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A self-balancing AVL tree maintains near-perfect binary search tree height after each insertion or deletion by ensuring that for any given node, the height difference between its left and right subtrees is at most one. This property prevents the performance degradation associated with skewed binary search trees. The core implementation revolves ...

LRU vs. LFU Eviction PoliciesLeast Recently Used (LRU) and Least Frequently Used (LFU) are common cache eviction strategies. LRU tracks the time since last access, evicting the oldest entry when capacity is reached. LFU prioritizes access frequency, evicting entries with the lowest hit count. When multiple entries share the same minimum frequen ...

Prefix Matching and Keyboard Layout Reconstruction This problem involves identifying possible next characters based on a given prefix and mapping them to a specific $4 \times 8$ grid layout. The core task is to filter a list of strings that start with a specific sequence and mark the character that immediately follows that sequence. #include &l ...

Self-Balancing Tree Structures Self-balancing binary search trees maintain logaritmhic height during insertions and deletions. This ensures efficietn search, insertion, and deletion operations. Below are implementations for three common variants: SBT, Treap, and Splay trees. Size Balanced Tree (SBT) #include <iostream> #include <cstdli ...

Hash Table Implementation #include <stdio.h> #include <stdlib.h> #include <string.h> #define TABLE_SIZE 20 typedef struct { int key; char* value; } KeyValue; typedef struct { void* data; int count; } Collection; typedef struct { KeyValue* slots[TABLE_SIZE]; } SimpleHashMap; SimpleHashMap* createMap() { ...

Arrays represent a fundamental data structure in C++ that stores collections of elements of the same type in contiguous memory locations. Each element can be accessed through its unique index, enabling efficient data manipulation and storage operations. Array Fundamentals A one-dimensional array organizes elements in a linear sequence. The key ...

Factorization into Factorial Divisors Given integers (n) and (m) where (1 \le m \le n!) and (n \le 20), decompose (m) into a sum of at most (n) divisors of (n!). A solution is guaranteed to exist. Define a sequence (d_i = \frac{n!}{i!}) for (i) from 1 to (n). By iterating downwards from (i=n) to (1) and greedily subtracting the largest possible ...

Core Mechanics and Hashing Python's set type delivers an unordered collection of distinct objects. Its underlying architecture relies on a hash table, which enables near-constant time complexity for insertion, lookup, and deletion operations. Hash Table Fundamentals A hash table maps keys to array indices using a deterministic hashing algorithm ...

Two-Dimensional Arrays Declaration The syntax for declaring a two-dimensional array is: storage_class data_type array_name[rows][columns]; int matrix[2][3] = {1, 2, 3, 4, 5, 6}; // Declares a 2x3 integer matrix Accessing Elements Elements are accessed using array_name[row_index][column_index], where indices start from zero. Note: Both row and ...

Vector Class Framework The basic framework for our custom vector implementation inculdes three main pointers: template<class T> class vector { private: iterator _start = nullptr; // Points to beginning of data iterator _finish = nullptr; // Points to end of valid data iterator _endOfStorage = nullptr; // Points to end of stora ...