Check if All the Integers in a Range Are Covered

Problem Description

You are given a 2D integer array ranges and two integers left and right. Each ranges[i] = [start_i, end_i] represents an inclusive interval between start_i and end_i. Return true if each integer in the inclusive range [left, right] is covered by at least one interval in ranges. Return false otherwise. An integer x is covered by an interval ranges[i] = [start_i, end_i] if start_i <= x <= end_i.

Key Insights

• An integer is considered covered if it falls within any of the provided intervals.
• We need to check the coverage of all integers from left to right.
• The constraints are small, allowing for a straightforward approach where we can iterate through the range.

Space and Time Complexity

Time Complexity: O(n), where n is the number of intervals in ranges.
Space Complexity: O(1), since we are using a constant amount of space regardless of input size.

Solution

To determine if all integers in the range [left, right] are covered, we can follow these steps:

1. Iterate over each integer from left to right.
2. For each integer, check if it falls within any of the intervals defined in ranges.
3. If we find any integer that is not covered by any interval, we return false.
4. If all integers are covered, we return true.

The algorithm utilizes a simple loop and condition checks, making it efficient given the constraints.

Code Solutions