結果

問題 No.724 円と円の間の円
ユーザー はむこはむこ
提出日時 2017-12-27 12:47:56
言語 C++11
(gcc 13.3.0)
結果
AC  
実行時間 210 ms / 2,000 ms
コード長 10,818 bytes
コンパイル時間 1,779 ms
コンパイル使用メモリ 177,860 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-21 07:49:21
合計ジャッジ時間 5,636 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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
other AC * 24
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.cpp: In function ‘void vizGraph(vvll&, int, std::string)’:
main.cpp:41:425: warning: ignoring return value of ‘int system(const char*)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   41 | void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
      |                                                                                                                                                                                                                                                                                                                                                                                                                                   ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

diff # 

#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
using ld = long double;  using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }

inline void input(int &v){ v=0;char c=0;int p=1; while(c<'0' || c>'9'){if(c=='-')p=-1;c=getchar();} while(c>='0' && c<='9'){v=(v<<3)+(v<<1)+c-'0';c=getchar();} v*=p; }
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T> ostream &operator<<(ostream &o, const deque<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const unordered_set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U, typename V>  ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
template <typename T, typename S, typename U> ostream &operator<<(ostream &o, const priority_queue<T, S, U> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.front(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const stack<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); }
void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
size_t random_seed; namespace std { using argument_type = P; template<> struct hash<argument_type> { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash<ll>{}(x.fi); seed ^= (hash<ll>{}(x.se) << 1); return seed; } }; }; // hash for various class
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
struct init_{init_(){ ios::sync_with_stdio(false); cin.tie(0); gettimeofday(&start, NULL); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
#define ldout fixed << setprecision(40) 
#define double long double

#define EPS (double)1e-14
#define INF (ll)1e18
#define mo  (ll)(1e9+7)

double dx(double a, double b, double r, double x) {

       double dx_result;
          dx_result = 2*(-a + x)*(-a - r + sqrtl(powl(r, 2) + powl(a - x, 2)))/sqrtl(powl(r, 2) + powl(a - x, 2)) + 2*(-b + x)*(-b + r + sqrtl(powl(r, 2) + powl(b - x, 2)))/sqrtl(powl(r, 2) + powl(b - x, 2));
             return dx_result;

}

double dr(double a, double b, double r, double x) {

       double dr_result;
          dr_result = (2*r/sqrtl(powl(r, 2) + powl(a - x, 2)) - 2)*(-a - r + sqrtl(powl(r, 2) + powl(a - x, 2))) + (2*r/sqrtl(powl(r, 2) + powl(b - x, 2)) + 2)*(-b + r + sqrtl(powl(r, 2) + powl(b - x, 2)));
             return dr_result;

}

double fx(double a, double r, double x) {

       double fx_result;
          fx_result = -a - r + sqrtl(powl(r, 2) + powl(a - x, 2));
             return fx_result;

}

double fy(double b, double r, double x) {

       double fy_result;
          fy_result = -b + r + sqrtl(powl(r, 2) + powl(b - x, 2));
             return fy_result;

}

double d2x(double a, double b, double r_0, double r_1, double x_0, double x_1, double y_0, double y_1) {

       double d2x_result;
          d2x_result = 2*(-a + x_1)*(-a - r_1 + sqrtl(powl(y_1, 2) + powl(a - x_1, 2)))/sqrtl(powl(y_1, 2) + powl(a - x_1, 2)) + 2*(-b + x_1)*(-b + r_1 + sqrtl(powl(y_1, 2) + powl(b - x_1, 2)))/sqrtl(powl(y_1, 2) + powl(b - x_1, 2)) + 2*(-x_0 + x_1)*(-r_0 - r_1 + sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2)))/sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2));
             return d2x_result;

}

double d2y(double a, double b, double r_0, double r_1, double x_0, double x_1, double y_0, double y_1) {

       double d2y_result;
          d2y_result = 2*y_1*(-b + r_1 + sqrtl(powl(y_1, 2) + powl(b - x_1, 2)))/sqrtl(powl(y_1, 2) + powl(b - x_1, 2)) + 2*y_1*(-a - r_1 + sqrtl(powl(y_1, 2) + powl(a - x_1, 2)))/sqrtl(powl(y_1, 2) + powl(a - x_1, 2)) + 2*(-y_0 + y_1)*(-r_0 - r_1 + sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2)))/sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2));
             return d2y_result;

}

double d2r(double a, double b, double r_0, double r_1, double x_0, double x_1, double y_0, double y_1) {

       double d2r_result;
          d2r_result = 2*a - 2*b + 2*r_0 + 6*r_1 - 2*sqrtl(powl(y_1, 2) + powl(a - x_1, 2)) + 2*sqrtl(powl(y_1, 2) + powl(b - x_1, 2)) - 2*sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2));
             return d2r_result;

}

double fa(double a, double r_1, double x_1, double y_1) {

       double fa_result;
          fa_result = -a - r_1 + sqrtl(powl(y_1, 2) + powl(a - x_1, 2));
             return fa_result;

}

double fb(double b, double r_1, double x_1, double y_1) {

       double fb_result;
          fb_result = -b + r_1 + sqrtl(powl(y_1, 2) + powl(b - x_1, 2));
             return fb_result;

}

double fc(double r_0, double r_1, double x_0, double x_1, double y_0, double y_1) {

       double fc_result;
          fc_result = -r_0 - r_1 + sqrtl(powl(x_0 - x_1, 2) + powl(y_0 - y_1, 2));
             return fc_result;

}


int main(void) {
    ll n; cin >> n;
    double a, b; cin >> a >> b;
    assert(1<=n&&n<=1000);
    assert(1<=a&&a<b&&b<=1000);
    ll iter = 5000;
    double dt = 0.01;
    /*
    cout << b << " " << 0 << " " << b << endl;;
    cout << a << " " << 0 << " " << a << endl;;
    */

    double res = 1000;
    rep(i, res) rep(j, res) {
        double xx=  i / res * (2*b);
        double yy = j / res * (2*b)-b;
        double score = fx(a,yy,xx)*fx(a,yy,xx)+fy(b,yy,xx)*fy(b,yy,xx);
        if (score > 100) continue;
//        cout << xx << " " << yy << " " << score << endl;;
    }

    double x = b+1, y = -1, r = b/2+1;
    if (n % 2 == 0) {
        rep(_, iter) {
//            cout << x << " " << r << endl;
            double delta_x = dx(a, b, r, x);
            double delta_r = dr(a, b, r, x);
//            cout << delta_x << " " << delta_r << "delta"<<endl;
            x -= delta_x * dt;
            r -= delta_r * dt;
//            cout << fx(a, r, x) << endl;
//            cout << fy(b, r, x) << endl;
        }
        y = r;
    } else {
        x = a + b;
        r = b - a;
        y = 0;
    }
//    cout << x << " " << y << " " << r << endl;

    ll f = 0;
    vector<double> hist_r = {INF};
    rep(i, (n-1)/2) {
        if (f) {
            double dr = hist_r[hist_r.size()-2] - hist_r[hist_r.size()-1];
//            cout <<r << " " << dr << endl;
            r -= dr;
            chmax(r, 0);
            continue;
        }
//        cout << i << endl;
        double x0 = x, y0 = y, r0 = r;
        x = 0, y = 0.01, r = 1;
        rep(_, iter) {
//            cout << x << " " << y << " " << r << endl;
            double delta_x = d2x(a, b, r0, r, x0, x, y0, y);
            double delta_y = d2y(a, b, r0, r, x0, x, y0, y);
            double delta_r = d2r(a, b, r0, r, x0, x, y0, y);
//double d2r(double a, double b, double r_0, double r_1, double x_0, double x_1, double y_0, double y_1) {
//            cout << delta_x << " " << delta_y << " " << delta_r << "delta"<<endl;
            x -= delta_x * dt;
            y -= delta_y * dt;
            r -= delta_r * dt;
            /*
            cout << fx(a, r, x) << endl;
            cout << fx(a, r, x) << endl;
            cout << fy(b, r, x) << endl;
            */
        }
//        cout <<ldout << x << " " << y << " " << r << endl;
        if (hist_r.back() < r) {
            f = 1;
            continue;
        }
        hist_r.pb(r);
    }
    cout << ldout << r << endl;


    return 0;
}
0