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 2015-04-26 22:46:28
言語 Java21
(openjdk 21)
結果
AC  
実行時間 141 ms / 5,000 ms
コード長 9,955 bytes
コンパイル時間 4,291 ms
コンパイル使用メモリ 80,068 KB
実行使用メモリ 59,772 KB
最終ジャッジ日時 2023-09-18 12:17:37
合計ジャッジ時間 10,270 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge13
このコードへのチャレンジ（β）

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 80 ms
52,628 KB
testcase_01 AC 71 ms
50,560 KB
testcase_02 AC 136 ms
53,744 KB
testcase_03 AC 106 ms
53,804 KB
testcase_04 AC 125 ms
53,980 KB
testcase_05 AC 115 ms
54,040 KB
testcase_06 AC 120 ms
53,744 KB
testcase_07 AC 131 ms
54,264 KB
testcase_08 AC 90 ms
52,796 KB
testcase_09 AC 126 ms
54,104 KB
testcase_10 AC 106 ms
53,544 KB
testcase_11 AC 107 ms
53,888 KB
testcase_12 AC 112 ms
53,716 KB
testcase_13 AC 105 ms
53,564 KB
testcase_14 AC 85 ms
52,260 KB
testcase_15 AC 141 ms
53,980 KB
testcase_16 AC 129 ms
53,988 KB
testcase_17 AC 109 ms
53,788 KB
testcase_18 AC 130 ms
53,880 KB
testcase_19 AC 135 ms
53,988 KB
testcase_20 AC 112 ms
59,560 KB
testcase_21 AC 117 ms
59,664 KB
testcase_22 AC 110 ms
59,772 KB
testcase_23 AC 87 ms
52,452 KB
testcase_24 AC 106 ms
57,404 KB
testcase_25 AC 104 ms
57,588 KB
testcase_26 AC 106 ms
57,832 KB
testcase_27 AC 102 ms
57,468 KB
testcase_28 AC 95 ms
55,392 KB
testcase_29 AC 113 ms
59,616 KB
testcase_30 AC 135 ms
53,992 KB
testcase_31 AC 77 ms
50,648 KB
testcase_32 AC 112 ms
53,460 KB
testcase_33 AC 125 ms
53,904 KB
testcase_34 AC 113 ms
53,560 KB
testcase_35 AC 111 ms
53,436 KB
testcase_36 AC 133 ms
54,148 KB
testcase_37 AC 90 ms
52,660 KB
testcase_38 AC 135 ms
53,892 KB
testcase_39 AC 113 ms
53,488 KB
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 no194a;

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 = 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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