結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー ぴろずぴろず
提出日時 2015-04-28 14:17:31
言語 Java
(openjdk 23)
結果
AC  
実行時間 151 ms / 5,000 ms
コード長 7,504 bytes
コンパイル時間 2,642 ms
コンパイル使用メモリ 89,056 KB
実行使用メモリ 47,920 KB
最終ジャッジ日時 2024-07-05 05:01:19
合計ジャッジ時間 8,801 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 37
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 # 

package no194b;

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 (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 = MatrixMod.zero(n+1,n+1);
        for(int i=0;i<n-1;i++) {
            m.e[i][i+1] = 1;
        }
        for(int i=0;i<n;i++) {
            m.e[n-1][i] = 1;
        }
        for(int i=0;i<=n;i++) {
            m.e[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;

        MatrixMod x = MatrixMod.vector(v);
        MatrixMod ans = m.pow(k-n).multiply(x);

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

}
class MatrixMod {
	public static long MOD = 1000000007;
	long[][] e;
	int n,m;
	public MatrixMod(long[][] e) {
		this.e = e;
		this.n = e.length;
		this.m = e[0].length;
	}
	public static MatrixMod identity(int n) {
		long[][] e = new long[n][n];
		for(int i=0;i<n;i++) e[i][i] = 1;
		return new MatrixMod(e);
	}
	public static MatrixMod zero(int n,int m) {
		return new MatrixMod(new long[n][m]);
	}
	public static MatrixMod vector(long[] v) {
		long[][] e = new long[v.length][1];
		for(int i=0;i<v.length;i++) e[i][0] = v[i];
		return new MatrixMod(e);
	}
	public MatrixMod add(MatrixMod b) {
		long[][] c = new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				c[i][j] = e[i][j] + b.e[i][j];
				if (c[i][j] >= MOD) {
					c[i][j] -= MOD;
				}
			}
		}
		return new MatrixMod(c);
	}
	public MatrixMod multiply(long k) {
		k = (k%MOD+MOD)%MOD;
		long[][] c = new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				c[i][j] = c[i][j] * k % MOD;
			}
		}
		return new MatrixMod(c);
	}
	public MatrixMod multiply(MatrixMod b) {
		long[][] c = new long[n][b.m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<b.m;j++) {
				for(int k=0;k<m;k++) {
					c[i][j] = (c[i][j] + e[i][k] * b.e[k][j]) % MOD;
				}
			}
		}
		return new MatrixMod(c);
	}
	public MatrixMod pow(long exp) {
		MatrixMod ret = identity(n);
		MatrixMod x = this;
		while(exp > 0) {
			if ((exp & 1) != 0) {
				ret = ret.multiply(x);
			}
			x = x.multiply(x);
			exp >>>= 1;
		}
		return ret;
	}
	public String toString() {
		return Arrays.deepToString(e);
	}
}
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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