problem
Főnév
problem
Kiejtés
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problem (tsz. problems)
Főnév
et problem sn
Kiejtés
- IPA: /ˈprɔb.lɛm/
Főnév
problem hn
Főnév
problem sn
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problemet sn
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problem hn (cirill írás проблем)
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problem nn
Főnév
problem (tsz. problems)
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))
2. Sorting Problems
- Bubble Sort (Simple but inefficient, O(n²))
- Merge Sort (Efficient divide-and-conquer approach, O(n log 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.