MAY99_3 - Easy Jug
One day Manku was very thirsty so he decided to drink exactly z litres of water. However , in front of him, there is a well of infinite amount of water and 2 empty jugs of quantity x litres and y litres respectively.
Now Manku can do the following operations to any jug
- Fill it completely from the well
- Empty it entirely
- Transfer as much water from Jug 1 to Jug 2, till Jug 1 gets empty or Jug 2 is completely filled.
Now since he has no measuring device so he will do these operations only to make any of the 2 jug having exactly z litres of water.
Now Your task is given value of x, y, z, tell whether it is possible for Manku to drink water or not.
First Line of Input contains T, the number of test cases. (T <= 25)
Then for each test case there are 3 numbers x, y, z given in separate line.
- 1 <= x <= 10^8
- 1 <= y <= 10^8
- 1 <= z <= 10^8
For each test case output "YES" if manku can drink exactly z litres of water else "NO".
Input: 5 2 4 3 2 5 1 9 3 6 3 8 7 6 1 10 Output: NO YES YES YES NO
- In Test case 1 Either Manku can have 2 or 4 litres of water so he cant drink 3 litres.
- In Test case 2 Manku can have 1 litre water by doing the following operations:
- -> Fill 2 litre Jug
- -> Transfer its water to 5 litre Jug
- -> Again Fill 2 litre Jug
- -> Again Transfer its entire water to 5 litre Jug
- Now 5 litre Jug will have total 4 litre water
- -> Again Fill 2 litre Jug
- -> Now transfer 1 litre water to 5 litre Jug
- because at present 5 litre Jug don't have space for more than 1 litre water
- Now the 2 litre Jug will have only 1 litre water left
- For Test case 3 we will transfer 3 litre water twice from 3 litre jug to 9 litre jug
- For test Case 4,
- transfer 3 times water of 3 litre jug to 8 litre jug
- Ultimately 3 litre Jug has 1 litre water left and 8 litre Jug is full
- Now empty 8 litre jug and pour remaining 1 litre of 3 litre jug in it
- Now fill 3 litre jug fully twice and transfer its water to 8 litre jug
- Now 8 litre Jug will have 7 litre water
- For Test case 5, we cant have 10 litre of water in any jug
Really easy algorithm
euclids extended algorithm works fine
using gcd , it will be easy for solving this question.
3289 82394 1 why answer is no for this
legendary advise..UNDERSTAND EVERY LINE OF PROBLEM CAREFULLY....AND THEN AFTER TAKE THESE TYPES OF COMMENTS VERY SERIOUSLY....
little corner case modification to CEQU and AC!
Prerequisites : Diophantine equation and Extended euclids algo. :)
too easy if the logic strikes in your mind
AC in one go had to think a lot about the logic
|Added by:||Mayank Tuteja|
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