結果
| 問題 |
No.555 世界史のレポート
|
| ユーザー |
 uwi
|
| 提出日時 | 2017-08-19 21:36:37 |
| 言語 | Java (openjdk 23) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 13,488 bytes |
| コンパイル時間 | 4,832 ms |
| コンパイル使用メモリ | 94,036 KB |
| 実行使用メモリ | 37,204 KB |
| 最終ジャッジ日時 | 2024-10-14 15:52:57 |
| 合計ジャッジ時間 | 6,461 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 18 WA * 2 |
ソースコード
package yukicoder;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Queue;
import java.util.Random;
import java.util.stream.Collectors;
public class N555 {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
int n = ni(), c = ni(), v = ni();
// minimize c*x+v(a[0]+a[1]+...+a[x-1])
// subject to (a[0]+1)*(a[1]+1)*...*(a[x-1]+1) >= n (... => maximize)
long min = Long.MAX_VALUE;
for(int x = 1;x <= 20;x++){
long under = (long)(Math.pow(n, 1./x)+1e-9);
if(under == 1)break;
// log(under)*A + log(under+1)*(x-A) >= log n
// A <= (log n - xlog(under+1))/(log(under)-log(under+1))
long amin = (long)((Math.log(n)-x*Math.log(under+1))/(Math.log(under) - Math.log(under+1)));
assert 0 <= amin;
assert amin <= x;
assert Math.pow(under, amin) * Math.pow(under+1, x-amin) >= n;
// tr(x, under, amin, (long)c*x+v*(amin*(under-1)+(x-amin)*(under)));
min = Math.min(min, (long)c*x+v*(amin*(under-1)+(x-amin)*(under)));
}
out.println(min);
}
public static List<FactorAndPower> factorize(long[] f, int mod)
{
List<FactorAndPower> faps = doSquareFreeFactorization(f, mod);
List<FactorAndPower> nfaps =
faps.stream().flatMap(fap -> {
List<FactorAndPower> res = doDistinctDegreeFactorization(fap.factor, mod);
for(FactorAndPower resfap : res)resfap.power = fap.power;
return res.stream();
}).collect(Collectors.toList());
List<FactorAndPower> nnfaps =
nfaps.stream().flatMap(fap -> {
List<FactorAndPower> res = doCantorZassenhaus(fap, mod, new Random());
return res.stream();
}).collect(Collectors.toList());
return nnfaps;
}
public static class FactorAndPower
{
long[] factor;
long power;
int degree;
public FactorAndPower(long[] factor, long power) {
this.factor = factor;
this.power = power;
}
public FactorAndPower(long[] factor, long power, int degree) {
this.factor = factor;
this.power = power;
this.degree = degree;
}
@Override
public String toString() {
return "FactorAndPower [factor=" + Arrays.toString(factor) + ", power=" + power + ", degree=" + degree
+ "]";
}
}
/**
* f -> f_1^1*f_2^2*f_3^3*... (% mod)
* @param f
* @param mod
* @return
*/
public static List<FactorAndPower> doSquareFreeFactorization(long[] f, int mod)
{
int i = 1;
List<FactorAndPower> R = new ArrayList<>();
long[] g = d(f, mod);
if(g.length > 0){
long[] c = gcd(f, g, mod);
long[] w = div(f, c, mod);
while(w.length != 1){
long[] y = gcd(w, c, mod);
long[] z = div(w, y, mod);
if(z.length > 1){
R.add(new FactorAndPower(z, i));
}
i++;
w = y;
c = div(c, y, mod);
}
if(c.length != 1){
// c <- c^(1/p)
long[] nc = new long[(c.length+mod-1)/mod];
for(int j = 0;j < c.length;j+=mod)nc[j/mod] = c[j];
c = nc;
List<FactorAndPower> res = doSquareFreeFactorization(c, mod);
for(FactorAndPower fap : res){
fap.power *= mod;
R.add(fap);
}
}
}else{
long[] nf = new long[(f.length+mod-1)/mod];
for(int j = 0;j < f.length;j+=mod)nf[j/mod] = f[j];
f = nf;
List<FactorAndPower> res = doSquareFreeFactorization(f, mod);
for(FactorAndPower fap : res){
fap.power *= mod;
R.add(fap);
}
}
return R;
}
// TODO check v^q-vへの改善がわからなかった
public static List<FactorAndPower> doCantorZassenhaus(FactorAndPower fap, int mod, Random gen)
{
assert mod % 2 == 1;
Queue<FactorAndPower> ret = new ArrayDeque<>();
int r = (fap.factor.length - 1) / fap.degree;
int d = fap.degree;
BigInteger E = BigInteger.valueOf(mod).pow(d).shiftRight(1);
ret.add(fap);
while(ret.size() < r){
long[] h = gen.longs(gen.nextInt(fap.factor.length-1)+1, 0, mod).toArray(); // choose randomly
long[] g = sub(pow(h, E, fap.factor, mod), new long[]{1}, mod);
for(int i = ret.size()-1;i >= 0;i--){
FactorAndPower u = ret.poll();
if(u.factor.length > d+1){
long[] gu = gcd(g, u.factor, mod);
if(gu.length > 1 && gu.length < u.factor.length){
ret.add(new FactorAndPower(gu, u.power, u.degree));
ret.add(new FactorAndPower(div(u.factor, gu, mod), u.power, u.degree));
continue;
}
}
ret.add(u);
}
}
return new ArrayList<>(ret);
}
public static List<FactorAndPower> doDistinctDegreeFactorization(long[] f, int mod)
{
long[] fstar = Arrays.copyOf(f, f.length);
int i = 1;
List<FactorAndPower> ret = new ArrayList<>();
while(fstar.length >= 2*i){
long[] xq = modulo(mod, fstar, mod);
long[][] Q = mulRowAndCompanionMatrixes(xq, f, mod); // Method 1
Q = pow(Q, i, mod);
long[] R = sub(Q[0], new long[]{0, 1}, mod);
long[] g = gcd(R, fstar, mod);
if(g.length > 1){
ret.add(new FactorAndPower(g, 1, i));
fstar = div(fstar, g, mod);
}
i++;
}
if(fstar.length > 1){
ret.add(new FactorAndPower(fstar, 1, fstar.length-1));
}
if(ret.isEmpty()){
ret.add(new FactorAndPower(f, 1, 1));
}
return ret;
}
/////////////////
public static long[] mul(long[] a, long[] b, int mod)
{
if(a.length == 0)return new long[0];
long[] c = new long[a.length+b.length-1];
long big = (Long.MAX_VALUE / mod - mod) * mod;
for(int i = 0;i < a.length;i++){
for(int j = 0;j < b.length;j++){
c[i+j] += a[i]*b[j];
if(c[i+j] >= big)c[i+j] -= big;
}
}
for(int i = 0;i < c.length;i++)c[i] %= mod;
return c;
}
public static long[] pow(long[] a, BigInteger E, long[] f, int mod)
{
long[] ret = {1};
for(int i = E.bitLength()-1;i >= 0;i--){
ret = modnaive(mul(ret, ret, mod), f, mod);
if(E.testBit(i)){
ret = modnaive(mul(ret, a, mod), f, mod);
}
}
return ret;
}
public static long[] sub(long[] a, long[] b, int mod)
{
long[] c = new long[Math.max(a.length, b.length)];
for(int i = 0;i < a.length;i++)c[i] += a[i];
for(int i = 0;i < b.length;i++)c[i] -= b[i];
for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
return normalize(c);
}
public static long[][] pow(long[][] A, long e, int mod)
{
long[][] MUL = A;
int n = A.length;
long[][] C = new long[n][n];
for(int i = 0;i < n;i++)C[i][i] = 1;
for(;e > 0;e>>>=1) {
if((e&1)==1)C = mul(C, MUL, mod);
MUL = mul(MUL, MUL, mod);
}
return C;
}
public static long[][] mul(long[][] A, long[][] B, int mod)
{
assert A[0].length == B.length;
int m = A.length;
int n = A[0].length;
int o = B[0].length;
long[][] C = new long[m][o];
for(int i = 0;i < m;i++){
for(int j = 0;j < o;j++){
long sum = 0;
for(int k = 0;k < n;k++){
sum += (long)A[i][k] * B[k][j];
sum %= mod;
}
C[i][j] = (int)sum;
}
}
return C;
}
public static long[] modulo(long n, long[] f, int mod)
{
assert f.length > 0;
int m = f.length;
if(m == 1)return new long[0];
long ih = invl(f[m-1], mod);
long[] a = new long[m-1];
for(int i = 0;i < m-1;i++)a[i] = ih*(mod-f[i])%mod;
return poWCompanionMatrixesRow0(a, n, mod);
}
public static long[] d(long[] f, int mod)
{
if(f.length == 0)return new long[0];
long[] ret = new long[f.length-1];
for(int i = 1;i < f.length;i++){
ret[i-1] = f[i] * i % mod;
}
return normalize(ret);
}
public static long[] gcd(long[] a, long[] b, int mod)
{
while(b.length > 0){
long[] c = modnaive(a, b, mod);
a = b; b = c;
}
if(a.length > 0){
long ih = invl(a[a.length-1], mod);
for(int i = 0;i < a.length;i++){
a[i] = a[i] * ih % mod;
}
}
return a;
}
static long[] normalize(long[] f)
{
for(int i = f.length-1;i >= 0;i--){
if(f[i] != 0){
return i == f.length-1 ? f : Arrays.copyOf(f, i+1);
}
}
return new long[0];
}
public static long[] modnaive(long[] a, long[] b, int mod)
{
int n = a.length, m = b.length;
if(n-m+1 <= 0)return a;
long[] r = Arrays.copyOf(a, n);
long ib = invl(b[m-1], mod);
for(int i = n-1;i >= m-1;i--){
long x = ib * r[i] % mod;
for(int j = m-1;j >= 0;j--){
r[i+j-(m-1)] -= b[j]*x;
r[i+j-(m-1)] %= mod;
if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
// r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
}
}
return normalize(r);
}
public static long[] div(long[] a, long[] b, int mod)
{
int n = a.length, m = b.length;
if(n-m+1 <= 0)return new long[0];
long[] r = Arrays.copyOf(a, n);
long[] q = new long[n-m+1];
long ib = invl(b[m-1], mod);
for(int i = n-1;i >= m-1;i--){
long x = ib * r[i] % mod;
q[i-(m-1)] = x;
for(int j = m-1;j >= 0;j--){
r[i+j-(m-1)] -= b[j]*x;
r[i+j-(m-1)] %= mod;
if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
// r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
}
}
return q;
}
public static long invl(long a, long mod) {
long b = mod;
long p = 1, q = 0;
while (b > 0) {
long c = a / b;
long d;
d = a;
a = b;
b = d % b;
d = p;
p = q;
q = d - c * q;
}
return p < 0 ? p + mod : p;
}
public static long[][] poWCompanionMatrixes(long[] A, long m, int mod)
{
int n = A.length;
long[] u = new long[A.length];
u[0] = 1;
long[][] CA = new long[n][n];
for(int i = 0;i < n-1;i++)CA[i][i+1] = 1;
CA[n-1] = A;
for(int i = 0;1L<<i <= m;i++){
if(m<<~i<0)u = mulRowAndMatrix(u, CA, mod);
// A^(n) -> A^(2n)
CA = mulRowAndCompanionMatrixes(mulRowAndMatrix(CA[0], CA, mod), A, mod);
}
return mulRowAndCompanionMatrixes(u, A, mod);
}
public static long[] poWCompanionMatrixesRow0(long[] A, long m, int mod)
{
int n = A.length;
long[] u = new long[A.length];
u[0] = 1;
long[][] CA = new long[n][n];
for(int i = 0;i < n-1;i++)CA[i][i+1] = 1;
CA[n-1] = A;
for(int i = 0;1L<<i <= m;i++){
if(m<<~i<0)u = mulRowAndMatrix(u, CA, mod);
// A^(n) -> A^(2n)
CA = mulRowAndCompanionMatrixes(mulRowAndMatrix(CA[0], CA, mod), A, mod);
}
return u;
}
public static long[][] mulRowAndCompanionMatrixes(long[] u, long[] A, int mod)
{
int n = u.length;
long[][] NA = new long[n][];
NA[0] = Arrays.copyOf(u, n);
for(int i = 1;i < n;i++){
long v = u[n-1];
for(int j = n-2;j >= 0;j--){
u[j+1] = u[j];
}
u[0] = 0;
for(int j = 0;j < n;j++){
u[j] += v * A[j];
u[j] %= mod;
}
NA[i] = Arrays.copyOf(u, n);
}
return NA;
}
private static long[] mulRowAndMatrix(long[] u, long[][] A, int mod)
{
int n = A.length;
long[] nu = new long[n];
for(int j = 0;j < n;j++){
long s = 0;
for(int i = 0;i < n;i++){
s += A[i][j] * u[i];
s %= mod;
}
nu[j] = s;
}
return nu;
}
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 N555().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)); }
}