Union Interval Calculator

What is Union Interval?

The union of intervals refers to combining multiple intervals into a single set of intervals that covers all the points from the original intervals without any gaps. This process merges overlapping or adjacent intervals to form the smallest possible set of intervals that contains all the original intervals.

Union intervals are commonly used in scheduling, time management, and data analysis to simplify complex time periods into a more manageable format.

Key Concepts

• Overlapping Intervals: Intervals that share common points.
• Adjacent Intervals: Intervals that touch at their endpoints.
• Disjoint Intervals: Intervals that do not overlap and are not adjacent.

Applications

Union intervals are used in various fields including:

• Scheduling and time management
• Data analysis and visualization
• Computer science algorithms
• Financial forecasting
• Resource allocation

How to Use the Calculator

Using the Union Interval Calculator is straightforward. Follow these steps:

1. Enter the start and end values for each interval you want to combine.
2. Click the "Add Interval" button to add more intervals if needed.
3. Click the "Calculate" button to compute the union of the intervals.
4. Review the results, which will show the merged intervals.
5. Use the "Reset" button to clear all inputs and start over.

Formula

The union of intervals is calculated by merging overlapping or adjacent intervals into the smallest possible set of intervals. The algorithm works as follows:

1. Sort all intervals based on their start values.
2. Initialize an empty list to store the merged intervals.
3. Iterate through each interval and merge it with the last interval in the merged list if they overlap or are adjacent.
4. If they do not overlap or are not adjacent, add the current interval to the merged list.

Example Calculation

Let's say you have the following intervals:

• [1, 3]
• [2, 6]
• [8, 10]
• [15, 18]

The union of these intervals would be:

• [1, 6]
• [8, 10]
• [15, 18]

In this example, the intervals [1, 3] and [2, 6] overlap and are merged into [1, 6]. The other intervals do not overlap or are adjacent, so they remain separate.