結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー uwiuwi
提出日時 2015-04-26 22:21:33
言語 Java21
(openjdk 21)
結果
AC  
実行時間 118 ms / 5,000 ms
コード長 4,707 bytes
コンパイル時間 3,948 ms
コンパイル使用メモリ 81,828 KB
実行使用メモリ 59,460 KB
最終ジャッジ日時 2024-07-05 02:57:36
合計ジャッジ時間 9,089 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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 87 ms
51,480 KB
testcase_01 AC 77 ms
51,456 KB
testcase_02 AC 116 ms
53,484 KB
testcase_03 AC 85 ms
51,332 KB
testcase_04 AC 110 ms
53,604 KB
testcase_05 AC 108 ms
53,460 KB
testcase_06 AC 109 ms
53,368 KB
testcase_07 AC 113 ms
53,420 KB
testcase_08 AC 79 ms
51,420 KB
testcase_09 AC 109 ms
53,272 KB
testcase_10 AC 92 ms
52,788 KB
testcase_11 AC 96 ms
52,972 KB
testcase_12 AC 105 ms
53,320 KB
testcase_13 AC 92 ms
52,492 KB
testcase_14 AC 81 ms
51,208 KB
testcase_15 AC 115 ms
53,456 KB
testcase_16 AC 111 ms
53,540 KB
testcase_17 AC 98 ms
52,896 KB
testcase_18 AC 115 ms
53,512 KB
testcase_19 AC 118 ms
53,572 KB
testcase_20 AC 79 ms
51,116 KB
testcase_21 AC 114 ms
59,460 KB
testcase_22 AC 75 ms
51,172 KB
testcase_23 AC 90 ms
52,824 KB
testcase_24 AC 111 ms
57,500 KB
testcase_25 AC 108 ms
55,724 KB
testcase_26 AC 109 ms
55,568 KB
testcase_27 AC 106 ms
57,040 KB
testcase_28 AC 98 ms
52,852 KB
testcase_29 AC 112 ms
59,408 KB
testcase_30 AC 117 ms
53,464 KB
testcase_31 AC 76 ms
51,132 KB
testcase_32 AC 109 ms
53,404 KB
testcase_33 AC 112 ms
53,568 KB
testcase_34 AC 108 ms
53,560 KB
testcase_35 AC 109 ms
53,352 KB
testcase_36 AC 109 ms
53,580 KB
testcase_37 AC 85 ms
51,480 KB
testcase_38 AC 115 ms
53,580 KB
testcase_39 AC 106 ms
53,400 KB
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ソースコード

diff # 

package contest;

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

public class Q381 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		long K = nl();
		int[] a = na(n);
		int mod = 1000000007;
		if(n > 30){
			long[] cum = new long[(int)K+2];
			for(int i = 1;i <= n;i++){
				cum[i] = cum[i-1] + a[i-1];
			}
			long w = -1;
			for(int i = n+1;i <= K;i++){
				long v = cum[i-1] - cum[i-n-1];
				if(v < 0)v += mod;
				w = v;
				cum[i] = cum[i-1] + v;
				if(cum[i] >= mod)cum[i] -= mod;
			}
			out.println(w + " " + cum[(int)K]);
		}else{
			int[][] M = new int[n+1][n+1];
			for(int i = 0;i < n;i++)M[0][i] = 1;
			for(int i = 1;i < n;i++)M[i][i-1] = 1;
			for(int i = 0;i < n+1;i++)M[n][i] = 1;
			int[] v = new int[n+1];
			for(int i = 0;i < n;i++){
				v[n-1-i] = a[i];
				v[n] += a[i];
			}
			v = pow(M, v, K-n);
			out.println(v[0] + " " + v[n]);
		}
	}
	
	///////// begin
	public static final int mod = 1000000007;
	public static final long m2 = (long)mod*mod;
	public static final long BIG = 8L*m2;
	
	// A^e*v
	public static int[] pow(int[][] A, int[] v, long e)
	{
		for(int i = 0;i < v.length;i++){
			if(v[i] >= mod)v[i] %= mod;
		}
		int[][] MUL = A;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v);
			MUL = p2(MUL);
		}
		return v;
	}
	
	// int matrix*int vector
	public static int[] mul(int[][] A, int[] v)
	{
		int m = A.length;
		int n = v.length;
		int[] w = new int[m];
		for(int i = 0;i < m;i++){
			long sum = 0;
			for(int k = 0;k < n;k++){
				sum += (long)A[i][k] * v[k];
				if(sum >= BIG)sum -= BIG;
			}
			w[i] = (int)(sum % mod);
		}
		return w;
	}
	
	// int matrix^2 (be careful about negative value)
	public static int[][] p2(int[][] A)
	{
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++){
			long[] sum = new long[n];
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					sum[j] += (long)A[i][k] * A[k][j];
					if(sum[j] >= BIG)sum[j] -= BIG;
				}
			}
			for(int j = 0;j < n;j++){
				C[i][j] = (int)(sum[j] % mod);
			}
		}
		return C;
	}
	
	//////////// end

	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new Q381().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}
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