Ⅰ.Context
In a synthetic bio-neural network, information is transmitted between N neurons through chemical and electrical signals. Your objective is to find the minimum Metabolic Cost to trnasmit a signal from a Source_Neuron to a Target_Neuron.
Ⅱ.Neuron Structure and Genetic Coding
Each neuron i is identified by a unique Protein Code (a string consisting of bases A, C, G, T).
  • Genetic Distance (G): The base cost to jump from neuron u to neuron v is defined as the Levenshtein Distance (minimum number of edits: insertions, deletions, or substitutions) between their Protein Code strings.
Ⅲ.Polarization States and Transitions
At any time step T, a neuron exists in one of three Polarization States: P ∈ {0,1,2}. When a signal jumps from u to v, the state of the signal evolves based on a 3x3 Transition Matrix M:
  • If is even:
  • If is odd:
  • (Note: Matrix M is 1-indexed in logic, e.g., ).
Ⅳ.Sypnatic Barriers (Constraints)
A connection from neuron u to v is only valid if all the following conditions are met:
  1. Chemotaxis Condition: The Protein Code of v must contain at least one sub-sequence of length 2 that exists within the Protein Code of u. (e.g., if u is AGCT, v must contain AG, GC, or CT).
  2. Energy Limit: The total accumulated cost from the source must not exceed .
  3. Temporal Gating: A neuron i enters a "refractory period" (disabled) if the current time step T is a multiple of its Stability Index . (i.e., if mod() == 0, the neuron cannot be entered).
Ⅴ.Metabolic Cost Calculation
The total cost to transition from u to v at time T with the current signal state is:
Where:
  • is a weight vector correspoding to the 3 polarization states.
  • Interference(T) = (simulating temporal electromagnetic noise).
Ⅵ.Input / Output Requirements
Input: * neurons: A struct array containing .code(string) and .S(integer).
  • M: A 3x3 state transition matrix.
  • W_state: A 1x3 weight vector.
  • E_max: Maximum energy allowed (scalar).
  • start_id, target_id: Indices of the start and neurons.
Output: * The minimum metabolic cost (scalar). Return -1 if the target is unreachable.
  • (Optional) The path taken (sequence of neuron IDs).
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Last Solution submitted on Mar 20, 2026

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Hoang Minh Tri

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