき位置。
	int xJumps = X / D;
	int yJumps = Y / D;

	auto ptri = makePascalTriangle(N, true);
	double ret = 0.0;
	REP(i, N + 1)
	{
		int xj = i; // x方向のジャンプ回数
		int yj = N - i; // y方向のジャンプ回数
		ret += mp[xj][xJumps + N] * mp[yj][yJumps + N] * ptri[N][i];
	}

	printf("%.16f\n", ret);
}

Submission Info

Judge Result