結果

問題 No.978 Fibonacci Convolution Easy
ユーザー uwiuwi
提出日時 2020-01-31 21:38:51
言語 Java21
(openjdk 21)
結果
AC  
実行時間 51 ms / 2,000 ms
コード長 4,944 bytes
コンパイル時間 4,153 ms
コンパイル使用メモリ 87,880 KB
実行使用メモリ 36,960 KB
最終ジャッジ日時 2024-09-18 20:52:13
合計ジャッジ時間 5,764 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 43 ms
36,960 KB
testcase_01 AC 43 ms
36,844 KB
testcase_02 AC 44 ms
36,764 KB
testcase_03 AC 44 ms
36,604 KB
testcase_04 AC 46 ms
36,744 KB
testcase_05 AC 47 ms
36,844 KB
testcase_06 AC 45 ms
36,748 KB
testcase_07 AC 46 ms
36,820 KB
testcase_08 AC 46 ms
36,760 KB
testcase_09 AC 44 ms
36,828 KB
testcase_10 AC 44 ms
36,840 KB
testcase_11 AC 44 ms
36,784 KB
testcase_12 AC 44 ms
36,844 KB
testcase_13 AC 45 ms
36,804 KB
testcase_14 AC 45 ms
36,576 KB
testcase_15 AC 44 ms
36,736 KB
testcase_16 AC 43 ms
36,852 KB
testcase_17 AC 45 ms
36,928 KB
testcase_18 AC 48 ms
36,724 KB
testcase_19 AC 51 ms
36,788 KB
testcase_20 AC 48 ms
36,792 KB
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ソースコード

diff # 

package contest200131;
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 D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), P = ni();
		int mod = 1000000007;
		// a[n]^2 = p^2*a[n-1]^2 + a[n-2]^2 + 
//		 2p*a[n-1]*a[n-2]
		
		// a[n]*a[n-1] = (pa[n-1] + a[n-2]) * a[n-1]
		// 
		int P2 = (int)((long)P*P%mod);
		int[][] M = {
				{P, 1, 0, 0, 0, 0, 0},
				{1, 0, 0, 0, 0, 0, 0},
				{0, 0, P2, 1, 2*P, 0, 0},
				{0, 0, 1, 0, 0, 0, 0},
				{0, 0, P, 0, 1, 0, 0},
				{1, 0, 0, 0, 0, 1, 0},
				{0, 0, 1, 0, 0, 0, 1},
		};
		int[] to = pow(M, new int[]{1, 0, 1, 0, 0, 0, 0}, n-1);
		out.println(((long)to[5]*to[5] + to[6]) % mod * invl(2, mod) % mod);
	}
	
	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 final int mod = 1000000007;
	public static final long m2 = (long)mod*mod;
	public static final long BIG = 8L*m2;
	
	// A^e*v
	public static int[] pow(int[][] A, int[] v, long e)
	{
		for(int i = 0;i < v.length;i++){
			if(v[i] >= mod)v[i] %= mod;
		}
		int[][] MUL = A;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v);
			MUL = p2(MUL);
		}
		return v;
	}
	
	// int matrix*int vector
	public static int[] mul(int[][] A, int[] v)
	{
		int m = A.length;
		int n = v.length;
		int[] w = new int[m];
		for(int i = 0;i < m;i++){
			long sum = 0;
			for(int k = 0;k < n;k++){
				sum += (long)A[i][k] * v[k];
				if(sum >= BIG)sum -= BIG;
			}
			w[i] = (int)(sum % mod);
		}
		return w;
	}
	
	// int matrix^2 (be careful about negative value)
	public static int[][] p2(int[][] A)
	{
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++){
			long[] sum = new long[n];
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					sum[j] += (long)A[i][k] * A[k][j];
					if(sum[j] >= BIG)sum[j] -= BIG;
				}
			}
			for(int j = 0;j < n;j++){
				C[i][j] = (int)(sum[j] % mod);
			}
		}
		return C;
	}

	
	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 D().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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