Binary Search Patterns — DSA Pattern

The Binary Search Patterns pattern applies when you need standard binary search, rotated arrays, first/last occurrence, and search on answer space. Its time complexity is O(log n) and space complexity O(1). It is used in 26 problems on Thita, including Binary Search, Capacity To Ship Packages Within D Days and Find First and Last Position of Element in Sorted Array. Common variations are On Sorted Array/List and Find First/Last Occurrence.

Master binary search algorithms including standard search, rotated array search, search on answer space, and finding boundaries. Essential for efficient O(log n) solutions.

Binary Search Patterns is pattern 3 of 16 in the Thita.ai DSA course. It covers standard binary search, rotated arrays, first/last occurrence, and search on answer space, split into 5 subpatterns and about 2.5 hours of study. It is one of the interview-critical patterns, so it is worth covering before your first onsite.

Subpatterns of Binary Search Patterns

Each subpattern below has its own theory page and problem set. They are listed in the order the course teaches them.

• On Sorted Array/List — Master standard binary search on sorted arrays. Learn search insert position, sqrt calculation, and 2D matrix search. (core technique)
• Find First/Last Occurrence — Learn to find first and last occurrence of elements using binary search. Master lower bound and upper bound concepts. (core technique)
• Find Min/Max in Rotated Sorted Array — Master binary search in rotated sorted arrays. Find minimum, search elements, and handle duplicates. (core technique)
• Median and Kth of Two Sorted Arrays — Master the binary search approach to find median of two sorted arrays in O(log(min(m,n))) time. (depth topic)
• On Answer / Condition Function — Learn binary search on answer space for optimization problems like Koko eating bananas and capacity to ship packages. (depth topic)

How to practise Binary Search Patterns on Thita.ai

Read the theory for a subpattern, then solve its problems in the browser editor. Your solution runs against the problem's test cases, and the AI coach gives a hint on the technique you are missing rather than the finished answer. Progress is tracked per subpattern, so the tracker shows which of the 5 Binary Search Patterns subpatterns you have covered. Topics covered here include binary search, binary search algorithm, search sorted array, rotated sorted array, binary search variations, search insert position, first last occurrence, binary search on answer.

Related DSA patterns

• Two Pointers — Fast-slow, converging, expanding from center, and in-place modification techniques.
• Sliding Window — Fixed-size, variable-size, and character frequency matching window techniques.
• Array/Matrix Manipulation Patterns — In-place operations, hashing, prefix sums, spiral traversal, and cyclic sort.
• Linked List Manipulation Patterns — In-place reversal, merging sorted lists, reordering, and intersection detection.
• Stack Patterns — Parentheses matching, monotonic stack, histogram, and expression evaluation.
• All 16 DSA patterns
• The DSA patterns sheet
• Coding practice