Algorithms terms
The step-by-step logic that powers efficient computation
Algorithms are the precise recipes that transform inputs into outputs efficiently. This category covers sorting, searching, graph traversal, dynamic programming, greedy approaches, divide-and-conquer, and complexity analysis. Understanding algorithmic thinking helps you recognise patterns in problems and reach for the right solution rather than reinventing a worse one.
More on Algorithms
History
Algorithms as a formal discipline emerged from mathematics and logic in the early 20th century, with roots tracing to Al-Khwarizmi's 9th-century work (whose name inspired the term itself). The field accelerated with the advent of computers in the 1940s–1950s, when researchers like Donald Knuth began systematizing algorithmic analysis and complexity theory, establishing Big-O notation as a standard measurement tool. The 1960s–1970s saw foundational breakthroughs: the formalization of P vs NP problems by Cook and Karp, development of major algorithms like Dijkstra's shortest path and quicksort, and the emergence of algorithm design paradigms such as dynamic programming and divide-and-conquer. Today, algorithmic thinking underpins software engineering practice across domains—from web search and machine learning to database optimization—with modern development emphasizing both theoretical correctness and practical performance analysis through empirical benchmarking.
Key concepts
- Big-O Notation
- Recursion Patterns
- Searching Algorithms
- Sorting Algorithms
- Divide and Conquer
- Dynamic Programming
- Graph Algorithms
- Greedy Algorithms
Best references
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Introduction to Algorithms (CLRS) The canonical computer science textbook covering algorithm design, analysis, and correctness. Essential reference for Big-O notation, sorting, graph algorithms, dynamic programming, and NP-completeness.
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Stanford CS161 Course Materials University-level algorithm course covering divide-and-conquer, sorting, searching, graph algorithms, dynamic programming, and complexity analysis with rigorous proofs.
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Competitive Programming by Halim & Halim Comprehensive reference for practical algorithm implementation, pattern recognition, and problem-solving techniques used in competitive programming and technical interviews.
✦ Latest in Algorithms
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Edges touching a Algorithms term.
- String Algorithms Leverages Dynamic Programming 15h
- Big-O Notation Measures Binary Trees 2d
- A* Pathfinding Algorithm Specializes Graph Algorithms 4d
- Big-O Notation Measures Fuzzy Search 4d
- Big-O Notation Measures Arrays 5d
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Most referenced — Algorithms
Big-O Notation 3Dijkstra's Shortest Path Algorithm 3Suffix Array 3A* Pathfinding Algorithm 1Topological Sort 1Backtracking 1Bit Manipulation 1Divide and Conquer 1
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Suffix Array
PHP 7.0+ A sorted array of all suffix starting positions of a string, enabling fast substring search in O(m log n) with far less memory than a suffix tree.
21h ago
algorithms advanced
Dijkstra's Shortest Path Algorithm
PHP 5.3+
1
A greedy graph algorithm that finds the shortest path from a source node to all other nodes in a weighted graph with non-negative edge weights.
3mo ago
algorithms advanced
Topological Sort
PHP 7.4+ An ordering of nodes in a directed acyclic graph (DAG) such that for every directed edge u→v, node u appears before v in the ordering.
3mo ago
algorithms intermediate
A* Pathfinding Algorithm
5
Heuristic search algorithm that finds the lowest-cost path using f(n)=g(n)+h(n), widely used in maps and game AI.
3mo ago
algorithms advanced
Amortized Analysis
Averaging the cost of an operation over a sequence — explaining why dynamic array append is O(1) amortised despite occasional O(n) resizes.
3mo ago
algorithms advanced
Divide and Conquer
Recursively break a problem into smaller subproblems, solve each independently, and combine results — the strategy behind mergesort, quicksort, binary search, and FFT.
3mo ago
algorithms intermediate
Hashing Algorithms Deep Dive
PHP 7.2+
Comparing hash functions for different use cases — MD5/SHA-1 (broken, legacy), SHA-256/BLAKE3 (data integrity), bcrypt/Argon2 (passwords), xxHash/MurmurHash (non-cryptographic, fast).
3mo ago
algorithms intermediate
P vs NP & NP-Completeness
P problems are solvable in polynomial time; NP problems have solutions verifiable in polynomial time. NP-complete problems are the hardest in NP — no polynomial-time algorithm is known.
3mo ago
algorithms advanced
Backtracking
An algorithmic technique that builds solutions incrementally, abandoning a path ('backtracking') when it determines the current path cannot lead to a valid solution.
3mo ago
algorithms advanced
Big-O Notation
PHP 5.0+
6
A mathematical notation describing how an algorithm's time or space requirements grow relative to input size, ignoring constants and lower-order terms.
3mo ago
algorithms intermediate
Bit Manipulation
Using bitwise operators (AND, OR, XOR, NOT, shifts) to manipulate individual bits — enabling compact storage, fast arithmetic, and O(1) set operations.
3mo ago
algorithms intermediate
Dynamic Programming
PHP 5.0+
1
An optimisation technique that solves problems by breaking them into overlapping subproblems, storing results to avoid redundant computation.
3mo ago
algorithms advanced
Graph Algorithms
PHP 5.0+
1
Algorithms for traversing, searching, and finding paths in graphs — BFS for shortest hops, DFS for exploration, Dijkstra for weighted shortest paths.
3mo ago
algorithms advanced
Greedy Algorithms
PHP 5.0+
1
Algorithms that make the locally optimal choice at each step — fast and simple, but only produce the globally optimal solution for problems with the greedy choice property.
3mo ago
algorithms intermediate
Recursion Patterns
PHP 5.0+ Functions that call themselves with smaller inputs — powerful for tree traversal, divide-and-conquer, and mathematical sequences, but requiring careful base cases and stack depth management.
3mo ago
algorithms intermediate
Searching Algorithms
PHP 5.0+
1
Linear search is O(n) and works on any array. Binary search is O(log n) but requires a sorted array. Hash lookup is O(1) and the right choice for most in-memory searches.
3mo ago
algorithms intermediate
Sliding Window
An algorithmic technique that maintains a window of elements over a sequence, expanding or contracting it to find subarrays or substrings satisfying a condition in O(n).
3mo ago
algorithms intermediate
Sorting Algorithms
PHP 5.0+ Algorithms for ordering a collection — ranging from O(n²) simple sorts to O(n log n) comparison sorts and O(n) non-comparison sorts for specific data.
3mo ago
algorithms intermediate
String Algorithms
3
Efficient string searching (KMP, Boyer-Moore, Rabin-Karp), edit distance (Levenshtein), and compression algorithms — foundational for search, diff tools, and bioinformatics.
3mo ago
algorithms advanced
Two-Pointer Technique
An algorithmic pattern using two indices that move through a sorted array to find pairs or subarrays satisfying a condition in O(n) instead of O(n²).
3mo ago
algorithms intermediate