#90316 (Java) No.194 フィボナッチ数列の理解(1)

• 問題: No.194 フィボナッチ数列の理解(1)
• ユーザー: 37zigen
• 提出日時: 2016-05-05 02:14:37
• 言語: Java (openjdk 23)
• 結果: AC
• 実行時間: 171 ms / 5,000 ms
• コード長: 5,866 bytes
• コンパイル時間: 2,825 ms
• コンパイル使用メモリ: 81,152 KB
• 実行使用メモリ: 55,780 KB
• 最終ジャッジ日時: 2024-10-05 09:20:26
• 合計ジャッジ時間: 7,822 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 37

ソースコード

import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    long MOD = 1_000_000_000 + 7;

    class Node {
        long value;
        Node next;

        Node(long value, Node next) {
            this.value = value;
            this.next = next;
        }
    }

    void test1(int n, long k, long[] a) {
        Node first = null;
        Node last = null;

        Node p = null;
        long sum = 0;
        for (int i = 0; i < n; i++) {
            Node tmp = new Node(a[i], null);
            if (first == null) {
                first = tmp;
                p = tmp;
            } else {
                p.next = tmp;
                p = tmp;
            }
            sum += a[i];
            sum %= MOD;
        }
        last = p;

        long tmp = sum;
        for (int i = n; i < k; i++) {
            Node node = new Node(tmp, null);

            sum += tmp;

            tmp -= first.value;
            first = first.next;
            last.next = node;
            last = last.next;
            tmp += last.value;

            tmp %= MOD;
            tmp += MOD;
            tmp %= MOD;
            sum %= MOD;
            sum += MOD;
            sum %= MOD;
        }
        System.out.println(last.value + " " + sum);
    }

    void test2(int n, long k, long[] a) {
        long[][] mat = new long[n + 1][n + 1];

        Arrays.fill(mat[0], 1);
        Arrays.fill(mat[1], 1);
        mat[1][0] = 0;
        for (int i = 1; i < n; i++) {
            mat[i + 1][i] = 1;
        }

        long[][] tmp = power(mat, k - n);
        long[] x = new long[n + 1];
        for (int i = 0; i < n; i++) {
            x[0] += a[i];
            x[i + 1] = a[n - i - 1];
        }
        long ans1 = 0, ans2 = 0;
        for (int i = 0; i < n + 1; i++) {
            ans2 += tmp[0][i] * x[i];
            ans1 += tmp[1][i] * x[i];
            ans1 %= MOD;
            ans2 %= MOD;
        }

        System.out.println(ans1 + " " + ans2);
    }

    long[][] power(long[][] a, long k) {
        int n = a.length;
        long[][] res = new long[n][n];
        long[][] tmp = new long[n][n];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                tmp[i][j] = a[i][j];
            }
            res[i][i] = 1;
        }

        while (0 < k) {
            if (k % 2 == 1) {
                res = mul(res, tmp);
            }
            tmp = mul(tmp, tmp);
            k >>= 1;
        }

        return res;
    }

    long[][] mul(long[][] a, long[][] b) {
        int n = a.length;
        long[][] res = new long[n][n];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                res[i][j] = 0;
                for (int k = 0; k < n; k++) {
                    res[i][j] += a[i][k] * b[k][j];
                    res[i][j] %= MOD;
                }
            }
        }

        return res;
    }

    void run() {
        MyScanner sc = new MyScanner();

        int n = sc.nextInt();
        long k = sc.nextLong();
        long[] a = sc.nextLongArray(n);

        if (n <= 10000 && k <= 1000000) {
            test1(n, k, a);
        } else {
            test2(n, k, a);
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }

    public void mapDebug(int[][] a) {
        System.out.println("--------map display---------");
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < a[i].length; j++) {
                System.out.printf("%3d ", a[i][j]);
            }
            System.out.println();
        }
        System.out.println("----------------------------" + '\n');
    }

    class MyScanner {
        int read() {
            try {
                return System.in.read();
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();
            return array;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();
            return array;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();
            return array;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}