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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 ...

Problem A: Minimum Steps to Visit All Points Given a array of distinct integers x₁, x₂, ..., xₙ and a starting position s on the number line. You can move left or right by one unit each step. Find the minimum number of steps required to visit all positions in the array, starting from position s. The optimal solution involves visiting the endpoi ...

std::tuple is a fixed-size collection of heterogeneous values introduced in C++11. It serves as a generalized pair, allowing developers to group disparate types without defining a custom struct. The template signature accepts a variadic pack of types: template<class... Types> class tuple; Unlike dynamic containers, its layout and size ar ...

The java.util.Collections class is a fundamental utility within the Java platform, providing a suite of static methods designed to perform various operations on collection objects. Described as offering "polymorphic algorithms," this class simplifies common tasks such as sorting, searching, modifying, and creating specialized versions ...