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:
  1. Kinematics: Every station moves with a constant velocity . Their positions change every second.
  2. Temporal Rifts: Spherical anomalies appear and disappear, disabling any station trapped inside.
  3. Dynamic Cost: The cost of sending 1 unit of energy between station is the squared Euclidean distance at the exact moment of the query.
  4. 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.
* [3, x, y, z, R, duration]: A rift appears at 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].
Solve

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Last Solution submitted on Mar 20, 2026

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Hoang Minh Tri Hoang Nguyen Khanh Ngan nangg

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