結果

問題 No.534 フィボナッチフィボナッチ数
コンテスト
ユーザー tanzaku
提出日時 2017-03-18 12:43:51
言語 Java
(openjdk 23)
結果
AC  
実行時間 53 ms / 2,000 ms
コード長 3,464 bytes
コンパイル時間 3,800 ms
コンパイル使用メモリ 78,476 KB
実行使用メモリ 36,840 KB
最終ジャッジ日時 2024-07-04 19:07:37
合計ジャッジ時間 6,499 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
other AC * 42
権限があれば一括ダウンロードができます

ソースコード

diff # 

import java.io.*;
import java.util.*;


public class _p1481_Validate {
	public static void main(String[] args) throws IOException {
		new _p1481_Validate().solve();
	}
	
	long fib(long n, int mod) {
		long[][] mat = new long[][]{
			new long[]{1,1,},
			new long[]{1,0,},
		};
		mat = powmat(n, mod, mat);
		long[][] x = new long[][]{
			new long[]{1,},
			new long[]{0,},
		};
		long res = mulmat(mat, x, mod)[1][0];
		return res;
	}
	void test() {
		long a = 0, b = 1;
		for (long i = 1; ; i++) {
			long t = b;
			b += a;
			a = t;
			b %= mod;
			if (a == 0 && b == 1) {
				dump(i);
				break;
			}
		}
	}

	static int mod = (int)1e9+7;
	void solve() throws IOException {
		if (false) { test(); return; }
		
		try (final InputValidator in = new InputValidator(System.in)) {
//		try (final Scanner in = new Scanner(System.in)) {
			long n = in.nextLong(0, 1_000000000_000000000L);
			in.newLine();
			in.eof();
			System.out.println(fib(fib(n, 2000000016), mod));
		}
	}

	// long
	// a [n,v] * b [v,m] => c[n,m]
	static long[][] mulmat(long[][] a, long[][] b, int mod) {
		assert(a[0].length == b.length);
		
		final int n = a.length;
		final int v = b.length;
		final int m = b[0].length;
		
		long[][] res = new long[n][m];
		for(int i = 0; i < n; i++)
			for(int k = 0; k < v; k++) {
				final long aa = a[i][k];
				for(int j = 0; j < m; j++) {
					res[i][j] += aa * b[k][j] % mod;
					res[i][j] %= mod;
				}
			}
		
		return res;
	}
	
	static long[][] powmat(long r, int mod, long[][] mat) {
		final int n = mat.length;
		long[][] x = new long[n][n];
		for(int i = 0; i < n; i++) {
			x[i][i] = 1;
		}
		
		for(;r > 0; r >>>= 1) {
			if((r&1) == 1) {
				x = mulmat(x, mat, mod);
			}
			mat = mulmat(mat, mat, mod);
		}

		return x;
	}
	
	// for debug
	static void dump(Object... o) {
		System.err.println(Arrays.deepToString(o));
	}
	
	static class InputValidator implements Closeable {
		final InputStream in;
		
		final int NO_BUFFER = -2;
		int buffer;
		
		public InputValidator(final InputStream in) {
			this.in = in;
			buffer = NO_BUFFER;
		}
		
		int read() throws IOException {
			final int res = buffer == NO_BUFFER ? in.read() : buffer;
			buffer = NO_BUFFER;
			return res;
		}
		
		void unread(int ch) throws IOException {
			buffer = ch;
		}
		
		// [low, high]
		long nextLong(long low, long high) throws IOException {
			long val = 0;
			int ch = -1;
			boolean read = false;
			while (true) {
				ch = read();
				if (!Character.isDigit(ch)) break;
				read = true;
				val = val * 10 + ch - '0';
				check(val <= high);
			}
			check(read);
			check(ch >= 0);
			check(val >= low);
			unread(ch);
			return val;
		}
		int nextInt(int low, int high) throws IOException { return (int)nextLong(low, high); }
		int[] nextInts(int n, int low, int high) throws IOException {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt(low, high);
				if (i + 1 != n) space();
			}
			newLineOrEOF();
			return res;
		}
		
		void space() throws IOException { int ch = read(); check(ch == ' '); }
		void newLine() throws IOException {
			int ch = read();
			if (ch == '\r') ch = read();
			check(ch == '\n');
		}
		void newLineOrEOF() throws IOException { int ch = read(); check(ch == '\r' || ch == '\n' || ch < 0); }
		void eof() throws IOException { int ch = read(); check(ch < 0); }
		void check(boolean b) { if (!b) throw new RuntimeException(); }

		@Override
		public void close() throws IOException {
		}
	}
}
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