Solution: Non-overlapping Intervals

Statement

Given an array of intervals where intervals[i] contains the half-open intervalAn interval that contains only one of its boundary elements. The “(” parenthesis denotes the exclusion of the starting point. The “]” bracket denotes the inclusion of the ending point., $(start_{i}​, end_{i}]$, your task is to find the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping.

Note: Two intervals $(a, b]$ and $(c, d]$ are considered overlapping if there exists a value $x$ such that $a < x \leq b$ and $c < x \leq d$. In other words, if there is any point within both intervals (excluding their starting points) where both intervals have values, they are considered overlapping. For example, the intervals $(7, 11]$ and $(10, 12]$ are overlapping, whereas the intervals $(2, 4]$ and $(4, 5]$ are non-overlapping.

Constraints:

• $1 \leq$intervals.length $\leq 10^3$

• intervals[i].length $== 2$

• $−5 \times 10^4 \leq start_{i} < end_{i} \leq 5 \times 10^4$

Solution

Here are the steps of the algorithm:

• Sort the intervals array in an ascending order based on the end time of each interval.

• Declare two variables that will assist us in the algorithm:

  • end: This stores the end time of the last included interval.

  • remove: This stores the number of intervals to be removed. It is initialized to $0$. ...