Maximum Quality Sum

Problem Overview

• Assign every packet to exactly one channel so each channel has at least one packet, maximizing the sum of channel qualities (medians), and round the final sum up.
• Input/Output: packets array and integer channels (1..len(packets)); return the maximum sum; n up to 5e5, packet size up to 1e9.
• Context: AWS server channel stress-test where quality is the median of its packet sizes.
• From Amazon interviews: a coding interview interview question problem.