Ⅰ. Description
In the year 2450, you are the Chief Architect of the Neo-Elysium defense grid. You must manage energy distribution between Nstations in 3D space. This is not a simple flow problem because:
- Kinematics: Every station moves with a constant velocity
. Their positions change every second. - Temporal Rifts: Spherical anomalies appear and disappear, disabling any station trapped inside.
- Dynamic Cost: The cost of sending 1 unit of energy between station
is the squared Euclidean distance at the exact moment of the query. - Capacity Constraints: Each station has a maximum storage capacity, and each link has a maximum throughput.
Ⅱ. Task
Write a function [max_flow, min_cost] = solve_aether(stations, events) that processes a sequence of events and returns the results for all optimization queries.
Input:
- stations: An
matrix: [x, y, z, vx, vy, vz, capacity] - events: A cell array where each element is a vector representing an event:
* [1, id, vx, vy, vz]: Update velocity of station id.
* [2, u, v, k]: Create a directed link from 
with capacity K.
with capacity K. * [3, x, y, z, R, duration]: A rift appears at 
with radius R for a certain duration.
with radius R for a certain duration. * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.
Output:
- A
matrix where Q is the number of Types 4 events. Each row is [TotalMaxFlow, TotalMinCost].
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aaaaa, any suggestion for me pls :(