DSA Notes
HubAlgorithm vs Data Structure — Key Differences, Definitions, and How They Work TogetherApplications of DSA — How Data Structures and Algorithms Power Real-World SoftwareTime and Space Complexity — A Complete BeginnerWhat is DSA? — A Complete BeginnerWhy Learn DSA? — Career Benefits, Real-World Impact, and Long-Term ValueAsymptotic Analysis — Complete Framework with Recurrence Relations and Master TheoremBest, Average, and Worst Case Analysis — A Practical Guide for Every AlgorithmBig O Notation — Complete Guide with Formal Definition, Rules, and ExamplesBig Omega Notation — Lower Bounds, Best Case, and Formal DefinitionBig Theta (Θ) Notation — Tight Bounds and Exact Growth RatesSpace Complexity — Memory Analysis, Auxiliary Space, and Time-Space TradeoffsTime Complexity Examples — 25 Worked Problems from Basic to AdvancedArray Interview Problems — 15 Classic Problems with Complete SolutionsArray Operations — Every Operation Explained with Code, Complexity, and Edge CasesArray Rotation — Algorithms, Techniques, and Interview ProblemsArray Searching — Linear Search, Binary Search, and Advanced TechniquesArrays — The Complete Introduction to the Most Fundamental Data StructureDynamic Arrays — How Python Lists and ArrayLists Work InternallyMultidimensional Arrays — 2D Arrays, Matrices, and Memory LayoutSliding Window Technique — Complete Guide with 10 Classic ProblemsAnagram Problems — Detection, Grouping, and Sliding Window VariationsPalindrome Problems — Check, Longest, Count, and Expand Around CenterPattern Searching — KMP, Rabin-Karp, and Boyer-Moore AlgorithmsString Interview Problems — 10 Classic Problems with Complete SolutionsString Matching — Longest Common Subsequence, Edit Distance, and Z-AlgorithmString Operations — Complete Reference with Complexity and ImplementationStrings — Complete Introduction to String Data Structure and OperationsCircular Linked List — Structure, Operations, and ApplicationsDoubly Linked List — Complete Implementation with Bidirectional OperationsLinked List Interview Problems — 12 Classic Problems with Complete SolutionsLinked Lists — A Complete Introduction with Memory Model and TypesLinked List Operations — Every Technique with Code and ComplexityReverse Linked List — All Approaches from Basic to AdvancedSingly Linked List — Complete Implementation with All OperationsBalanced Parentheses — Stack-Based Validation with All VariantsInfix, Prefix, and Postfix Expressions — Stack-Based Conversion and EvaluationStack Implementation — Three Complete Implementations with Edge CasesStack Interview Problems — 10 Classic Problems with Complete SolutionsStack — Complete Introduction to LIFO Data StructureStack Using Arrays — Memory Layout, Capacity Management, and PerformanceStack Using Linked List — Implementation, Analysis, and When to Use ItCircular Queue — The Ring Buffer Explained with ImplementationDeque — Double-Ended Queue with Complete Implementation and ApplicationsPriority Queue — Complete Guide from Concept to ImplementationQueue Applications — BFS, Level-Order Traversal, 01-BFS, and MoreQueue Implementation — Array, Linked List, and Two-Stack ApproachesQueue Interview Problems — 10 Classic Problems with Complete SolutionsQueue — Complete Introduction to the FIFO Data StructureAVL Tree - Self-Balancing Binary Search TreeBinary Search Tree (BST)Binary Tree - Structure and OperationsFenwick Tree (Binary Indexed Tree)Red-Black Tree - Another Balanced BSTSegment Tree - Range Query Data StructureTree Interview Problems CollectionTree Data Structure FundamentalsTree Traversals - Inorder, Preorder, Postorder, Level OrderHeap — Complete Introduction to the Priority-Based Tree Data StructureHeap Operations — Complete Reference with Complexity AnalysisHeap Problems — 8 Classic Interview Problems with Complete SolutionsMax Heap — Complete Implementation and ApplicationsMin Heap — Complete Implementation with All OperationsPriority Queue Using Heap — Implementation, Applications, and PatternsBellman-Ford Algorithm — Shortest Path with Negative Weights and Cycle DetectionBFS Algorithm — Breadth-First Search with All Applications and VariantsDFS Algorithm — Depth-First Search with Cycle Detection and All ApplicationsDijkstraFloyd-Warshall Algorithm — All-Pairs Shortest Paths with Complete AnalysisGraph Interview Problems — 12 Classic Problems with Complete SolutionsGraph — Complete Introduction to the Most Powerful Data StructureGraph Representation — Adjacency List, Matrix, Edge List with Complete AnalysisKruskalMinimum Spanning Tree — Definition, Properties, and ApplicationsPrimShortest Path Algorithms — Complete Comparison and Selection GuideTopological Sorting — DFS and BFS (KahnUnion-Find (DSU) in Graphs — Connected Components and Dynamic ConnectivitySeparate Chaining — Complete Implementation and AnalysisCollision Handling — Chaining vs Open Addressing Complete ComparisonHash Functions — Design, Properties, and Common ImplementationsHashing — Complete Introduction to Hash Tables and Hash FunctionsHashing Problems — 10 Classic Interview Problems with Complete SolutionsOpen Addressing — Linear Probing, Quadratic Probing, and Double HashingBubble Sort — Complete Analysis with Optimizations and When to Use ItCounting Sort — O(n+k) Sorting That Breaks the Comparison Lower BoundHeap Sort — Guaranteed O(n log n) with O(1) SpaceInsertion Sort — The O(n) Best Case Sort That Powers PythonMerge Sort — Complete Guide to the Guaranteed O(n log n) Stable SortQuick Sort — The Fastest Practical Sorting Algorithm with Complete AnalysisRadix Sort — O(nk) Digit-by-Digit Sorting for Large Integer RangesSelection Sort — Complete Analysis with Swaps Minimization PropertySorting Algorithm Comparison — The Complete Decision GuideSorting — Complete Introduction to Sorting AlgorithmsBinary Search — Complete Guide with All Variants and Proof of CorrectnessInterpolation Search — O(log log n) Search for Uniformly Distributed DataLinear Search — Complete Guide with All Variants and ApplicationsSearch Algorithm Comparison — Choosing the Right Search for Every SituationSearching Interview Problems — 10 Classic Problems with Complete SolutionsTernary Search — Finding Maximum/Minimum of Unimodal FunctionsBacktracking Introduction — The Recursive Exploration with UndoRecursion Basics — The Complete BeginnerRecursion Problems — 12 Classic Problems from Basic to AdvancedRecursion Tree — Visualizing Recursion for Complexity AnalysisRecursion vs Iteration — When to Use Each and How to ConvertTail Recursion — Definition, Optimization, and Converting to IterationDP Interview Problems — 12 Classic Problems with Pattern Recognition GuideDynamic Programming — Complete Introduction with Properties and Problem IdentificationFibonacci DP — From Exponential to Linear with Memoization and Matrix ExponentiationKnapsack Problem — 0/1, Unbounded, and Fractional with Complete AnalysisLongest Common Subsequence — Complete Guide with DP Table and String VariantsLongest Increasing Subsequence — O(n log n) with Patience SortingMatrix Chain Multiplication — Interval DP with Complete AnalysisMemoization — Top-Down Dynamic Programming with CachingTabulation — Bottom-Up Dynamic Programming with Complete Table BuildingActivity Selection Problem — Greedy Scheduling with Proof of CorrectnessFractional Knapsack — Greedy by Value Density with ProofGreedy Interview Problems — 10 Classic Problems with Complete SolutionsGreedy Algorithms — Complete Introduction with Proof TechniquesHuffman Coding — Optimal Prefix-Free Data CompressionJob Sequencing Problem — Greedy Scheduling with DeadlinesBacktracking — The Complete Guide to Recursive Exploration with UndoBacktracking Problems — 12 Classic Interview Problems with Complete SolutionsN-Queens Problem — Complete Solution with Backtracking and OptimizationRat in a Maze — Backtracking Path Finding with All SolutionsSubset Generation — All Subsets, Combinations, and Partitions with BacktrackingSudoku Solver — Backtracking with Constraint PropagationCodeforces Guide — Complete Strategy to Reach 1800+ RatingCommon CP Techniques — Essential Algorithms Every Competitive Programmer Must KnowContest Strategies — How to Perform Your Best in Competitive Programming ContestsCompetitive Programming — Complete Introduction for BeginnersFast Input/Output — Why I/O Speed Matters and Complete Templates for C++ and PythonLeetCode Guide — Complete Strategy to Crack FAANG InterviewsBit Manipulation — Complete Guide with All Tricks and Interview ProblemsBloom Filter — Space-Efficient Probabilistic Membership TestingComputational Geometry — Points, Lines, Convex Hull, and Geometric AlgorithmsDisjoint Set Union (DSU) — Union-Find with Path Compression and Union by RankRandomized Algorithms — Las Vegas, Monte Carlo, and Probabilistic TechniquesSkip List — The Probabilistic Data Structure that Competes with Balanced BSTsSuffix Array — Construction, LCP Array, and String Search ApplicationsTrie Data Structure — Complete Guide with Implementation and ApplicationsAutocomplete System Using TrieLibrary Management System Using DSARoute Finder Using GraphsMini Search Engine ProjectSocial Network Analysis Using GraphsEssential Coding Patterns for InterviewsDSA Cheatsheet: Quick ReferenceEssential DSA Interview QuestionsFAANG DSA Sheet: Company-Specific Patterns and ProblemsProblem Solving Strategies for Coding InterviewsComplexity CheatsheetImportant Algorithms SummaryBest Practice Platforms for DSARecommended Books for DSA
Complete reference for all string operations — reversal, rotation, compression, checking palindrome, counting characters, removing duplicates, replacing characters, converting case, splitting and joining — each with implementation, time and space complexity, and edge cases.
1. Reversal
Example
def reverse_string(s):
# Method 1: Slicing — O(n), creates new string
return s[::-1]
def reverse_string_inplace(s):
# Method 2: Two-pointer on char array — O(n), O(n) for array conversion
chars = list(s)
left, right = 0, len(chars) - 1
while left < right:
chars[left], chars[right] = chars[right], chars[left]
left += 1
right -= 1
return ''.join(chars)
print(reverse_string("hello")) # "olleh"
print(reverse_string("abcde")) # "edcba"
Reverse Words in a String
Example
def reverse_words(s):
"""Reverse order of words, not characters."""
return ' '.join(s.split()[::-1])
print(reverse_words(" Hello World ")) # "World Hello"
def reverse_words_inplace(s):
"""Reverse words without extra space (interview version)."""
chars = list(s.strip())
# Step 1: Reverse entire string
chars.reverse()
# Step 2: Reverse each word
start = 0
for i in range(len(chars) + 1):
if i == len(chars) or chars[i] == ' ':
chars[start:i] = chars[start:i][::-1]
start = i + 1
return ''.join(chars)
3. String Compression
Example
def compress_string(s):
"""
Compress by replacing repeated characters: "aaabbc" → "a3b2c1"
Return original if compressed is longer.
"""
if not s:
return s
result = []
count = 1
for i in range(1, len(s)):
if s[i] == s[i-1]:
count += 1
else:
result.append(s[i-1] + (str(count) if count > 1 else ''))
count = 1
result.append(s[-1] + (str(count) if count > 1 else ''))
compressed = ''.join(result)
return compressed if len(compressed) < len(s) else s
print(compress_string("aaabbc")) # "a3b2c"
print(compress_string("abc")) # "abc" (no benefit)
4. Remove Duplicates
python example
def remove_duplicates_keep_order(s):
"""Remove duplicate characters, keep first occurrence. O(n)."""
seen = set()
result = []
for char in s:
if char not in seen:
seen.add(char)
result.append(char)
return ''.join(result)
print(remove_duplicates_keep_order("programming")) # "progamin"5. Character Frequency Count
Example
from collections import Counter
def char_frequency(s):
"""Count frequency of each character. O(n)."""
return dict(Counter(s))
print(char_frequency("hello")) # {'h':1, 'e':1, 'l':2, 'o':1}
def most_frequent_char(s):
freq = Counter(s)
return freq.most_common(1)[0] # ('l', 2) for "hello"
6. Case Conversion
python example
s = "Hello World"
print(s.upper()) # "HELLO WORLD"
print(s.lower()) # "hello world"
print(s.title()) # "Hello World"
print(s.swapcase()) # "hELLO wORLD"
print(s.capitalize()) # "Hello world"
def toggle_case(s):
"""Toggle case of each character."""
return ''.join(c.lower() if c.isupper() else c.upper() for c in s)
print(toggle_case("HeLLo")) # "hEllO"7. Check Permutation / Anagram
Example
def is_anagram(s1, s2):
"""Check if s1 and s2 are anagrams. O(n)."""
if len(s1) != len(s2):
return False
return Counter(s1) == Counter(s2)
# O(1) space version for lowercase letters
def is_anagram_array(s1, s2):
if len(s1) != len(s2): return False
count = [0] * 26
for c in s1: count[ord(c) - ord('a')] += 1
for c in s2: count[ord(c) - ord('a')] -= 1
return all(x == 0 for x in count)
print(is_anagram("listen", "silent")) # True
print(is_anagram("hello", "world")) # False
8. String Formatting
python example
name, age, score = "Alice", 25, 98.5
# f-strings (Python 3.6+) — recommended
print(f"Name: {name}, Age: {age}, Score: {score:.1f}")
# "Name: Alice, Age: 25, Score: 98.5"
# Padding and alignment
print(f"{'left':<10}|{'center':^10}|{'right':>10}")
# "left | center | right"
# Number formatting
print(f"{1234567:,}") # "1,234,567"
print(f"{0.1234:.2%}") # "12.34%"
print(f"{255:#010b}") # "0b11111111"9. Splitting and Joining
Example
# Split by delimiter
s = "a,b,c,d"
print(s.split(',')) # ['a', 'b', 'c', 'd']
print(s.split(',', 2)) # ['a', 'b', 'c,d'] — max 2 splits
# Split by whitespace (handles multiple spaces, tabs, newlines)
s = " hello world "
print(s.split()) # ['hello', 'world']
# Join
words = ['hello', 'world']
print(' '.join(words)) # "hello world"
print('-'.join(words)) # "hello-world"
print(''.join(words)) # "helloworld"
# Join efficiently
chars = ['a', 'b', 'c']
result = ''.join(chars) # O(n) — best way to build strings
10. Find and Replace
python example
s = "Hello World Hello"
# Find
print(s.find("Hello")) # 0 (first occurrence)
print(s.rfind("Hello")) # 12 (last occurrence)
print(s.find("xyz")) # -1 (not found)
# Count occurrences
print(s.count("Hello")) # 2
# Replace
print(s.replace("Hello", "Hi")) # "Hi World Hi"
print(s.replace("Hello", "Hi", 1)) # "Hi World Hello" — replace only first
# Strip characters
s = "***hello***"
print(s.strip('*')) # "hello"
print(s.lstrip('*')) # "hello***"Complexity Summary
| Operation | Time | Space | Notes |
|---|---|---|---|
| Access s[i] | O(1) | O(1) | |
| Length len(s) | O(1) | O(1) | Stored |
| Slice s[i:j] | O(j-i) | O(j-i) | Creates new string |
| Concatenate s1+s2 | O(n+m) | O(n+m) | Creates new string |
| Find/search | O(n) | O(1) | Linear scan |
| Replace | O(n) | O(n) | Creates new string |
| Split | O(n) | O(n) | Returns list |
| Join n strings | O(total_length) | O(total_length) | One allocation |
| Upper/lower | O(n) | O(n) | New string |
| Reverse | O(n) | O(n) | New string |
| Count char | O(n) | O(1) |
*Next Lesson: Pattern Searching*
Exam Focus
Revise definitions, diagrams, examples, and short-answer points for String Operations — Complete Reference with Complexity and Implementation.
Interview Use
Prepare one clear explanation, one practical example, and one common mistake for this Data Structures & Algorithms topic.
Search Terms
data-structures-algorithms, data structures & algorithms, data, structures, algorithms, strings, string, operations
Related Data Structures & Algorithms Topics
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