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POUR1 - Pouring water

#gcd #recursion

Given two vessels, one of which can accommodate a litres of water and the other - b litres of water, determine the number of steps required to obtain exactly c litres of water in one of the vessels.

At the beginning both vessels are empty. The following operations are counted as 'steps':

emptying a vessel,
filling a vessel,
pouring water from one vessel to the other, without spilling, until one of the vessels is either full or empty.

Input

An integer t, 1<=t<=100, denoting the number of testcases, followed by t sets of input data, each consisting of three positive integers a, b, c, not larger than 40000, given in separate lines.

Output

For each set of input data, output the minimum number of steps required to obtain c litres, or -1 if this is impossible.

Example

Sample input:

Sample output:

2
-1

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	chachaji_harsh: 2017-12-04 17:35:45 how is it a DP problem
	mahilewets: 2017-08-29 20:18:26 I think BFS is bad here Because 40000 limitation If limitation is like 255 We can easily afford BFS even with three vessels
	arthur1991: 2017-03-26 07:38:10 i love qianqian
	osama2003: 2017-01-25 00:31:58 -1 .. nguenthanhloc
	muneebaadil: 2017-01-04 21:37:23 Doing through BFS+maps too. But TLE. Using the following algorithm. Each node having pair (x, y) derives four more pairs (provided that this node isn't visited before) (a, y), (x, b), (x-min(x, b-y), y+min(x, b-y)), (x+min(y, a-x), y-min(y, a-x)) and finally the node having pair(x, y) is marked visited. What am I doing wrong?
	flyingduchman_: 2016-12-27 14:37:10 Actual problem: You are at the side of a river. You have a "a" liter jug and a "b" liter jug. The jugs do not have markings to allow measuring smaller quantities. How canyou use the jugs to measure "c" liter of water? Representing the problem in equation: ax + by = c where x = number of time one jug is poured/discharged(+ve/-ve) y = number of time the other jug is poured/discharged(+ve/-ve) Theorem. The Diophantine equation ax+by = c is solvable if and only if gcd(a, b) divides c. Corner case :c must satisfy: c <= max(a,b) Simulation: You must simulate by doing "pouring action" only in one jug and "discharging action" only in the opposite jug. (1)pour in a, discharge in b: if a is empty pour a full, if b is full the discharge and make b empty. Otherwise, transfer water from a to b. Each of those three condition is a step & can happen only once at a time. (2)pour in b, discharge in a: if b is empty pour it full, if a is full make it empty. Otherwise, transfer water from b to a. count total steps for (1) and (2), the minimum is the answer.
	kushalanand: 2016-10-29 23:37:15 My 69th. BFS + maps :D
	albus111: 2016-09-16 07:23:49 Is there a math formula for this question?
	conquistador: 2016-08-12 20:28:31 My 100th.. .Beginners believe in yourself . YOU CAN SOLVE IT. Dont rely on spojtoolkit for this question. Last edit: 2016-08-12 21:13:54
	Rajat Sharma: 2016-08-03 20:26:02 AC Java : GCD along with logic(if conditions) after solving this problem , one ll know : euclidean algorithm, extended euclidean algorithm, and most importantly this R (i+1) = R (i-1) - Q (i) R (i) which provides the synopsis for the extended euclidean algorithm. Last edit: 2016-08-03 20:32:31

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Added by:	adrian
Date:	2004-05-31
Time limit:	1s
Source limit:	50000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: NODEJS PERL6 VB.NET
Resource:	An ancient problem, formulated in these words by Mr Tadeusz Ratajczak