#22442 (Java21) No.194 フィボナッチ数列の理解(1)

提出ソース

結果

問題	No.194 フィボナッチ数列の理解(1)
ユーザー	ぴろず
提出日時	2015-04-26 22:34:29
言語	Java21 (openjdk 21)
結果	MLE
実行時間	-
コード長	8,095 bytes
コンパイル時間	2,815 ms
コンパイル使用メモリ	91,828 KB
実行使用メモリ	743,576 KB
最終ジャッジ日時	2024-07-05 03:03:43
合計ジャッジ時間	15,977 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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	77 ms 52,744 KB
testcase_01	AC	87 ms 52,328 KB
testcase_02	AC	142 ms 53,504 KB
testcase_03	AC	101 ms 52,956 KB
testcase_04	AC	126 ms 53,328 KB
testcase_05	AC	121 ms 53,484 KB
testcase_06	AC	123 ms 53,300 KB
testcase_07	AC	140 ms 53,416 KB
testcase_08	AC	98 ms 52,736 KB
testcase_09	AC	126 ms 53,316 KB
testcase_10	AC	114 ms 53,472 KB
testcase_11	AC	120 ms 53,320 KB
testcase_12	AC	125 ms 53,420 KB
testcase_13	AC	112 ms 53,272 KB
testcase_14	AC	93 ms 52,768 KB
testcase_15	AC	151 ms 53,416 KB
testcase_16	AC	142 ms 53,700 KB
testcase_17	AC	120 ms 53,264 KB
testcase_18	AC	141 ms 53,520 KB
testcase_19	AC	150 ms 53,420 KB
testcase_20	AC	93 ms 52,672 KB
testcase_21	MLE	-
testcase_22	AC	82 ms 51,232 KB
testcase_23	MLE	-
testcase_24	MLE	-
testcase_25	MLE	-
testcase_26	MLE	-
testcase_27	TLE	-
testcase_28	--	-
testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
testcase_33	--	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-
testcase_37	--	-
testcase_38	--	-
testcase_39	--	-

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ソースコード

raw source code

package no194;

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

public class Main {
	static IO io = new IO();
	public static long MOD = 1000000007;
	public static void main(String[] args) {
		int n = io.nextInt();
		long k = io.nextLong();
		int[] a = new int[n+1];
		for(int i=1;i<=n;i++) {
			a[i] = io.nextInt();
		}
		if (false && k <= 1000000) {
			solve1(n,(int) k,a);
		}else{
			solve2(n,k,a);
		}
	}
	public static void solve1(int n,int k,int[] a) {
		long[] f = new long[k+1];
		long sum = 0;
		long psum = 0;
		for(int i=1;i<=n;i++) {
			f[i] = a[i];
			psum += a[i];
			sum += a[i];
		}
		for(int i=n+1;i<=k;i++) {
			f[i] = psum;
			sum = (sum + f[i]) % MOD;
			psum = (psum - f[i-n] + f[i] + MOD) % MOD;
		}
		System.out.println(f[k] + " " + sum);
	}
	public static void solve2(int n,long k,int[] a) {
		MatrixMod m = new MatrixMod(n+1,n+1);
		for(int i=0;i<n-1;i++) {
			m.a[i][i+1] = 1;
		}
		for(int i=0;i<n;i++) {
			m.a[n-1][i] = 1;
		}
		for(int i=0;i<=n;i++) {
			m.a[n][i] = 1;
		}
		long[] v = new long[n+1];
		long sum = 0;
		for(int i=0;i<n;i++) {
			v[i] = a[i+1];
			sum += v[i];
		}
		v[n] = sum;

//		System.out.println(m);

		MatrixMod x = new MatrixMod(v);
		MatrixMod ans = m.powThis(k-n).multiplyRightToThis(x);

//		System.out.println(x);
		System.out.println(ans.a[n-1][0] + " " + ans.a[n][0]);
	}

}
class MatrixMod {
	public static final long MOD = 1000000007;
	public long[][] a;
	public MatrixMod(long[][] a) {
		if (a.length == 0 || a[0].length == 0) {
			throw new RuntimeException("Unexpected size matrix");
		}
		this.a = a;
	}
	public MatrixMod(long[] vector) {
		this(new long[vector.length][1]);
		for(int i=0;i<vector.length;i++) {
			a[i][0] = vector[i];
		}
	}
	public MatrixMod(int rows,int columns) {
		this(new long[rows][columns]);
	}
	public MatrixMod(int idMatrixSize) {
		this(new long[idMatrixSize][idMatrixSize]);
		for(int i=0;i<idMatrixSize;i++) {
			a[i][i] = 1;
		}
	}
	public MatrixMod set(MatrixMod A) {
		this.a = A.a;
		return this;
	}
	public int rows() {
		return a.length;
	}
	public int columns() {
		return a[0].length;
	}
	public static MatrixMod add(MatrixMod A,MatrixMod B) {
		if (A.rows() != B.rows() || A.columns() != B.columns()) {
			throw new RuntimeException("Undefined addition");
		}
		MatrixMod C = new MatrixMod(A.rows(),A.columns());
		for(int i=0;i<A.rows();i++) {
			for(int j=0;j<A.columns();j++) {
				C.a[i][j] = (A.a[i][j] + B.a[i][j]) % MOD;
			}
		}
		return C;
	}
	public static MatrixMod multiply(MatrixMod A,long c) {
		for(int i=0;i<A.rows();i++) {
			for(int j=0;j<A.columns();j++) {
				A.a[i][j] = (A.a[i][j] * c) % MOD;
			}
		}
		return A;
	}
	public static MatrixMod multiply(MatrixMod A,MatrixMod B) {
		if (A.columns() != B.rows()) {
			throw new RuntimeException("Undefined multiplicaiton");
		}
		MatrixMod C = new MatrixMod(A.rows(),B.columns());
		for(int i=0;i<A.rows();i++) {
			for(int j=0;j<B.columns();j++) {
				for(int k=0;k<A.columns();k++) {
					C.a[i][j] = (C.a[i][j] + A.a[i][k] * B.a[k][j]) % MOD;
				}
			}
		}
		return C;
	}
	public static MatrixMod pow(MatrixMod A,long n) {
		if (A.rows() != A.columns()) {
			throw new RuntimeException("Undefined multiplicaiton");
		}
		MatrixMod M = A.clone();
		MatrixMod X = new MatrixMod(A.rows());
		while(n>0) {
			if (n%2==1) {
				X.multiplyRightToThis(M);
			}
			n/=2;
			if (n>0) {
				M.multiplyRightToThis(M);
			}
		}
		return X;
	}
	public MatrixMod addToThis(MatrixMod B) {
		set(add(this,B));
		return this;
	}
	public MatrixMod multiplyThis(long c) {
		set(multiply(this, c));
		return this;
	}
	public MatrixMod multiplyRightToThis(MatrixMod B) {
		set(multiply(this,B));
		return this;
	}
	public MatrixMod powThis(long n) {
		set(pow(this, n));
		return this;
	}
	public MatrixMod clone() {
		MatrixMod A = new MatrixMod(rows(), columns());
		for(int i=0;i<rows();i++) {
			for(int j=0;j<columns();j++) {
				A.a[i][j] = a[i][j];
			}
		}
		return A;
	}
	public int hashCode() {
		int hashcode = 0;
		for(int i=0;i<rows();i++) {
			hashcode ^= Arrays.hashCode(a[i]);
		}
		return hashcode;
	}
	public boolean equals(Object o) {
		if (!(o instanceof MatrixMod)) {
			return false;
		}
		MatrixMod A = (MatrixMod) o;
		if (this.rows() != A.rows() || this.columns() != A.columns()) {
			return false;
		}
		for(int i=0;i<A.rows();i++) {
			if (!Arrays.equals(a[i], A.a[i])) {
				return false;
			}
		}
		return true;
	}
	public String toString() {
		return Arrays.deepToString(a);
	}
}

class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	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;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(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 char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(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 char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}

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結果

テストケース

ソースコード