Apothecary
SRM 204 · 2004-07-21 · by vorthys
Problem Statement
An accurate scale is one of the most important tools of the apothecary (an old-time pharmacist). To measure the weight of an object, the apothecary places the object on one pan of the scale, along with some weights of known size, and adds more weights of known size to the other pan until the scales balance. For example, if an object weighs 17 grains, the apothecary could balance the scales by placing a 1-grain weight and a 9-grain weight in the pan with the object, and a 27-grain weight in the other pan.
The apothecary owns weights in a range of sizes starting at 1 grain. In particular, he owns one weight for each
power of 3: 1 grain, 3 grains, 9 grains, 27 grains, etc. Determine, for an object weighing W grains, how to distribute the weights among the
pans to balance the object. This distribution will be unique. Return a
Constraints
- W is between 1 and 1000000, inclusive.
17
Returns: { -9, -1, 27 }
The example above.
1
Returns: { 1 }
A 1-grain weight is placed in the pan opposite the object being measured.
2016
Returns: { -243, -9, 81, 2187 }
A 9-grain weight and a 243-grain weight are placed in the pan with the object, and an 81-grain weight and a 2187-grain weight are placed in the opposite pan.
1000000
Returns: { -531441, -59049, -6561, -243, -27, 1, 81, 729, 2187, 1594323 }
2
Returns: { -1, 3 }
Submissions are judged against all 41 archived test cases, of which 5 are shown here. Case numbers match the judge’s.
Language: C++17 · define a public class Apothecary with a public method vector<int> balance(int W) · 41 test cases · 2 s / 256 MB per case