The Four Core Patterns of Binary Search
Understanding Binary Search Patterns
Binary search can be applied to a wide variety of problems, but most of them follow one of these four core patterns.
Each pattern represents a different way of thinking about and applying binary search to solve problems.
Standard Binary Search
Boundary Binary Search
Learning Objective
Understand the core patterns of binary search and how they can be applied to solve different types of problems.
The Four Core Patterns of Binary Search
While binary search can be applied to many different problems, most binary search solutions follow one of these four core patterns. Understanding these patterns will help you recognize when and how to apply binary search to new problems.
Standard Binary Search
The classic algorithm for finding a target value in a sorted array.
Examples: Finding a specific element, checking if an element exists
Boundary Binary Search
Finding the boundary between two regions in a sorted array.
Examples: First/last occurrence, insertion point, peak element
Rotated Array Pattern
Searching in a sorted array that has been rotated at some pivot point.
Examples: Finding minimum in rotated array, searching in rotated array
Search Space Reduction
Using binary search to reduce the search space for optimization problems.
Examples: Finding square root, minimizing maximum values
Standard Binary Search
Choosing the Right Pattern
When faced with a problem that might be solved using binary search, ask yourself these questions to identify the most appropriate pattern:
For Standard Binary Search
"Am I searching for a specific value in a sorted array with no duplicates?"
For Boundary Binary Search
"Am I looking for a boundary between two regions, like the first or last occurrence of a value?"
For Rotated Array Pattern
"Am I working with a sorted array that has been rotated at some point?"
For Search Space Reduction
"Am I trying to find an optimal value that minimizes or maximizes something?"