Editorial for ICPC NEERC 2010 B - Binary Operation

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Write a procedure to compute for single digits: $\displaystyle a_0 \times \underbrace{a \times a \times \dots \times a}_{c\text{ times}}$ $a_{0} \times \underset{c times}{\underset{⏟}{a \times a \times \dots \times a}}$
- Repeat multiplies until it loops (after at most $10$ $10$ muls)
- Use offset and period length to compute the result
Write a procedure to compute for single digits: $\displaystyle a_0 \times \underbrace{a' \times (a+1)' \times \dots \times b'}_{d\text{ times}}$ $a_{0} \times \underset{d times}{\underset{⏟}{a^{'} \times (a + 1)^{'} \times \dots \times b^{'}}}$ where $+1$ $+ 1$ wraps to $0$ $0$ ; and $a'$ $a^{'}$ means " $a \times a \times \dots \times a$ $a \times a \times \dots \times a$ " $c$ $c$ times (as above)
- Compute loop similarly (can be as long as $100$ $100$ )
Compute the result digit by digit using two of the above procedures
- For a digit $i$ $i$ , round the number $a$ $a$ up and $b$ $b$ down to the nearest multiple of $10^i$ $10^{i}$
- Represent the number range $[a, b]$ $[a, b]$ as:
  - $X \dots XXaXX \dots X$ $X \dots X X a X X \dots X$
  - $X \dots XX(a+1)00 \dots 0$ $X \dots X X (a + 1) 00 \dots 0$
  - $X \dots XXb00 \dots 0$ $X \dots X X b 00 \dots 0$
  - $X \dots XXbXX \dots X$ $X \dots X X b X X \dots X$

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