結果

問題 No.1080 Strange Squared Score Sum
ユーザー uwi
提出日時 2020-06-12 23:05:56
言語 Java
(openjdk 23)
結果
AC  
実行時間 970 ms / 5,000 ms
コード長 8,665 bytes
コンパイル時間 4,886 ms
コンパイル使用メモリ 83,624 KB
実行使用メモリ 59,420 KB
最終ジャッジ日時 2024-06-24 05:49:07
合計ジャッジ時間 17,322 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
sample AC * 2
other AC * 20
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ソースコード

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プレゼンテーションモードにする

package contest200612;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class E2 {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    void solve()
    {
        int n = ni();
        int mod = 1000000009;
        int[][] fif = enumFIF(n, mod);
        int m = n > 2000 ? 100 : n;
        long[][] dp = new long[4][m+1];
        dp[0][0] = 1;
        for(int v = 1;v <= n;v++){
            long[][] ndp = new long[4][m+1];
            for(int f = 0;f*v <= m;f++){
                long M = pow(v+1, 2*f, mod) * fif[1][f] % mod;
                for(int i = 0;i < 4;i++){
                    for(int j = 0;j+f*v <= m;j++){
                        ndp[i+f&3][j+f*v] += dp[i][j] * M;
                        ndp[i+f&3][j+f*v] %= mod;
                    }
                }
            }
            dp = ndp;
        }
        long[] base = new long[m];
        for(int i = 1;i <= m;i++){
            long sum = 0;
            for(int j = 0;j < 4;j++){
                sum += (long)(j >= 2 ? mod-1 : 1) * dp[j][i];
                sum %= mod;
            }
            base[i-1] = sum;
        }
        
        if(n > m){
            long[][] res = guessLeaned(mod, base);
            base = Arrays.copyOf(base, n);
            int t = res.length;
            for(int i = m+1;i <= n;i++){
                base[i-1] = f(res, Arrays.copyOfRange(base, i-t, i-1), i-1, mod);
            }
        }
        
        for(int i = 0;i < n;i++){
            out.println(base[i]*fif[0][n]%mod);
        }
    }
    
    public static long f(long[][] ged, long[] prevs, long x, int mod)
    {
        int n = ged.length;
        assert prevs.length == n-1;
        x -= n-1;
        
        long s = 0;
        long tar = 0;
        for(int i = 0;i < n;i++){
            long co = 0;
            for(int j = ged[i].length-1;j >= 0;j--){
                co = (co * x + ged[i][j]) % mod;
            }
            if(i < n-1){
                s += co * prevs[i];
                s %= mod;
            }else{
                tar = co;
            }
        }
        
        long ret = -invl(tar, mod) * s % mod;
        if(ret < 0)ret += mod;
        return ret;
    }
    
    public static long[][] guessLeaned(int mod, long... a)
    {
        int n = a.length;
        
        // #formula >= #variable
        // n-r+2 >= r(r+1)/2
        for(int r = n;r >= 1;r--){
            if(n-r+2 < r*(r+1)/2)continue;
            int[][] M = new int[n-r+2][r*(r+1)/2];
            for(int i = 0;i < n-r+1;i++){
                int p = 0;
                for(int j = 0;j < r;j++){
                    long prod = 1;
                    for(int k = 0;k <= r-j-1;k++){
                        M[i][p++] = (int)(prod*a[i+j]%mod);
                        prod = prod * i % mod;
                    }
                }
            }
            M[n-r+1][0] = 1;
            
            int[] v = new int[n-r+2];
            v[n-r+1] = 1;
            
            Result res = gaussElimination(M, v, mod);
            if(res.exists){
                long[][] ret = new long[r][];
                int p = 0;
                for(int i = 0;i < r;i++){
                    ret[i] = new long[r-i];
                    for(int j = 0;j < r-i;j++){
                        ret[i][j] = res.sol[p++];
                    }
                }
                
                // reformat
                int ilast = r;
                for(int i = r-1;i >= 0;i--){
                    int last = ret[i].length;
                    while(last > 0 && ret[i][last-1] == 0)last--;
                    ret[i] = Arrays.copyOf(ret[i], last);
                    if(last == 0 && i+1 == ilast){
                        ilast--;
                    }
                }
                ret = Arrays.copyOf(ret, ilast);
                
                return ret;
            }
        }
        return null;
    }
    
    
    
    public static int[][] enumFIF(int n, int mod) {
        int[] f = new int[n + 1];
        int[] invf = new int[n + 1];
        f[0] = 1;
        for (int i = 1; i <= n; i++) {
            f[i] = (int) ((long) f[i - 1] * i % mod);
        }
        long a = f[n];
        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;
        }
        invf[n] = (int) (p < 0 ? p + mod : p);
        for (int i = n - 1; i >= 0; i--) {
            invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
        }
        return new int[][] { f, invf };
    }
    
    public static Result gaussElimination(int[][] M, int[] v, int mod)
    {
        int n = M.length, m = M[0].length;
        int[] head = new int[n];
        
        // if not needed, comment out.
        for(int[] row : M){
            for(int i = 0;i < row.length;i++){
                row[i] %= mod;
                if(row[i] < 0)row[i] += mod;
            }
        }
        
        // 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] != 0){
                    // pivot found
                    if(prow != row){
                        // swap rows
                        for(int k = 0;k < m;k++){
                            int u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u;
                        }
                        int dum = v[prow]; v[prow] = v[row]; v[row] = dum;
                    }
                    pivotFound = true;
                    break out;
                }
            }
            if(!pivotFound)continue;
            head[row] = col;
            
            // diag to 1
            long imul = invl(M[row][col], mod);
            for(int k = 0;k < m;k++){
                M[row][k] = (int)(M[row][k] * imul % mod);
            }
            v[row] = (int)(v[row] * imul % mod);
            
            for(int j = row+1;j < n;j++){
                if(M[j][col] != 0){
                    long mul = mod-M[j][col];
                    for(int k = col;k < m;k++){
                        M[j][k] = (int)((M[j][k] + M[row][k] * mul) % mod);
                    }
                    v[j] = (int)((v[j] + v[row] * mul) % mod);
                }
            }
            row++;
        }
        
        Result ret = new Result();
        ret.mat = M;
        for(int i = row;i < n;i++){
            if(v[i] != 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]] != 0){
                    long mul = mod-M[j][head[i]];
                    for(int k = head[i];k < m;k++){
                        M[j][k] = (int)((M[j][k] + M[i][k] * mul) % mod);
                    }
                    v[j] = (int)((v[j] + v[i] * mul) % mod);
                }
            }
        }
        
        int[] retv = new int[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 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 class Result
    {
        public int[][] mat;
        public int[] sol;
        public int rank;
        public boolean exists;
    }
    
    public 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;
    }
    
    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 E2().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)); }
}
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