¶ totally useless Posted 21 years, 10 months ago on February 28, 2004
gah. It's 4:30 am, and I can't sleep. i hate it when i can't shut my brain off.

stacy was telling me about her interviews in new york today, and told me a brain teaser she and eugene were joking about. It goes like this: You have two jugs. Jug A can hold 3 gallons of water, and jug B can hold 5. Using just these two jugs and a running faucet, how do you measure out 4 gallons?

So it's a pretty simple one, and the answer is:

1. fill B (A: 0, B: 5)
2. fill A with B (A: 3, B: 2)
3. empty A (A: 0, B: 2)
4. fill A with B (A: 2, B: 0)
5. fill B (A: 2, B: 5)
6. fill A with B (A: 3, B: 4)

Then I couldn't sleep, and started thinking about generalizing the problem and came up with the following generalization:

Problem:Given n jugs with capacities c₁, ..., c_n, find the shortest sequence of actions that allow you to measure out k gallons of water.

Solution:This is a classic example of uninformed search.

state space:	a vector [j1, ..., jn], where ji is the current amount of water, in gallons, in jug i
actions:	fill jug i empty jug i fill jug i with jug j
transition function:	[j1, ..., ji-1, ji, ji+1, ..., jn], fill i → [j1, ..., ji-1, ci, ji+1, ...,jn] [j1, ..., ji-1, ji, ji+1, ..., jn], empty i → [j1, ..., ji-1, 0, ji+1, ...,jn] [j1, ..., , ji, ..., jj, ..., jn], fill i with j → [j1, ..., p, ..., r, ..., jn], where p = min( ci, ji + jj ) and r = max(0, jj - (ci - ji))
start state:	[ 0, ..., 0 ]
goal states:	any state [j1, ..., jn] such that there is some jug i such that ji = k

Given that formalization, you can apply a simple search algorithm like breadth first search to find the shortest sequence of actions that will give you your desired measurement. This search is complete, so if BFS finishes without entering a goal state, then you can conclude that the task is impossible.

So there you have it, a generalization of one of those totally useless brain teasers that you might get in a job interview. Damnit, why can't I come up with a useful insight for once???

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