# Inserting and merging a new interval into a set of intervals

## Question

Given a sorted set of intervals (sorted based on the 1st value of a given range) that do not overlap, write a function to insert a new interval into the set of intervals. You can merge values in the sorted set to accommodate the new interval. Below are a few examples:

**Example 1:**

Set of intervals: `[1, 2], [7, 10]`

Insert: `[2, 5]`

New set of intervals: `[1, 5], [7, 10]`

**Example 2:**

Set of intervals: `[1, 2], [4, 7], [8, 10], [12, 16]`

Insert: `[4, 9]`

New set of intervals: `[1, 2], [4, 10], [12, 16]`

**Example 3:**

Set of intervals: `[1, 2], [4, 7]`

Insert: `[4, 9]`

New set of intervals: `[1, 2], [4, 9]`