# Chapter 5. Gaps and islands

Itzik Ben-Gan

This chapter describes problems known as gaps and islands and their solutions. I start out with a description of gaps and islands problems, describe the common variations on the problems, and provide sample data and desired results. Then I move on to ways of handling gaps and islands problems, covering multiple solutions to each problem and discussing both their logic and performance. The chapter concludes with a summary of the solutions.

### Description of gaps and islands problems

Gaps and islands problems involve missing values in a sequence. Solving the gaps problem requires finding the ranges of missing values, whereas solving the islands problem involves finding the ranges of existing values.

The sequences of values in gaps and islands problems can be numeric, such as a sequence of order IDs, some of which were deleted. An example of the gaps problem in this case would be finding the ranges of deleted order IDs. An example of the islands problem would be finding the ranges of existing IDs.

### Summary 