Array/Matrix Manipulation Patterns — DSA Pattern

The Array/Matrix Manipulation Patterns pattern applies when you need in-place operations, hashing, prefix sums, spiral traversal, and cyclic sort. Its time complexity is O(n) for linear array operations; O(m×n) for matrix traversal (m, n = matrix dimensions) and space complexity O(1) for in-place techniques; O(n) for hashing-based ones. It is used in 24 problems on Thita, including Add Binary, Add to Array-Form of Integer and Diagonal Traverse. Common variations are Product Except Self (Prefix/Suffix Products) and Merge Sorted Array (In-place from End).

Master array and matrix manipulation techniques including in-place rotation, spiral traversal, prefix/suffix products, and cyclic sort. Essential patterns for coding interviews at FAANG companies.

Array/Matrix Manipulation Patterns is pattern 4 of 16 in the Thita.ai DSA course. It covers in-place operations, hashing, prefix sums, spiral traversal, and cyclic sort, split into 10 subpatterns and about 4 hours of study. It is one of the interview-critical patterns, so it is worth covering before your first onsite.

Subpatterns of Array/Matrix Manipulation Patterns

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

• Merge Sorted Array (In-place from End) — Learn the merge sorted array technique starting from the end. Essential for space-efficient array merging in coding interviews. (core technique)
• Spiral Traversal — Master spiral traversal pattern for 2D matrices. Learn to traverse matrices in spiral order for interview problems. (core technique)
• Set Matrix Zeroes (In-place Marking) — Learn the in-place marking technique to set entire rows and columns to zero efficiently without extra space. (core technique)
• Hashing - Frequency Map / Counting — Master hash map frequency counting for array problems. Count occurrences, find duplicates, and solve majority element problems efficiently. (core technique)
• Prefix Sum - Subarray Sum / Range Query — Master prefix sum technique for efficient subarray sum and range query problems. Solve subarray sum equals K and contiguous array problems. (core technique)
• Product Except Self (Prefix/Suffix Products) — Master the prefix and suffix products technique to calculate product of array except self without division. (important variation)
• Plus One (Handling Carry) — Learn to handle carry operations when adding one to a number represented as an array of digits. (depth topic)
• Array - Cyclic Sort — Master cyclic sort pattern to find missing, duplicate, or misplaced numbers in arrays with O(n) time and O(1) space. (depth topic)
• Hashing - Previously Seen / Existence Check — Use hash sets for O(1) existence checks. Track previously seen elements to detect duplicates, find pairs, and validate sequences. (depth topic)
• In-place Rotation — Learn in-place rotation techniques for arrays and matrices. Rotate without using extra space. (depth topic)

How to practise Array/Matrix Manipulation 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 10 Array/Matrix Manipulation Patterns subpatterns you have covered. Topics covered here include array manipulation, matrix manipulation, in-place rotation, spiral matrix traversal, set matrix zeroes, product except self, prefix products, suffix products.

Related DSA patterns

• Sliding Window — Fixed-size, variable-size, and character frequency matching window techniques.
• Binary Search Patterns — Standard binary search, rotated arrays, first/last occurrence, and search on answer space.
• Linked List Manipulation Patterns — In-place reversal, merging sorted lists, reordering, and intersection detection.
• Stack Patterns — Parentheses matching, monotonic stack, histogram, and expression evaluation.
• String Manipulation Patterns — Palindrome checking, anagram detection, pattern matching, and string conversion.
• All 16 DSA patterns
• The DSA patterns sheet
• Coding practice