Description
[EMERGENCY TRANSMISSION - GALACTIC COMMAND]
Subject: Mission Omega-7 - Navigation through the K-94 Tesseract Anomaly.
Background:
The Omega-7 probe has entered a non-Euclidean hyper-dimensional region known as a Tesseract Grid. The probe’s onboard computer is failing, and you must provide a sequence of movements to reach the "Stability Core" before the probe's energy reserves deplete or it is crushed by a Quantum Anomaly.
1.The 4D Toroidal Spacetime:
The grid is a 4-dimensional hyper-cube of size 
. Coordinates are given as 
where 
. The space is toroidal in all four dimensions: moving from 
in any direction with a step of 
results in 0.
. Coordinates are given as where . The space is toroidal in all four dimensions: moving from in any direction with a step of results in 0.2.Goal Decoding (The Eigen-Lock):
The coordinates of the Stability Core 
are hidden within a 4 x 4 Quantum Matrix M. To decode 
:
are hidden within a 4 x 4 Quantum Matrix M. To decode :- Find the four eigenvalues of
. - Take the absolute value of each eigenvalue.
- Sort these values in ascending order:
- Apply a permutation vector
( where P contains indices 1 to 4) such that 
- The final coordinates are
3.Dynamic Quantum Anomalies (4D Cellular Automata):
The grid is infested with anomalies. Let 
be a logical 4D array where 
means an anomaly exists. The field evolves every second 
based on the number of neighbors K(where each cell has 
- 1 = 80 neighbors):
be a logical 4D array where means an anomaly exists. The field evolves every second based on the number of neighbors K(where each cell has - 1 = 80 neighbors):- Birth: A cell becomes active if it was dead and has exactly B neighbors.
- Survival: An active cell remains active if it has between
and 
neighbors. - Energy Flux: Each active neighbor of a cellB at time t increases the "Action Cost" of moving into that cell by 0.1
4.Space Warping ( The Wormhole Effect ):
There are two special coordinates, 
and 
. If the probe enters at time t, it is instantly transported to at time 
(and vice versa) with a fixed cost of 0.5, regardless of local anomalies.
and . If the probe enters at time t, it is instantly transported to at time (and vice versa) with a fixed cost of 0.5, regardless of local anomalies.5.Energy and Action Constraints:
- Max Energy: The probe starts with
. - Consumption: Each move (including staying still) consumes 1.0 unit of energy. If
, the mission fails. - Action Cost: The total "Action" to be minimized is the sum of costs:
- Movement: In one second, the probe can move to any of its 80 neighbors or stay in place. However, it cannot enter a cell that is currently "Active"
at time t.
Goal: Find the minimum total Action to reach 
steps and before energy runs out.
steps and before energy runs out.Solution Stats
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??? It shouldn't be that hard bro
Oh, your testcase was wrong too XD, I completed it in one line, check again bro
...
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