結果
| 問題 | No.620 ぐるぐるぐるりん |
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2017-12-19 04:51:39 |
| 言語 | Java (openjdk 23) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 10,883 bytes |
| 記録 | |
| コンパイル時間 | 7,165 ms |
| コンパイル使用メモリ | 96,404 KB |
| 実行使用メモリ | 66,108 KB |
| 最終ジャッジ日時 | 2024-06-13 02:01:43 |
| 合計ジャッジ時間 | 19,176 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 24 TLE * 4 |
ソースコード
package adv2017;
import java.awt.geom.Point2D;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.Arrays;
import java.util.InputMismatchException;
public class N620_2 {
InputStream is;
PrintWriter out;
String INPUT = "";
MathContext mc = new MathContext(50);
void solve()
{
int U = ni();
if(!(1 <= U && U <= 1000))throw new AssertionError("U");
for(;U > 0;U--){
int T = ni();
BigDecimal P = new BigDecimal(ns(), mc);
BigDecimal OMEGA = new BigDecimal(ns(), mc);
BigDecimal V = new BigDecimal(ns(), mc);
BigDecimal GX = new BigDecimal(ns(), mc);
BigDecimal GY = new BigDecimal(ns(), mc);
if(!(1 <= T && T <= 15))throw new AssertionError("T");
if(!(0 <= P.doubleValue() && P.doubleValue() <= 1e9))throw new AssertionError("P");
if(!(-10 <= OMEGA.doubleValue() && OMEGA.doubleValue() <= 10))throw new AssertionError("omega");
if(!(-10 <= V.doubleValue() && V.doubleValue() <= 10))throw new AssertionError("v");
if(!(-100 <= GX.doubleValue() && GX.doubleValue() <= 100))throw new AssertionError("gx");
if(!(-100 <= GY.doubleValue() && GY.doubleValue() <= 100))throw new AssertionError("gy");
/*
(1+v -ω ux)
(ω 1+v uy)
(0 0 1)
*
*/
BigDecimal[][] M = {
{BigDecimal.ONE.add(V), OMEGA.negate()},
{OMEGA, BigDecimal.ONE.add(V)}
};
BigDecimal[][] E = {
{BigDecimal.ONE, BigDecimal.ZERO},
{BigDecimal.ZERO, BigDecimal.ONE}
};
BigDecimal[][][] MS = new BigDecimal[T+1][][];
MS[0] = E;
for(int i = 1;i <= T;i++){
MS[i] = mul(MS[i-1], M, mc);
}
BigDecimal[][] Q = new BigDecimal[2*T+2][2*T+2];
for(int i = 0;i < 2*T+2;i++){
for(int j = 0;j < 2*T+2;j++){
Q[i][j] = BigDecimal.ZERO;
}
}
for(int i = 0;i < 2*T;i++){
Q[i][i] = BigDecimal.ONE;
}
// Q = I
// c = 0
// E = MS[T-1] MS[T-2] MS[T-3] ...
for(int i = 0;i < T;i++){
for(int j = 0;j < 2;j++){
for(int k = 0;k < 2;k++){
Q[2*i+k][2*T+j] = Q[2*T+j][2*i+k] = MS[T-1-i][j][k];
}
}
}
BigDecimal[] d = new BigDecimal[2*T+2];
for(int i = 0;i < 2*T;i++)d[i] = BigDecimal.ZERO;
d[2*T] = GX.subtract(MS[T][0][0]);
d[2*T+1] = GY.subtract(MS[T][1][0]);
// tr(MS[T]);
Result res = gaussElimination(Q, d, BigDecimal.ZERO, mc);
BigDecimal[] x = res.sol;
check(OMEGA, V, x, T, GX, GY, P, mc);
for(int i = 0;i < 2*T;i+=2){
out.printf("%.14f %.14f\n", x[i], x[i+1]);
}
}
}
static void check(BigDecimal OMEGA, BigDecimal V, BigDecimal[] x, int T, BigDecimal GX, BigDecimal GY, BigDecimal P, MathContext mc)
{
BigDecimal[] v = new BigDecimal[]{BigDecimal.ONE, BigDecimal.ZERO, BigDecimal.ONE};
BigDecimal used = BigDecimal.ZERO;
for(int i = 0;i < T;i++){
used = used.add(x[i*2].multiply(x[i*2], mc));
used = used.add(x[i*2+1].multiply(x[i*2+1], mc));
BigDecimal[][] M = {
{BigDecimal.ONE.add(V), OMEGA.negate(), x[i*2]},
{OMEGA, BigDecimal.ONE.add(V), x[i*2+1]},
{BigDecimal.ZERO, BigDecimal.ZERO, BigDecimal.ONE}
};
v = mul(M, v, mc);
}
// tr(used, P);
// assert used <= P;
// tr(v, GX, GY);
if(!(Point2D.distance(v[0].doubleValue(), v[1].doubleValue(), GX.doubleValue(), GY.doubleValue()) <= 1e-4))throw new RuntimeException();
}
public static BigDecimal[] mul(BigDecimal[][] A, BigDecimal[] v, MathContext mc)
{
int m = A.length;
int n = v.length;
BigDecimal[] w = new BigDecimal[m];
for(int i = 0;i < m;i++){
BigDecimal sum = BigDecimal.ZERO;
for(int k = 0;k < n;k++){
sum = sum.add(A[i][k].multiply(v[k], mc), mc);
}
w[i] = sum;
}
return w;
}
public static BigDecimal[][] p2(BigDecimal[][] A, MathContext mc)
{
int n = A.length;
BigDecimal[][] C = new BigDecimal[n][n];
for(int i = 0;i < n;i++){
for(int j = 0;j < n;j++){
C[i][j] = BigDecimal.ZERO;
}
}
for(int i = 0;i < n;i++){
for(int k = 0;k < n;k++){
for(int j = 0;j < n;j++){
C[i][j] = C[i][j].add(A[i][k].multiply(A[k][j], mc), mc);
}
}
}
return C;
}
// A^e*v
public static BigDecimal[] pow(BigDecimal[][] A, BigDecimal[] v, long m, MathContext mc)
{
BigDecimal[][] mu = A;
BigDecimal[] r = v;
for(;m > 0;m>>>=1){
if((m&1)==1)r = mul(mu, r, mc);
mu = p2(mu, mc);
}
return r;
}
// 普通の累乗計算セット ここまで
// ret[n]=A^(2^n)
public static BigDecimal[][][] generateP2(BigDecimal[][] A, int n, MathContext mc)
{
BigDecimal[][][] ret = new BigDecimal[n+1][][];
ret[0] = A;
for(int i = 1;i <= n;i++)ret[i] = p2(ret[i-1], mc);
return ret;
}
// A[0]^e*v
// A[n]=A[0]^(2^n)
public static BigDecimal[] pow(BigDecimal[][][] A, BigDecimal[] v, long e, MathContext mc)
{
for(int i = 0;e > 0;e>>>=1,i++) {
if((e&1)==1)v = mul(A[i], v, mc);
}
return v;
}
// メモ累乗計算セット ここまで
public static BigDecimal[][] add(BigDecimal[][] A, BigDecimal[][] B, MathContext mc)
{
int m = A.length;
int n = A[0].length;
BigDecimal[][] C = new BigDecimal[m][n];
for(int i = 0;i < m;i++){
for(int j = 0;j < n;j++){
C[i][j] = A[i][j].add(B[i][j], mc);
}
}
return C;
}
public static BigDecimal[][] sub(BigDecimal[][] A, BigDecimal[][] B, MathContext mc)
{
int m = A.length;
int n = A[0].length;
BigDecimal[][] C = new BigDecimal[m][n];
for(int i = 0;i < m;i++){
for(int j = 0;j < n;j++){
C[i][j] = A[i][j].subtract(B[i][j], mc);
}
}
return C;
}
// double行列の積
public static BigDecimal[][] mul(BigDecimal[][] A, BigDecimal[][] B, MathContext mc)
{
assert A[0].length == B.length;
int m = A.length;
int n = A[0].length;
int o = B[0].length;
BigDecimal[][] C = new BigDecimal[m][o];
for(int i = 0;i < m;i++){
for(int j = 0;j < o;j++){
C[i][j] = BigDecimal.ZERO;
}
}
for(int i = 0;i < m;i++){
for(int k = 0;k < n;k++){
for(int j = 0;j < o;j++){
C[i][j] = C[i][j].add(A[i][k].multiply(B[k][j], mc), mc);
}
}
}
return C;
}
public static Result gaussElimination(BigDecimal[][] M, BigDecimal[] v, BigDecimal eps, MathContext mc)
{
int n = M.length, m = M[0].length;
int[] head = new int[n];
// Forward Elimination
int row = 0;
for(int col = 0;col < m;col++){
// select pivot
boolean pivotFound = false;
out:
for(int prow = row;prow < n;prow++){
if(M[prow][col].abs().compareTo(eps) > 0){
// pivot found
if(prow != row){
// swap rows
for(int k = 0;k < m;k++){
BigDecimal u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u;
}
BigDecimal dum = v[prow]; v[prow] = v[row]; v[row] = dum;
}
pivotFound = true;
break out;
}
}
if(!pivotFound)continue;
head[row] = col;
// diag to 1
BigDecimal imul = BigDecimal.ONE.divide(M[row][col], mc);
for(int k = 0;k < m;k++)M[row][k] = M[row][k].multiply(imul, mc);
v[row] = v[row].multiply(imul, mc);
for(int j = row+1;j < n;j++){
if(M[j][col].abs().compareTo(eps) > 0){
BigDecimal mul = M[j][col].negate();
for(int k = col;k < m;k++){
M[j][k] = M[j][k].add(M[row][k].multiply(mul, mc), mc);
}
v[j] = v[j].add(v[row].multiply(mul), mc);
}
}
row++;
}
Result ret = new Result();
ret.mat = M;
for(int i = row;i < n;i++){
if(v[i].abs().compareTo(eps) > 0){
ret.rank = row;
ret.exists = false;
return ret;
}
}
for(int i = row-1;i >= 0;i--){
for(int j = i-1;j >= 0;j--){
if(M[j][head[i]].abs().compareTo(eps) > 0){
BigDecimal mul = M[j][head[i]].negate();
for(int k = head[i];k < m;k++){
M[j][k] = M[j][k].add(M[i][k].multiply(mul, mc), mc);
}
v[j] = v[j].add(v[i].multiply(mul, mc), mc);
}
}
}
BigDecimal[] retv = new BigDecimal[m];
for(int i = 0;i < row;i++){
retv[head[i]] = v[i];
}
ret.sol = retv;
ret.rank = row;
ret.exists = true;
return ret;
}
public static class Result
{
public BigDecimal[][] mat;
public BigDecimal[] sol;
public int rank;
public boolean exists;
}
void run() throws Exception
{
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
// @Override
// public void run() {
// long s = System.currentTimeMillis();
// solve();
// out.flush();
// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// }
// };
// t.start();
// t.join();
}
public static void main(String[] args) throws Exception { new N620_2().run(); }
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
private int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private double nd() { return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }
private String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private long[] nal(int n)
{
long[] a = new long[n];
for(int i = 0;i < n;i++)a[i] = nl();
return a;
}
private char[][] nm(int n, int m) {
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private int[][] nmi(int n, int m) {
int[][] map = new int[n][];
for(int i = 0;i < n;i++)map[i] = na(m);
return map;
}
private int ni() { return (int)nl(); }
private long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}