#462580 (Java21) No.1025 Modular Equation

• 問題: No.1025 Modular Equation
• ユーザー: 37zigen
• 提出日時: 2020-04-11 06:19:54
• 言語: Java21 (openjdk 21)
• 結果: AC
• 実行時間: 3,007 ms / 5,000 ms
• コード長: 4,678 bytes
• コンパイル時間: 2,323 ms
• コンパイル使用メモリ: 78,888 KB
• 実行使用メモリ: 59,600 KB
• 最終ジャッジ日時: 2023-10-17 11:49:41
• 合計ジャッジ時間: 51,317 ms
• ジャッジサーバーID （参考情報）: judge13 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	56 ms; 53,420 KB
testcase_01	AC	55 ms; 53,412 KB
testcase_02	AC	60 ms; 52,424 KB
testcase_03	AC	76 ms; 54,500 KB
testcase_04	AC	76 ms; 54,356 KB
testcase_05	AC	71 ms; 54,348 KB
testcase_06	AC	63 ms; 53,976 KB
testcase_07	AC	72 ms; 54,224 KB
testcase_08	AC	73 ms; 54,580 KB
testcase_09	AC	2,695 ms; 59,100 KB
testcase_10	AC	2,395 ms; 59,292 KB
testcase_11	AC	2,068 ms; 58,920 KB
testcase_12	AC	1,760 ms; 58,716 KB
testcase_13	AC	1,569 ms; 56,796 KB
testcase_14	AC	1,722 ms; 59,052 KB
testcase_15	AC	1,437 ms; 58,844 KB
testcase_16	AC	1,532 ms; 58,820 KB
testcase_17	AC	1,438 ms; 59,156 KB
testcase_18	AC	1,537 ms; 59,152 KB
testcase_19	AC	1,711 ms; 59,064 KB
testcase_20	AC	1,890 ms; 59,172 KB
testcase_21	AC	1,703 ms; 59,356 KB
testcase_22	AC	1,939 ms; 59,600 KB
testcase_23	AC	2,079 ms; 59,128 KB
testcase_24	AC	3,007 ms; 58,980 KB
testcase_25	AC	2,215 ms; 58,900 KB
testcase_26	AC	1,797 ms; 59,332 KB
testcase_27	AC	1,672 ms; 59,140 KB
testcase_28	AC	1,458 ms; 58,956 KB
testcase_29	AC	1,687 ms; 59,052 KB
testcase_30	AC	2,044 ms; 59,088 KB
testcase_31	AC	1,954 ms; 58,904 KB
testcase_32	AC	2,538 ms; 58,888 KB
testcase_33	AC	56 ms; 51,492 KB
testcase_34	AC	177 ms; 58,872 KB

ソースコード

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.NoSuchElementException;

class DJSet {
	int n;
	int[] upper;
	
	public DJSet(int n) {
		this.n=n;
		upper=new int[n];
		Arrays.fill(upper, -1);
	}
	
	int root(int x) {
		return upper[x]<0?x:(upper[x]=root(upper[x]));
	}
	
	boolean equiv(int x,int y) {
		return root(x)==root(y);
	}
	
	void setUnion(int x,int y) {
		x=root(x);y=root(y);
		if (x==y) return;
		if (upper[x]<upper[y]) {
			x^=y;y^=x;x^=y;
		}
		if (upper[x]==upper[y]) --upper[y];
		upper[x]=y;
		--n;
	}
}

public class Main {

	public static void main(String[] args) {
		new Main().run();
	}
	
	final long MOD=(long)1e9+7;
	
	long ADD(long a,long b) {
		return a+b>=MOD?a+b-MOD:a+b;
	}
	
	long gcd(long a,long b) {
		return a==0?b:gcd(b%a,a);
	}
	
	long pow_mod(long a,long n,long p) {
		long ret=1;
		for (;n>0;n>>=1,a=a*a%p) if(n%2==1) ret=ret*a%p;
		return ret;
	}
	
	long primitive_root(long p) {
		if (p==2) return 1;
		out:for (long root=2;root<p;++root) {
			for (long div=2;div*div<=p-1;++div) {
				if ((p-1)%div!=0) continue;
				for (long d:new long[] {div,(p-1)/div}) {
					if (pow_mod(root,d,p)==1) continue out;
				}
			}
			return root;
		}
		throw new AssertionError();
	}
	
	void run() {
		FastScanner sc=new FastScanner();
		PrintWriter pw=new PrintWriter(System.out);
		long p=sc.nextLong();
		int n=sc.nextInt();
		long k=gcd(sc.nextInt(),p-1);
		long b=sc.nextLong();
		long g=primitive_root(p);
		long[] gk=new long[(int)((p-1)/k)+1];
		gk[0]=1;gk[1]=pow_mod(g, k, p);
		for (int i=2;i<gk.length;++i) gk[i]=gk[i-1]*gk[1]%p;
		long[][] dp=new long[2][(int)p];
		int[] ds_root=new int[(int)p];		
		DJSet ds=new DJSet((int)p);
		dp[0][0]=1;
		for (int i=1;i<p;++i) ds.setUnion(i, (int)(i*gk[1]%p));
		int[] list=new int[ds.n];
		{
			int pos=0;
			for (int i=0;i<p;++i) if (ds.root(i)==i) list[pos++]=i;
		}
		for (int i=0;i<p;++i) ds_root[i]=ds.root(i);
		int e=0;
		for (int i=1;i<=n;++i) {
			int a=sc.nextInt();
			for (int j=0;j<p;++j) dp[i%2][j]=dp[(i-1)%2][j];
			if (a==0) {
				++e;
				continue;
			}
			for (int to:list) {
				long sum=dp[i%2][ds_root[to]];
				for (int j=0;j<(p-1)/k;++j) {
					int from=(int)((to+(p-a)*gk[j])%p);
					if (dp[(i-1)%2][ds_root[from]]==0) continue;
					sum+=dp[(i-1)%2][ds_root[from]]*k;
				}
				dp[i%2][ds_root[to]]=sum%MOD;
			}
		}
		pw.println(dp[n%2][ds_root[(int)b]]*pow_mod(p, e, MOD)%MOD);
		pw.close();
	}
	
	void tr(Object...objects) {System.out.println(Arrays.deepToString(objects));}
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    
    public double nextDouble() { return Double.parseDouble(next());}
}