sahal's blog

Extended Euclid!
By sahal, history, 5 years ago, In English

can anyone help me? How to solve this problem in Extended Euclid algorithm??? https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1574

  • Vote: I like it
  • 0
  • Vote: I do not like it

»
5 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Why Extended Euclid algorithm? We can apply simple logic. Let's represent the number $$$N$$$ as $$$10*a+b$$$ where $$$b \lt 10$$$ and $$$M = a$$$. So we are given the number $$$X=N-M=10*a+b-a = 9*a+b$$$. We can easily see that if $$$b \neq 0$$$ and $$$b \neq 9$$$ (i.e. $$$X$$$ % $$$9 \neq 0$$$) then $$$a = X / 9$$$, $$$b = X$$$ % $$$9$$$ and $$$N$$$ can be unique restored. If $$$b$$$ is $$$0$$$ or $$$9$$$ (i.e. $$$X \% 9 = 0$$$) then for $$$N$$$ we have two possibilities: $$$10*(X/9)-1$$$ and $$$10*(X/9)$$$.

→ Reply
  • »
    »
    5 years ago, # ^ |
      Vote: I like it 0 Vote: I do not like it

    Thank you , I know this but the problem was given in Extended Euclid Volume. That's why i wanted to know that approach.

    → Reply