Order Interval Consolidation and Trading Gap Detection

Exchange regulatory compliance algorithms at Jane Street and HRT verify that designated market makers maintain continuous quoting presence. You are given a list of candidate quoting intervals intervals where intervals[i] = [s_i, e_i] ($s_i \le e_i$) and an integer session_end representing the trading session span $[0, session\_end]$.

Your Task

Implement consolidate_intervals_and_gaps(intervals: list[list[int]], session_end: int) -> tuple[list[list[int]], list[list[int]]] that returns:

1. merged: A list of consolidated, mutually disjoint quote coverage intervals sorted by start time.
2. gaps: A list of blackout gap intervals $[g_{start}, g_{end}]$ ($g_{start} < g_{end}$) within the session $[0, session\_end]$ during which no quote coverage was present.

Constraints

• $0 \le \text{len}(intervals) \le 10^5$
• $0 \le s_i \le e_i \le session\_end \le 10^9$

Examples

intervals = [[1, 3], [2, 6], [8, 10], [15, 18]]
session_end = 20
# Merged intervals: [[1, 6], [8, 10], [15, 18]]
# Gaps: [[0, 1], [6, 8], [10, 15], [18, 20]]
# Output: ([[1, 6], [8, 10], [15, 18]], [[0, 1], [6, 8], [10, 15], [18, 20]])