What is the optimal time complexity of solving Minimum Interval to Include Each Query?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Minimum Interval to Include Each Query?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Minimum Interval to Include Each Query?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Minimum Interval to Include Each Query?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

Back to Practice Dashboard

Top 150 InterviewEasy

Minimum Interval to Include Each Query

Learn how to solve the 'Minimum Interval to Include Each Query' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

You are given a 2D integer array intervals, where intervals[i] = [left_i, right_i] describes the ith interval starting at left_i and ending at right_i (inclusive). The size of an interval is defined as right_i - left_i + 1. You are also given an integer array queries. The answer to the jth query is the size of the smallest interval i such that left_i <= queries[j] <= right_i. If no such interval exists, the answer is -1.

Return an array containing the answers to the queries.

Write a function minInterval(intervals: List[List[int]], queries: List[int]) -> List[int].

Constraints

•1 <= len(intervals) <= 10^5
•1 <= len(queries) <= 10^5
•intervals[i].length == 2
•1 <= left_i <= right_i <= 10^7
•1 <= queries[j] <= 10^7

Examples

Example 1

Input

intervals = [[1,4],[2,4],[3,6],[4,4]], queries = [2,3,4,5]

Output

[3,3,1,4]

Explanation

Smallest interval containing 2 is [2,4] (size 3). For 3 is [2,4] (size 3). For 4 is [4,4] (size 1). For 5 is [3,6] (size 4).

Example 2

Input

intervals = [[2,3],[2,5],[1,8],[20,25]], queries = [2,19,5,22]

Output

[2,-1,4,6]

Explanation

For 2: [2,3] (size 2). For 19: none (-1). For 5: [2,5] (size 4). For 22: [20,25] (size 6).

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor