結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー fujisufujisu
提出日時 2015-04-27 05:11:36
言語 Java21
(openjdk 21)
結果
AC  
実行時間 189 ms / 5,000 ms
コード長 4,381 bytes
コンパイル時間 2,376 ms
コンパイル使用メモリ 88,904 KB
実行使用メモリ 44,488 KB
最終ジャッジ日時 2024-07-05 03:30:58
合計ジャッジ時間 8,683 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 81 ms
38,108 KB
testcase_01 AC 80 ms
37,840 KB
testcase_02 AC 149 ms
40,936 KB
testcase_03 AC 98 ms
39,668 KB
testcase_04 AC 122 ms
40,608 KB
testcase_05 AC 120 ms
40,516 KB
testcase_06 AC 120 ms
40,436 KB
testcase_07 AC 135 ms
40,588 KB
testcase_08 AC 96 ms
39,584 KB
testcase_09 AC 133 ms
40,372 KB
testcase_10 AC 114 ms
40,440 KB
testcase_11 AC 115 ms
40,480 KB
testcase_12 AC 118 ms
40,464 KB
testcase_13 AC 114 ms
39,804 KB
testcase_14 AC 100 ms
39,268 KB
testcase_15 AC 144 ms
40,864 KB
testcase_16 AC 137 ms
40,592 KB
testcase_17 AC 114 ms
40,088 KB
testcase_18 AC 140 ms
40,608 KB
testcase_19 AC 145 ms
40,536 KB
testcase_20 AC 150 ms
43,568 KB
testcase_21 AC 189 ms
44,476 KB
testcase_22 AC 150 ms
43,724 KB
testcase_23 AC 136 ms
42,352 KB
testcase_24 AC 165 ms
44,376 KB
testcase_25 AC 157 ms
44,432 KB
testcase_26 AC 162 ms
44,488 KB
testcase_27 AC 131 ms
43,944 KB
testcase_28 AC 148 ms
43,736 KB
testcase_29 AC 155 ms
43,876 KB
testcase_30 AC 143 ms
40,736 KB
testcase_31 AC 77 ms
39,720 KB
testcase_32 AC 115 ms
40,140 KB
testcase_33 AC 129 ms
40,144 KB
testcase_34 AC 115 ms
40,208 KB
testcase_35 AC 112 ms
40,176 KB
testcase_36 AC 138 ms
40,600 KB
testcase_37 AC 105 ms
39,396 KB
testcase_38 AC 143 ms
40,672 KB
testcase_39 AC 117 ms
40,216 KB
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ソースコード

diff # 

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();
		}
	}
}
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