Check an Interval Against Existing Intervals for Conflicts

Problem Statement

You are given an unsorted list of existing time reservations, intervals, where each reservation is represented as a half-open interval [start, end). You are also given a new candidate reservation [start, end).

Two half-open intervals [a, b) and [c, d) conflict if they share at least one point in time. That is, they conflict if and only if max(a, c) < min(b, d). If two intervals merely touch at their endpoints (for example, [1, 3) and [3, 5)), they do not conflict.

Write a function to determine if the candidate interval conflicts with any interval in the existing list.

Function Signature

def has_conflict(intervals: list[tuple[int, int]], candidate: tuple[int, int]) -> bool:
    pass

Inputs

• intervals: A list of tuples (start, end) representing existing booked intervals. Each tuple satisfies start < end.
• candidate: A tuple (start, end) representing the interval to check, with start < end.

Output

• Return True if candidate conflicts with at least one interval in intervals; otherwise return False.

Examples

Example 1

intervals = [(1, 4), (6, 10), (12, 15)]
candidate = (4, 6)
# Output: False
# Explanation: Candidate touches (1, 4) at 4 and (6, 10) at 6, but shares no interior points.

Example 2

intervals = [(10, 15), (1, 5), (20, 25)]
candidate = (4, 7)
# Output: True
# Explanation: Candidate overlaps with (1, 5) on the interval [4, 5).

Constraints

• 0 <= len(intervals) <= 10^5
• -10^9 <= start < end <= 10^9 for all intervals including candidate

Edge Cases to Consider

• Empty intervals list: should immediately return False.
• Exact endpoint matches: candidate start equals an existing end, or candidate end equals an existing start.
• Candidate completely enclosed by or completely enclosing an existing interval.