OFFSET
1,7
COMMENTS
In the two-jug problem we are given an infinite supply of water and two empty jugs with integer liter capacities A and B, A>=B>=1. We must use the least number of steps to measure exactly N integer liters of water in jug A, irrespective of jug B. Each step is one of the following: empty a jug, fill a jug, or pour from one jug to the other. Pouring stops as soon as the source jug is empty or the destination jug is full. It is known that the amount N can be made if and only if N is a multiple of gcd(A,B).
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
1997 ACM South Central USA programming contest, Problem and Code
Wolfram Mathworld, Three Jug Problem
EXAMPLE
Triangle begins:
-1;
-1,-1;
1, 1, 1;
2, -1, 2, -1;
4, 2, 2, 6, -1;
6, -1, 2, -1, 10, -1;
6, 4, 2, 2, 6, 10, -1;
6, -1, 2, -1, 2, -1, 10, -1;
6, 6, 2, 8, 8, 2, 10, 10, -1;
6, -1, 2, -1, -1, -1, 2, -1, 10, -1;
For example T(5,4) = 6.
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Dmitry Kamenetsky, Aug 17 2010
STATUS
approved