Üdvözlöm, Ön a problem szó jelentését keresi. A DICTIOUS-ban nem csak a problem szó összes szótári jelentését megtalálod, hanem megismerheted az etimológiáját, a jellemzőit és azt is, hogyan kell a problem szót egyes és többes számban mondani. Minden, amit a problem szóról tudni kell, itt található. A problem szó meghatározása segít abban, hogy pontosabban és helyesebben fogalmazz, amikor beszélsz vagy írsz. Aproblem és más szavak definíciójának ismerete gazdagítja a szókincsedet, és több és jobb nyelvi forráshoz juttat.
Classic computer science problems have been widely studied and solved using various algorithms, data structures, and computational techniques. Here’s a list of some well-known problems and their solutions:
1. Searching Problems
Binary Search (Efficient search in a sorted list, O(log n))
Linear Search (Simple but inefficient for large datasets, O(n))
Quick Sort (Fast in practice, O(n log n) average case)
Heap Sort (Uses a heap structure, O(n log n))
3. Graph Problems
Shortest Path Problem (Solved by Dijkstra’s Algorithm, Bellman-Ford, A*)
Minimum Spanning Tree (MST) (Solved by Kruskal’s and Prim’s algorithms)
Topological Sorting (Solved using Kahn’s algorithm or DFS)
Graph Traversal (Solved using BFS and DFS)
4. Dynamic Programming Problems
Fibonacci Sequence (Solved using memoization or bottom-up DP)
Knapsack Problem (0/1 Knapsack and Fractional Knapsack)
Longest Common Subsequence (LCS)
Matrix Chain Multiplication
Subset Sum Problem
Edit Distance (String Similarity)
Coin Change Problem
5. Computational Geometry Problems
Convex Hull Problem (Solved using Graham’s scan or Jarvis’s march)
Closest Pair of Points (Solved using Divide and Conquer)
Line Intersection Problem (Sweep line algorithm)
6. String Processing Problems
Pattern Matching (Solved by KMP, Rabin-Karp, Boyer-Moore algorithms)
Suffix Array and Suffix Tree Problems (Used for fast substring search)
Palindrome Checking (Manacher’s Algorithm for longest palindromic substring)
7. Number Theory and Cryptography
Greatest Common Divisor (GCD) (Solved using Euclidean algorithm)
Primality Testing (Miller-Rabin, AKS primality test)
Integer Factorization (Pollard’s rho algorithm)
Modular Exponentiation (Used in cryptography)
8. Artificial Intelligence and Machine Learning
Game Playing (Minimax Algorithm) (Used in chess, tic-tac-toe, etc.)
Neural Networks (Backpropagation Algorithm)
Clustering (K-Means Algorithm)
Decision Trees and Random Forests
9. Parallel and Distributed Computing
MapReduce (Used for distributed computing)
Load Balancing Algorithms
Synchronization Problems (Solved using semaphores, locks)
10. Computational Complexity and NP-Hard Problems
Traveling Salesman Problem (TSP) (Solved using Dynamic Programming or Approximation Algorithms)
Graph Coloring Problem (Backtracking or Greedy approaches)
Boolean Satisfiability Problem (SAT) (Solved using the DPLL algorithm)
These problems have been extensively studied, and efficient solutions exist for most of them. However, for NP-hard problems, exact solutions may not be feasible, and approximations or heuristics are used.