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Realtime Middle Value Estimator Solution

Problem Statement

Design a system that maintains a sequence of numbers and calculates the median after each new number is added, ensuring the median is always up-to-date. The system should handle a large volume of numbers efficiently.

Example 1
Input
Numbers: [12, 4, 56, 7, 23, 1]
Output
["N",null,"m",null,"e",null,"m",null]

Explanation: The median is calculated as the middle value in the sorted sequence. When the sequence length is even, the median is the average of the two middle values.

Constraints

  • The input stream can contain any positive or negative integers.
  • The system should handle a large volume of numbers efficiently.
  • Memory usage should be optimized.

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