Query an Indexed In-Memory Numeric Table

Problem Statement

You are tasked with building a lightweight indexing system for an in-memory table of records. Each record consists of a unique row ID (an integer) and a set of numeric columns. The table is immutable once created.

Implement a class IndexedTable with the following requirements:

1. __init__(self, data): The input data is a list of dictionaries, where each dict has an id key and several numeric column keys (e.g., {'id': 1, 'age': 25, 'score': 90}). Preprocess this data to support efficient range queries on any column.
2. query(self, filters): The filters argument is a dictionary where keys are column names and values are tuples (min_val, max_val) (inclusive). The method should return a sorted list of ids that satisfy all provided filters (logical AND).

Constraints

• The number of rows N is up to 100,000.
• The number of columns is small (constant).
• query should perform significantly faster than a full table scan.

Example

table = IndexedTable([
    {'id': 1, 'age': 20, 'score': 80},
    {'id': 2, 'age': 30, 'score': 90},
    {'id': 3, 'age': 25, 'score': 70}
])

# Returns [2, 3] because both satisfy age >= 25 and score >= 70
table.query({'age': (25, 35), 'score': (70, 100)})

Edge Cases

• Empty filters (return all row IDs).
• Filters covering no records (return empty list).
• Columns requested that do not exist in the dataset.