結果
| 問題 |
No.194 フィボナッチ数列の理解(1)
|
| コンテスト | |
| ユーザー |
 ぴろず
|
| 提出日時 | 2015-04-26 22:34:29 |
| 言語 | Java (openjdk 23) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 8,095 bytes |
| コンパイル時間 | 2,815 ms |
| コンパイル使用メモリ | 91,828 KB |
| 実行使用メモリ | 743,576 KB |
| 最終ジャッジ日時 | 2024-07-05 03:03:43 |
| 合計ジャッジ時間 | 15,977 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 19 TLE * 1 MLE * 5 -- * 12 |
ソースコード
package no194;
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 (false && 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) {}}
}