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 |
提出日時 | 2015-04-28 14:17:31 |
言語 | Java21 (openjdk 21) |
結果 |
AC
|
実行時間 | 141 ms / 5,000 ms |
コード長 | 7,504 bytes |
コンパイル時間 | 2,922 ms |
コンパイル使用メモリ | 83,200 KB |
実行使用メモリ | 59,720 KB |
最終ジャッジ日時 | 2023-09-18 14:04:09 |
合計ジャッジ時間 | 8,125 ms |
ジャッジサーバーID (参考情報) |
judge11 / judge14 |
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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 | 71 ms
51,068 KB |
testcase_01 | AC | 74 ms
50,740 KB |
testcase_02 | AC | 140 ms
53,816 KB |
testcase_03 | AC | 100 ms
53,652 KB |
testcase_04 | AC | 114 ms
54,152 KB |
testcase_05 | AC | 107 ms
54,120 KB |
testcase_06 | AC | 118 ms
52,120 KB |
testcase_07 | AC | 124 ms
53,840 KB |
testcase_08 | AC | 88 ms
52,384 KB |
testcase_09 | AC | 120 ms
53,812 KB |
testcase_10 | AC | 103 ms
53,744 KB |
testcase_11 | AC | 103 ms
54,004 KB |
testcase_12 | AC | 108 ms
53,896 KB |
testcase_13 | AC | 102 ms
53,780 KB |
testcase_14 | AC | 90 ms
52,648 KB |
testcase_15 | AC | 131 ms
53,840 KB |
testcase_16 | AC | 125 ms
54,060 KB |
testcase_17 | AC | 97 ms
53,752 KB |
testcase_18 | AC | 128 ms
53,824 KB |
testcase_19 | AC | 141 ms
53,848 KB |
testcase_20 | AC | 112 ms
59,644 KB |
testcase_21 | AC | 115 ms
59,592 KB |
testcase_22 | AC | 110 ms
59,720 KB |
testcase_23 | AC | 85 ms
52,420 KB |
testcase_24 | AC | 102 ms
57,544 KB |
testcase_25 | AC | 101 ms
57,680 KB |
testcase_26 | AC | 104 ms
57,812 KB |
testcase_27 | AC | 100 ms
57,664 KB |
testcase_28 | AC | 91 ms
53,392 KB |
testcase_29 | AC | 111 ms
59,652 KB |
testcase_30 | AC | 135 ms
54,300 KB |
testcase_31 | AC | 73 ms
51,064 KB |
testcase_32 | AC | 107 ms
53,992 KB |
testcase_33 | AC | 117 ms
54,036 KB |
testcase_34 | AC | 112 ms
54,100 KB |
testcase_35 | AC | 105 ms
54,004 KB |
testcase_36 | AC | 129 ms
53,988 KB |
testcase_37 | AC | 84 ms
52,612 KB |
testcase_38 | AC | 138 ms
54,168 KB |
testcase_39 | AC | 107 ms
53,824 KB |
ソースコード
package no194b; 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 = MatrixMod.zero(n+1,n+1); for(int i=0;i<n-1;i++) { m.e[i][i+1] = 1; } for(int i=0;i<n;i++) { m.e[n-1][i] = 1; } for(int i=0;i<=n;i++) { m.e[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; MatrixMod x = MatrixMod.vector(v); MatrixMod ans = m.pow(k-n).multiply(x); System.out.println(ans.e[n-1][0] + " " + ans.e[n][0]); } } class MatrixMod { public static long MOD = 1000000007; long[][] e; int n,m; public MatrixMod(long[][] e) { this.e = e; this.n = e.length; this.m = e[0].length; } public static MatrixMod identity(int n) { long[][] e = new long[n][n]; for(int i=0;i<n;i++) e[i][i] = 1; return new MatrixMod(e); } public static MatrixMod zero(int n,int m) { return new MatrixMod(new long[n][m]); } public static MatrixMod vector(long[] v) { long[][] e = new long[v.length][1]; for(int i=0;i<v.length;i++) e[i][0] = v[i]; return new MatrixMod(e); } public MatrixMod add(MatrixMod b) { long[][] c = new long[n][m]; for(int i=0;i<n;i++) { for(int j=0;j<m;j++) { c[i][j] = e[i][j] + b.e[i][j]; if (c[i][j] >= MOD) { c[i][j] -= MOD; } } } return new MatrixMod(c); } public MatrixMod multiply(long k) { k = (k%MOD+MOD)%MOD; long[][] c = new long[n][m]; for(int i=0;i<n;i++) { for(int j=0;j<m;j++) { c[i][j] = c[i][j] * k % MOD; } } return new MatrixMod(c); } public MatrixMod multiply(MatrixMod b) { long[][] c = new long[n][b.m]; for(int i=0;i<n;i++) { for(int j=0;j<b.m;j++) { for(int k=0;k<m;k++) { c[i][j] = (c[i][j] + e[i][k] * b.e[k][j]) % MOD; } } } return new MatrixMod(c); } public MatrixMod pow(long exp) { MatrixMod ret = identity(n); MatrixMod x = this; while(exp > 0) { if ((exp & 1) != 0) { ret = ret.multiply(x); } x = x.multiply(x); exp >>>= 1; } return ret; } public String toString() { return Arrays.deepToString(e); } } 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) {}} }