Problem of The Week 5: Bucket and Bucket

You are tasked with determining the number of actions required to measure an exact number of liters using two buckets of different sizes. The solution must follow a series of rules and constraints, given below

Rules:

1. Allowed Actions:
   • Pouring: Transfer water from one bucket to another until either:
     a) the first bucket is empty, or
     b) the second bucket is full.
   • Emptying: Completely empty one bucket, doing nothing to the other.
   • Filling: Completely fill one bucket, doing nothing to the other.
2. Constraints on Final State:
   After any action, you cannot arrive at a state where:
   • The starting bucket is empty, and
   • The other bucket is full.

Input:

1. Bucket One Capacity (size1): The maximum capacity of bucket one (in liters).
2. Bucket Two Capacity (size2): The maximum capacity of bucket two (in liters).
3. Target Volume (target): The exact amount of water (in liters) to measure.
4. Starting Bucket: The bucket that must be filled first, either “bucket one” or “bucket two”.

Output:

1. Total Number of Actions (actions): The total number of actions required to measure the desired number of liters, including the first fill of the starting bucket.
2. Final Target Bucket: Which bucket (bucket one or bucket two) contains the desired number of liters at the end.
3. Remaining Volume in the Other Bucket: The number of liters left in the bucket that does not contain the target volume.

Example:

• Bucket One: 7 liters
• Bucket Two: 11 liters
• Target: 6 liters
• Starting Bucket: Bucket One

Steps:

1. Fill bucket one (7 liters).
2. Pour bucket one into bucket two (bucket one: 0 liters, bucket two: 7 liters).
3. Fill bucket one again (7 liters).
4. Pour bucket one into bucket two until bucket two is full (bucket one: 3 liters, bucket two: 11 liters).
5. Empty bucket two (bucket one: 3 liters, bucket two: 0 liters).
6. Pour bucket one into bucket two (bucket one: 0 liters, bucket two: 3 liters).
7. Fill bucket one again (7 liters).
8. Pour bucket one into bucket two until bucket two contains 6 liters (bucket one: 4 liters, bucket two: 6 liters).

Output:

• Total Actions: 8
• Final Target Bucket: Bucket Two (6 liters)
• Remaining Volume in Other Bucket: 4 liters