結果
| 問題 | No.620 ぐるぐるぐるりん |
| ユーザー |
 はむこ
|
| 提出日時 | 2017-12-19 02:13:46 |
| 言語 | C++11 (gcc 11.4.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 17,813 bytes |
| コンパイル時間 | 2,490 ms |
| コンパイル使用メモリ | 209,256 KB |
| 実行使用メモリ | 6,824 KB |
| 最終ジャッジ日時 | 2024-12-17 20:11:34 |
| 合計ジャッジ時間 | 6,741 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
コンパイルメッセージ
main.cpp: In function ‘void vizGraph(vvll&, int, std::string)’:
main.cpp:43:425: warning: ignoring return value of ‘int system(const char*)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
43 | 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
#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
#define ZERO(a) memset(a,0,sizeof(a))
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); }
#define exists find_if
#define forall all_of
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 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;}
string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; }
template <typename T> ostream &operator<<(ostream &o, const priority_queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} o << endl; 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
namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template <typename T> struct myhash{ std::size_t operator()(const T& val) const { return (hash<T>{}(val)%mod_key)^hash_key; } }; };
template <typename T> class uset:public std::unordered_set<T,myhash::myhash<T>> { using SET=std::unordered_set<T,myhash::myhash<T>>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} };
uint32_t randxor() { static uint32_t x=1+(uint32_t)random_seed,y=362436069,z=521288629,w=88675123; uint32_t t; t=(x^(x<<11));x=y;y=z;z=w; return( w=(w^(w>>19))^(t^(t>>8)) ); }
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_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); 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 rand randxor
#define ldout fixed << setprecision(40)
typedef long double number;
const number eps = 1e-8;
using vec = vector<number>;
using mat = vector<vec>;
ostream &operator<<(ostream &o, const vec &v) {
for (int i = 0; i < v.size(); i++) { cout << v[i] << " "; } cout << endl;
return o;
}
ostream &operator<<(ostream &o, const mat &v) {
for (int i = 0; i < v.size(); i++) { cout << v[i]; }
return o;
}
// O( n^2 )
vec zero(int n) {
return vec(n);
}
// O( n m )
mat zero(int n, int m) {
mat A(n, vec(m, 0));
return A;
}
// O( n^2 )
mat identity(int n) {
mat A(n, vec(n, 0));
for (int i = 0; i < n; ++i) A[i][i] = 1; // 積の単位元（和の単位元は？）
return A;
}
// O( n^2 )
vec mul(const mat &A, const vec &x) {
vec y(A.size(), 0);
for (int i = 0; i < A.size(); ++i)
for (int j = 0; j < A[0].size(); ++j)
y[i] += A[i][j] * x[j]; // 加群の積と和の演算子
return y;
}
// O( n^3 )
mat mul(const mat &A, const mat &B) {
mat C(A.size(), vec(B[0].size(), 0));
for (int i = 0; i < C.size(); ++i)
for (int j = 0; j < C[i].size(); ++j)
for (int k = 0; k < A[i].size(); ++k)
C[i][j] += A[i][k] * B[k][j]; // 加群の積と和の演算子
return C;
}
// O( n^3 log e )
mat pow(const mat &A, int e) {
return e == 0 ? identity(A.size()) :
e % 2 == 0 ? pow(mul(A, A), e/2) : mul(A, pow(A, e-1));
}
// O( n )
number inner_product(const vec &a, const vec &b) {
number ans = 0;
for (int i = 0; i < a.size(); ++i)
ans += a[i] * b[i];
return ans;
}
// O( n^3 )
number det(mat A) {
const int n = A.size();
number D = 1;
for (int i = 0; i < n; ++i) {
int pivot = i;
for (int j = i+1; j < n; ++j)
if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
swap(A[pivot], A[i]);
D *= A[i][i] * (i != pivot ? -1 : 1);
if (abs(A[i][i]) < eps) break;
for(int j = i+1; j < n; ++j)
for(int k = n-1; k >= i; --k)
A[j][k] -= A[i][k] * A[j][i] / A[i][i];
}
return D;
}
// O(n)
number tr(const mat &A) {
number ans = 0;
for (int i = 0; i < A.size(); ++i)
ans += A[i][i];
return ans;
}
// O( n^3 ).
int rank(mat A) {
const int n = A.size(), m = A[0].size();
int r = 0;
for (int i = 0; r < n && i < m; ++i) {
int pivot = r;
for (int j = r+1; j < n; ++j)
if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
swap(A[pivot], A[r]);
if (abs(A[r][i]) < eps) continue;
for (int k = m-1; k >= i; --k)
A[r][k] /= A[r][i];
for(int j = r+1; j < n; ++j)
for(int k = i; k < m; ++k)
A[j][k] -= A[r][k] * A[j][i];
++r;
}
return r;
}
struct LUinfo {
vector<number> value;
vector<int> index;
};
// O( n^3 ), Gaussian forward elimination
LUinfo LU_decomposition(mat A) {
const int n = A.size();
LUinfo data;
for (int i = 0; i < n; ++i) {
int pivot = i;
for (int j = i+1; j < n; ++j)
if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
swap(A[pivot], A[i]);
data.index.push_back(pivot);
// if A[i][i] == 0, LU decomposition failed.
for(int j = i+1; j < n; ++j) {
A[j][i] /= A[i][i];
for(int k = i+1; k < n; ++k)
A[j][k] -= A[i][k] * A[j][i];
data.value.push_back(A[j][i]);
}
}
for(int i = n-1; i >= 0; --i) {
for(int j = i+1; j < n; ++j)
data.value.push_back(A[i][j]);
data.value.push_back(A[i][i]);
}
return data;
}
// O( n^2 ) Gaussian backward substitution
vec LU_backsubstitution(const LUinfo &data, vec b) {
const int n = b.size();
int k = 0;
for (int i = 0; i < n; ++i){
swap(b[data.index[i]], b[i]);
for(int j = i+1; j < n; ++j)
b[j] -= b[i] * data.value[k++];
}
for (int i = n-1; i >= 0; --i) {
for (int j = i+1; j < n; ++j)
b[i] -= b[j] * data.value[k++];
b[i] /= data.value[k++];
}
return b;
}
// reduce Hessenberg form (inplace).
// O ( n^3 )
void hessenberg(mat &A) {
const int n = A.size();
for (int k = 1; k <= n-2; ++k) {
vec u(n);
for (int i = k; i < n; ++i) u[i] = A[i][k-1];
number ss = 0;
for (int i = k+1; i < n; ++i) ss += u[i] * u[i];
if (abs(ss) <= 0.0) continue;
number s = sqrt( ss + u[k]*u[k] );
if (u[k] > 0.0) s = -s;
u[k] -= s;
number uu = sqrt( ss + u[k]*u[k] );
for (int i = k; i < n; ++i) u[i] /= uu;
vec f(n), g(n);
for (int i = 0; i < n; ++i)
for (int j = k; j < n; ++j)
f[i] += A[i][j] * u[j],
g[i] += A[j][i] * u[j];
number gamma = inner_product(u, g);
for (int i = 0; i < n; ++i)
f[i] -= gamma * u[i],
g[i] -= gamma * u[i];
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
A[i][j] = A[i][j] - 2*u[i]*g[j] - 2*f[i]*u[j];
}
}
// find all eigenvalues using Hessenberg-QR Method
// O( n^3 + M n^2 ) where M is the number of iterations.
vector<number> eigenvalues(mat A) {
const int n = A.size();
hessenberg(A);
vector<number> s(n), c(n);
for (int m = n; m >= 2; ) {
if (abs(A[m-1][m-2]) < eps) { --m; continue; }
number shift = A[m-1][m-1];
for (int i = 0; i < m; ++i) A[i][i] -= shift;
for (int k = 0; k < m-1; ++k) {
number a = A[k][k], b = A[k+1][k], r = sqrt(a*a + b*b);
s[k] = r == 0.0 ? 0.0 : b/r,
c[k] = r == 0.0 ? 0.0 : a/r;
for (int j = k; j < m; ++j) {
number x = A[k][j], y = A[k+1][j];
A[ k ][j] = c[k] * x + s[k] * y;
A[k+1][j] = -s[k] * x + c[k] * y;
}
}
for (int k = 0; k < m-1; ++k) {
for (int i = 0; i <= k+1; ++i) {
number x = A[i][k], y = A[i][k+1];
A[i][ k ] = c[k] * x + s[k] * y;
A[i][k+1] = -s[k] * x + c[k] * y;
}
}
for (int i = 0; i < m; ++i) A[i][i] += shift;
}
vector<number> lambda;
for (int i = 0; i < n; ++i)
lambda.push_back( A[i][i] );
return lambda;
}
// find the corresponding eigenvector from the eigenvalue.
// O ( n^3 + M n^2 ) where M is the number of iterations.
vec eigenvector(mat A, number lambda) {
const int n = A.size();
vec y(n); y[0] = 1;
for (int i = 0; i < n; ++i) A[i][i] -= lambda;
LUinfo data = LU_decomposition(A);
number mu, v2, v2s;
do {
vec v = LU_backsubstitution(data, y); // A v = y
mu = inner_product(v, y);
v2 = inner_product(v, v);
v2s = sqrt(v2);
for (int j = 0; j < n; ++j) y[j] = v[j] / v2s;
} while (abs(1.0-mu*mu/v2) > eps);
return y;
}
mat operator*(const mat& t1, const mat& t2) {
assert(t1[0].size() == t2.size());
mat ret = zero(t1.size(), t2[0].size());
rep(i, t1.size()) {
rep(j, t2[0].size()) {
rep(k, t1[0].size()) {
ret[i][j] += t1[i][k] * t2[k][j];
}
}
}
return ret;
}
vec operator*(const mat& t1, const vec& t2) {
assert(t1[0].size() == t2.size());
vec ret(t1.size());
rep(i, t1.size()) {
rep(j, t2.size()) {
ret[i] += t1[i][j] * t2[j];
}
}
return ret;
}
vec operator+(const vec& t1, const vec& t2) {
assert(t1.size() == t2.size());
vec ret(t1.size());
rep(i, t1.size()) {
ret[i] = t1[i] + t2[i];
}
return ret;
}
mat operator+(const mat& t1, const mat& t2) {
assert(t1.size() == t2.size() && t1[0].size() == t2[0].size());
mat ret = zero(t1.size(), t1[0].size());
rep(i, t1.size()) {
rep(j, t1[0].size()) {
ret[i][j] = t1[i][j] + t2[i][j];
}
}
return ret;
}
vec operator-(const vec& t1, const vec& t2) {
assert(t1.size() == t2.size());
vec ret(t1.size());
rep(i, t1.size()) {
ret[i] = t1[i] - t2[i];
}
return ret;
}
mat operator-(const mat& t1, const mat& t2) {
assert(t1.size() == t2.size() && t1[0].size() == t2[0].size());
mat ret = zero(t1.size(), t1[0].size());
rep(i, t1.size()) {
rep(j, t1[0].size()) {
ret[i][j] = t1[i][j] - t2[i][j];
}
}
return ret;
}
mat operator-(const mat& t1) {
mat ret = t1;
rep(i, ret.size()) {
rep(j, ret[0].size()) {
ret[i][j] *= -1;
}
}
return ret;
}
mat inverse(const mat& t) {
assert(t.size() == t[0].size());
assert(t.size() == 2); // TODO
mat ret = zero(2, 2);
ret[0][0] = t[1][1];
ret[0][1] = -t[1][0];
ret[1][0] = -t[0][1];
ret[1][1] = t[0][0];
rep(i, 2) rep(j, 2) {
ret[i][j] /= (t[0][0] * t[1][1] - t[0][1] * t[1][0]);
}
return ret;
}
mat transpose(const mat& t) {
mat ret = zero(t[0].size(), t.size());
rep(i, t.size()) rep(j, t[0].size()) {
ret[j][i] = t[i][j];
}
return ret;
}
mat block(const mat& t, ll si, ll sj, ll i0, ll j0) {
assert(i0+si<=t.size() && j0+sj <= t[0].size());
mat ret = zero(si, sj);
rep(i, si) rep(j, sj) {
ret[i][j] = t[i0+i][j0+j];
}
return ret;
}
number omega = 0.01;
number v = 0.0001;
vec f(vec x, vec u) {
mat F_x = zero(2, 2);
F_x[0][0] = v+1, F_x[0][1] = -omega;
F_x[1][0] = omega, F_x[1][1] = v+1;
return F_x * x + u;
}
// Sx(S+U)
mat getF(void) {
mat F = zero(2, 4);
F[0][0] = v+1; F[0][1] = -omega; F[0][2] = 1; F[0][3] = 0;
F[1][0] = omega; F[1][1] = v+1; F[1][2] = 0; F[1][3] = 1;
return F;
}
// Sx1
vec getf(void) {
return zero(2);
}
pair<number, number> evaluate(number g_x, number g_y, number output_coeff, ll T) {
// X=U=2
vector<mat> C(T+1, zero(4, 4));
vector<vec> c(T+1, zero(4));
C[T][0][0] = 1, C[T][1][1] = 1;
c[T][0] = -g_x, c[T][1] = -g_y;
rep(t, T+1) C[t][2][2] = output_coeff, C[t][3][3] = output_coeff;
vector<mat> Q(T+1, zero(4, 4)); // (S+U)x(S+U)
vector<vec> q(T+1, zero(4)); // (S+U)x1
vector<mat> V(T+2, zero(2, 2)); // SxS
vector<vec> v(T+2, zero(2)); // Sx1
vector<mat> K(T+2, zero(2, 2)); // UxS
vector<vec> k(T+2, zero(2)); // Ux1
for (int t = T; t >= 0; t--) {
mat F = getF(); // Sx(S+U)
vec f = getf(); // Sx1
Q[t] = C[t] + transpose(F) * V[t+1] * F;
q[t] = c[t] + transpose(F) * V[t+1] * f + transpose(F) * v[t+1];
mat Qxx = block(Q[t], 2, 2, 0, 0);
mat Quu = block(Q[t], 2, 2, 2, 2);
mat Qxu = block(Q[t], 2, 2, 0, 2);
mat Qux = block(Q[t], 2, 2, 2, 0);
vec qx = zero(2); qx[0] = q[t][0], qx[1] = q[t][1];
vec qu = zero(2); qu[0] = q[t][2], qu[1] = q[t][3];
K[t] = -inverse(Quu) * Qux;
k[t] = -inverse(Quu) * qu;
V[t] = Qxx + Qxu * K[t] + transpose(K[t]) * Qux + transpose(K[t]) * Quu * K[t];
v[t] = qx + Qxu * k[t] + transpose(K[t]) * qu + transpose(K[t]) * Quu * k[t];
}
vector<vec> x(T+2, zero(2));
vector<vec> u(T+2, zero(2));
x[0][0] = 1, x[0][1] = 0;
rep(t, T) {
vec u_tmp = K[t] * x[t] + k[t];
u[t] = u_tmp;
x[t+1] = f(x[t], u[t]);
}
// rep(i, T+1) cout << " " << x[i][0] << " " << x[i][1] << endl;
rep(i, T) cout << u[i][0] << " " << u[i][1] << endl;
number usum = 0;
rep(i, T) usum += u[i][0] * u[i][0] + u[i][1] * u[i][1];
return mp(usum, sqrt(pow(x[T][0] - g_x, 2) + pow(x[T][1] - g_y, 2)));
}
// omega = 1, v = 0.1
// omega = 1, v = 1
int main(int argc, char** argv) {
cout << ldout;
number g_x, g_y, output_coeff = 1e-9;
number k;
ll T;
cin >> T >> k >> omega >> v >> g_x >> g_y;
auto err = evaluate(g_x, g_y, output_coeff, T);
// cerr << err << endl;
return 0;
}