given a collection of intervals, decide whether there is a subset of non-overlapping intervals of size at least k.

Non-overlapping intervals:

If the intervals(say interval a & interval b) doesn’t overlap then the set of pairs form by [a. end, b. start] is the non-overlapping interval.

Interval:

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers {\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Overlapping intervals:

Let’s take the below mentioned overlapping intervals example to explain the idea: If both ranges have at least one common point, then we say that they’re overlapping. In other words, we say that two ranges and are overlapping if: On the other hand, non-overlapping ranges don’t have any points in common.

Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.

Examples:

interval (a) = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }

Output: [5, 7]

The only interval which doesn’t overlaps with the other intervals is [5, 7].

Non-overlapping intervals:non-overlapping interval.Interval:In mathematics, a (real)intervalis asetof real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of allreal numbers{\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).Overlapping intervals:rangeshave at least one common point, then we say that they’re overlapping. In other words, we say that two ranges and are overlapping if: On the other hand,non-overlapping rangesdon’t have any points in common.Non -overlapping :