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Codeforces Round #373 (Div. 1) C. Sasha and Array

競技プログラミング Codeforces

問題

http://codeforces.com/contest/718/problem/C

下記の二種類のクエリを処理せよ。

  1. 数列 \{a_{i}\} のlからrまでにvずつ足せ。
  2. 数列 \{a_{i}\} のlからrまでの各a_{i} についてfib(a_{i}) を求め、その和を出力しろ。

解法

StarrySkyTree の各ノードに行列をもたせる。

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

/*
                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
            pass System Test!
*/

public class E {
  private static class Task {

    final int MOD = (int) (1e9 + 7);
    Matrix base = new Matrix(new long[]{1, 1, 1, 0});
    Matrix one = new Matrix(new long[]{1, 0, 0, 1});
    Matrix zero = new Matrix(new long[4]);

    void solve(FastScanner in, PrintWriter out) {
      int N = in.nextInt();
      int Q = in.nextInt();
      int[] a = in.nextIntArray(N);

      Matrix[] ms = new Matrix[N];
      for (int i = 0; i < N; i++) {
        ms[i] = powMatrix(base, a[i] - 1);
      }

      StarrySkyTreeMatrix seg = new StarrySkyTreeMatrix(ms);

      for (int i = 0; i < Q; i++) {
        int t = in.nextInt();
        if (t == 1) {
          int l = in.nextInt() - 1;
          int r = in.nextInt() - 1;
          int v = in.nextInt();
          seg.add(l, r + 1, powMatrix(base, v));
        } else {
          int l = in.nextInt() - 1;
          int r = in.nextInt() - 1;
          out.println(seg.getSum(l, r + 1).mat[0]);
        }
      }
    }

    class StarrySkyTreeMatrix {
      final int N = 1 << 17;
      Matrix[] seg, segAdd;
      StarrySkyTreeMatrix(Matrix[] ms) {
        seg = new Matrix[N * 2];
        segAdd = new Matrix[N * 2];
        for (int i = 0; i < N * 2; i++) {
          seg[i] = zero;
          segAdd[i] = one;
        }
        for (int i = 0; i < ms.length; i++) {
          seg[i + N] = ms[i];
        }
        for (int i = N - 1; i > 0; i--) {
          seg[i] = addMatrix(seg[i * 2], seg[i * 2 + 1]);
        }
      }

      void add(int a, int b, Matrix v) {
        add(a, b, v, 0, N, 1);
      }

      void add(int a, int b, Matrix v, int l, int r, int k) {
        if (r <= a || b <= l) return;
        if (a <= l && r <= b) {
          segAdd[k] = productMatrix(segAdd[k], v);
          return;
        }
        add(a, b, v, l, (l + r) / 2, k * 2);
        add(a, b, v, (l + r) / 2, r, k * 2 + 1);
        seg[k] = addMatrix(
          productMatrix(seg[k * 2], segAdd[k * 2]),
          productMatrix(seg[k * 2 + 1], segAdd[k * 2 + 1])
        );
      }

      Matrix getSum(int a, int b) {
        return getSum(a, b, 0, N, 1);
      }

      Matrix getSum(int a, int b, int l, int r, int k) {
        if (b <= l || r <= a) return zero;
        if (a <= l && r <= b) return productMatrix(seg[k], segAdd[k]);
        Matrix x = getSum(a, b, l, (l + r) / 2, k * 2);
        Matrix y = getSum(a, b, (l + r) / 2, r, k * 2 + 1);
        return productMatrix(segAdd[k], addMatrix(x, y));
      }
    }

    class Matrix {
      long[] mat;
      Matrix(long[] mat) {
        this.mat = mat;
      }
    }

    Matrix addMatrix(Matrix a, Matrix b) {
      Matrix c = new Matrix(new long[4]);
      for (int i = 0; i < 4; i++) {
        c.mat[i] = a.mat[i] + b.mat[i];
        if (c.mat[i] > MOD) c.mat[i] -= MOD;
      }
      return c;
    }

    Matrix productMatrix(Matrix a, Matrix b) {
      Matrix c = new Matrix(new long[4]);
      c.mat[0] = (a.mat[0] * b.mat[0] + a.mat[1] * b.mat[2]) % MOD;
      c.mat[1] = (a.mat[0] * b.mat[1] + a.mat[1] * b.mat[3]) % MOD;
      c.mat[2] = (a.mat[2] * b.mat[0] + a.mat[3] * b.mat[2]) % MOD;
      c.mat[3] = (a.mat[2] * b.mat[1] + a.mat[3] * b.mat[3]) % MOD;
      return c;
    }

    Matrix powMatrix(Matrix a, long p) {
      Matrix ret = new Matrix(new long[]{1, 0, 0, 1});
      while (p > 0) {
        if (p % 2 == 1) ret = productMatrix(ret, a);
        a = productMatrix(a, a);
        p /= 2;
      }
      return ret;
    }

  }

  /**
   * ここから下はテンプレートです。
   */
  public static void main(String[] args) {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 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 void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      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();
    }

    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();
      }
    }

    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;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

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

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

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

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) array[i] = next().toCharArray();
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}