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.
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Dijkstra's Shortest Path Algorithm PHP 5.3+ 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.
1mo 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.
1mo ago
algorithms intermediate
A* Pathfinding Algorithm
Heuristic search algorithm that finds the lowest-cost path using f(n)=g(n)+h(n), widely used in maps and game AI.
2mo 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.
2mo 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.
2mo 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).
2mo 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.
2mo 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.
2mo ago
algorithms advanced
Big-O Notation PHP 5.0+ A mathematical notation describing how an algorithm's time or space requirements grow relative to input size, ignoring constants and lower-order terms.
2mo 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.
2mo ago
algorithms intermediate
Dynamic Programming PHP 5.0+ An optimisation technique that solves problems by breaking them into overlapping subproblems, storing results to avoid redundant computation.
2mo ago
algorithms advanced
Graph Algorithms PHP 5.0+ Algorithms for traversing, searching, and finding paths in graphs — BFS for shortest hops, DFS for exploration, Dijkstra for weighted shortest paths.
2mo ago
algorithms advanced
Greedy Algorithms PHP 5.0+ 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.
2mo 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.
2mo ago
algorithms intermediate
Searching Algorithms PHP 5.0+ 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.
2mo 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).
2mo 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.
2mo ago
algorithms intermediate
String Algorithms
Efficient string searching (KMP, Boyer-Moore, Rabin-Karp), edit distance (Levenshtein), and compression algorithms — foundational for search, diff tools, and bioinformatics.
2mo 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).
2mo ago
algorithms intermediate