結果
| 問題 | No.1331 Moving Penguin |
| ユーザー |
 uwi
|
| 提出日時 | 2021-01-08 21:51:11 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 337 ms / 1,500 ms |
| コード長 | 17,972 bytes |
| コンパイル時間 | 5,898 ms |
| コンパイル使用メモリ | 92,604 KB |
| 実行使用メモリ | 41,608 KB |
| 最終ジャッジ日時 | 2024-11-07 14:38:26 |
| 合計ジャッジ時間 | 19,895 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 49 |
ソースコード
package contest210108;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
public class C2 {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni();
int[] a = na(n);
long[] dp = new long[n];
int S = (int)Math.sqrt(n);
dp[0] = 1;
final int mod = 1000000007;
long[][] stock = new long[S+1][S+1];
for(int i = 0;i < n;i++){
for(int j = 1;j <= S;j++){
dp[i] += stock[j][i%j];
}
dp[i] %= mod;
if(a[i] != 1 && i+1 < n) {
dp[i + 1] += dp[i];
if (dp[i + 1] >= mod) dp[i + 1] -= mod;
}
if(a[i] <= S){
stock[a[i]][i%a[i]] += dp[i];
}else{
for(int j = i+a[i];j < n;j+=a[i]){
dp[j] += dp[i];
}
}
}
out.println(dp[n-1]);
}
public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
// public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033};
// public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};
public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
{
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
return nttmb(fa, m, true, P, g);
}
public static long[] convoluteSimplyS(long[] a, long[] b, int P, int g)
{
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
long[] fa = nttsb(a, m, false, P, g);
long[] fb = a == b ? fa : nttsb(b, m, false, P, g);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
return nttsb(fa, m, true, P, g);
}
public static long[] convolute(long[] a, long[] b)
{
int USE = 3;
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
long[][] fs = new long[USE][];
for(int k = 0;k < USE;k++){
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for(int i = 0;i < fs[0].length;i++){
for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j];
fs[0][i] = ret;
}
return fs[0];
}
public static long[] convolute(long[] a, long[] b, int USE, int mod)
{
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
long[][] fs = new long[USE][];
for(int k = 0;k < USE;k++){
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for(int i = 0;i < fs[0].length;i++){
for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod;
fs[0][i] = ret;
}
return fs[0];
}
// static int[] wws = new int[270000]; // outer faster
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
{
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
int[] wws = new int[1<<h-1];
long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
long w = (1L<<32)%P;
for(int k = 0;k < 1<<h-1;k++){
wws[k] = (int)w;
w = modh(w*dw, M, H, P);
}
long J = invl(P, 1L<<32);
for(int i = 0;i < h;i++){
for(int j = 0;j < 1<<i;j++){
for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
long u = (dst[s] - dst[t] + 2*P)*wws[k];
dst[s] += dst[t];
if(dst[s] >= 2*P)dst[s] -= 2*P;
// long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
long Q = (u<<32)*J>>>32;
dst[t] = (u>>>32)-(Q*P>>>32)+P;
}
}
if(i < h-1){
for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
}
}
for(int i = 0;i < n;i++){
if(dst[i] >= P)dst[i] -= P;
}
for(int i = 0;i < n;i++){
int rev = Integer.reverse(i)>>>-h;
if(i < rev){
long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
}
}
if(inverse){
long in = invl(n, P);
for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
}
return dst;
}
// Modified Shoup + Barrett
private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g)
{
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
long[] wws = new long[1<<h-1];
long[] ws = new long[1<<h-1];
long w = 1;
for(int k = 0;k < 1<<h-1;k++){
wws[k] = (w<<32)/P;
ws[k] = w;
w = modh(w*dw, M, H, P);
}
for(int i = 0;i < h;i++){
for(int j = 0;j < 1<<i;j++){
for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
long ndsts = dst[s] + dst[t];
if(ndsts >= 2*P)ndsts -= 2*P;
long T = dst[s] - dst[t] + 2*P;
long Q = wws[k]*T>>>32;
dst[s] = ndsts;
dst[t] = ws[k]*T-Q*P&(1L<<32)-1;
}
}
// dw = dw * dw % P;
if(i < h-1){
for(int k = 0;k < 1<<h-i-2;k++){
wws[k] = wws[k*2];
ws[k] = ws[k*2];
}
}
}
for(int i = 0;i < n;i++){
if(dst[i] >= P)dst[i] -= P;
}
for(int i = 0;i < n;i++){
int rev = Integer.reverse(i)>>>-h;
if(i < rev){
long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
}
}
if(inverse){
long in = invl(n, P);
for(int i = 0;i < n;i++){
dst[i] = modh(dst[i] * in, M, H, P);
}
}
return dst;
}
static final long mask = (1L<<31)-1;
public static long modh(long a, long M, int h, int mod)
{
long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
return r < mod ? r : r-mod;
}
private static long[] garnerPrepare(int[] m)
{
int n = m.length;
assert n == m.length;
if(n == 0)return new long[0];
long[] gamma = new long[n];
for(int k = 1;k < n;k++){
long prod = 1;
for(int i = 0;i < k;i++){
prod = prod * m[i] % m[k];
}
gamma[k] = invl(prod, m[k]);
}
return gamma;
}
private static long[] garnerBatch(int[] u, int[] m, long[] gamma)
{
int n = u.length;
assert n == m.length;
long[] v = new long[n];
v[0] = u[0];
for(int k = 1;k < n;k++){
long temp = v[k-1];
for(int j = k-2;j >= 0;j--){
temp = (temp * m[j] + v[j]) % m[k];
}
v[k] = (u[k] - temp) * gamma[k] % m[k];
if(v[k] < 0)v[k] += m[k];
}
return v;
}
private static long pow(long a, long n, long mod) {
// a %= mod;
long ret = 1;
int x = 63 - Long.numberOfLeadingZeros(n);
for (; x >= 0; x--) {
ret = ret * ret % mod;
if (n << 63 - x < 0)
ret = ret * a % mod;
}
return ret;
}
private 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 void main(String[] args) {
new C2().run();
}
public void run()
{
long S = System.currentTimeMillis();
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new FastWriter(System.out);
solve();
out.flush();
long G = System.currentTimeMillis();
tr(G-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();
}
private boolean eof()
{
if(lenbuf == -1)return true;
int lptr = ptrbuf;
while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
try {
is.mark(1000);
while(true){
int b = is.read();
if(b == -1){
is.reset();
return true;
}else if(!isSpaceChar(b)){
is.reset();
return false;
}
}
} catch (IOException e) {
return true;
}
}
private final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){
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 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[] 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 int ni()
{
int num = 0, 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 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();
}
}
public static class FastWriter
{
private static final int BUF_SIZE = 1<<13;
private final byte[] buf = new byte[BUF_SIZE];
private final OutputStream out;
private int ptr = 0;
private FastWriter(){out = null;}
public FastWriter(OutputStream os)
{
this.out = os;
}
public FastWriter(String path)
{
try {
this.out = new FileOutputStream(path);
} catch (FileNotFoundException e) {
throw new RuntimeException("FastWriter");
}
}
public FastWriter write(byte b)
{
buf[ptr++] = b;
if(ptr == BUF_SIZE)innerflush();
return this;
}
public FastWriter write(char c)
{
return write((byte)c);
}
public FastWriter write(char[] s)
{
for(char c : s){
buf[ptr++] = (byte)c;
if(ptr == BUF_SIZE)innerflush();
}
return this;
}
public FastWriter write(String s)
{
s.chars().forEach(c -> {
buf[ptr++] = (byte)c;
if(ptr == BUF_SIZE)innerflush();
});
return this;
}
private static int countDigits(int l) {
if (l >= 1000000000) return 10;
if (l >= 100000000) return 9;
if (l >= 10000000) return 8;
if (l >= 1000000) return 7;
if (l >= 100000) return 6;
if (l >= 10000) return 5;
if (l >= 1000) return 4;
if (l >= 100) return 3;
if (l >= 10) return 2;
return 1;
}
public FastWriter write(int x)
{
if(x == Integer.MIN_VALUE){
return write((long)x);
}
if(ptr + 12 >= BUF_SIZE)innerflush();
if(x < 0){
write((byte)'-');
x = -x;
}
int d = countDigits(x);
for(int i = ptr + d - 1;i >= ptr;i--){
buf[i] = (byte)('0'+x%10);
x /= 10;
}
ptr += d;
return this;
}
private static int countDigits(long l) {
if (l >= 1000000000000000000L) return 19;
if (l >= 100000000000000000L) return 18;
if (l >= 10000000000000000L) return 17;
if (l >= 1000000000000000L) return 16;
if (l >= 100000000000000L) return 15;
if (l >= 10000000000000L) return 14;
if (l >= 1000000000000L) return 13;
if (l >= 100000000000L) return 12;
if (l >= 10000000000L) return 11;
if (l >= 1000000000L) return 10;
if (l >= 100000000L) return 9;
if (l >= 10000000L) return 8;
if (l >= 1000000L) return 7;
if (l >= 100000L) return 6;
if (l >= 10000L) return 5;
if (l >= 1000L) return 4;
if (l >= 100L) return 3;
if (l >= 10L) return 2;
return 1;
}
public FastWriter write(long x)
{
if(x == Long.MIN_VALUE){
return write("" + x);
}
if(ptr + 21 >= BUF_SIZE)innerflush();
if(x < 0){
write((byte)'-');
x = -x;
}
int d = countDigits(x);
for(int i = ptr + d - 1;i >= ptr;i--){
buf[i] = (byte)('0'+x%10);
x /= 10;
}
ptr += d;
return this;
}
public FastWriter write(double x, int precision)
{
if(x < 0){
write('-');
x = -x;
}
x += Math.pow(10, -precision)/2;
// if(x < 0){ x = 0; }
write((long)x).write(".");
x -= (long)x;
for(int i = 0;i < precision;i++){
x *= 10;
write((char)('0'+(int)x));
x -= (int)x;
}
return this;
}
public FastWriter writeln(char c){
return write(c).writeln();
}
public FastWriter writeln(int x){
return write(x).writeln();
}
public FastWriter writeln(long x){
return write(x).writeln();
}
public FastWriter writeln(double x, int precision){
return write(x, precision).writeln();
}
public FastWriter write(int... xs)
{
boolean first = true;
for(int x : xs) {
if (!first) write(' ');
first = false;
write(x);
}
return this;
}
public FastWriter write(long... xs)
{
boolean first = true;
for(long x : xs) {
if (!first) write(' ');
first = false;
write(x);
}
return this;
}
public FastWriter writeln()
{
return write((byte)'\n');
}
public FastWriter writeln(int... xs)
{
return write(xs).writeln();
}
public FastWriter writeln(long... xs)
{
return write(xs).writeln();
}
public FastWriter writeln(char[] line)
{
return write(line).writeln();
}
public FastWriter writeln(char[]... map)
{
for(char[] line : map)write(line).writeln();
return this;
}
public FastWriter writeln(String s)
{
return write(s).writeln();
}
private void innerflush()
{
try {
out.write(buf, 0, ptr);
ptr = 0;
} catch (IOException e) {
throw new RuntimeException("innerflush");
}
}
public void flush()
{
innerflush();
try {
out.flush();
} catch (IOException e) {
throw new RuntimeException("flush");
}
}
public FastWriter print(byte b) { return write(b); }
public FastWriter print(char c) { return write(c); }
public FastWriter print(char[] s) { return write(s); }
public FastWriter print(String s) { return write(s); }
public FastWriter print(int x) { return write(x); }
public FastWriter print(long x) { return write(x); }
public FastWriter print(double x, int precision) { return write(x, precision); }
public FastWriter println(char c){ return writeln(c); }
public FastWriter println(int x){ return writeln(x); }
public FastWriter println(long x){ return writeln(x); }
public FastWriter println(double x, int precision){ return writeln(x, precision); }
public FastWriter print(int... xs) { return write(xs); }
public FastWriter print(long... xs) { return write(xs); }
public FastWriter println(int... xs) { return writeln(xs); }
public FastWriter println(long... xs) { return writeln(xs); }
public FastWriter println(char[] line) { return writeln(line); }
public FastWriter println(char[]... map) { return writeln(map); }
public FastWriter println(String s) { return writeln(s); }
public FastWriter println() { return writeln(); }
}
public static void trnz(int... o)
{
for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
System.out.println();
}
// print ids which are 1
public static void trt(long... o)
{
Queue<Integer> stands = new ArrayDeque<>();
for(int i = 0;i < o.length;i++){
for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
}
System.out.println(stands);
}
public static void tf(boolean... r)
{
for(boolean x : r)System.out.print(x?'#':'.');
System.out.println();
}
public static void tf(boolean[]... b)
{
for(boolean[] r : b) {
for(boolean x : r)System.out.print(x?'#':'.');
System.out.println();
}
System.out.println();
}
public void tf(long[]... b)
{
if(INPUT.length() != 0) {
for (long[] r : b) {
for (long x : r) {
for (int i = 0; i < 64; i++) {
System.out.print(x << ~i < 0 ? '#' : '.');
}
}
System.out.println();
}
System.out.println();
}
}
public void tf(long... b)
{
if(INPUT.length() != 0) {
for (long x : b) {
for (int i = 0; i < 64; i++) {
System.out.print(x << ~i < 0 ? '#' : '.');
}
}
System.out.println();
}
}
private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}