bfs-state-space

name	bfs-state-space
description	Model minimum-move problems as BFS over a state space. Use when solving bucket pouring puzzles, sliding tiles, or any problem asking for the shortest sequence of moves to reach a goal.
topic	State-Space Search
token_cost	120
related	["dfs-vs-bfs","dynamic-programming"]
keywords	["bucket","pouring","state space","minimum moves","shortest sequence","reach goal","transitions","visited states","water","pour","fill","empty"]

When to use

When a problem asks for the MINIMUM number of moves/steps to reach a goal state (bucket pouring, puzzle solving, sliding tiles), model it as BFS over a state space.

Rules

• State = a tuple of all values that fully describe the situation (e.g. (bucket_a, bucket_b))
• From each state, enumerate every legal transition and produce the next state
• Use a visited set keyed on the state tuple to avoid cycles
• BFS from the start state; the first time you pop a state matching the goal, its distance is the minimum move count
• Track which bucket holds the goal and the other bucket's value at that point
• NEVER skip the visited check — cycles will cause infinite loops
• ALWAYS encode forbidden moves as filters on transitions, not as special cases

Example

Transitions for bucket pouring: fill A, fill B, empty A, empty B, pour A→B, pour B→A.

Edge cases

If start_bucket is forbidden as an immediate "fill the wrong one first" move, encode that as a filter on the initial transitions.

Example

Bucket pouring: state = (a, b). Transitions: fill A, fill B, empty A, empty B, pour A→B, pour B→A. BFS from (0, 0); first time a state has a goal value, that distance is the minimum.