Types Of Problems

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 Algorithms are everywhere — from searching your phone contacts to finding the fastest route on Google Maps. But before learning algorithms, it's important to understand what kind of problem you are solving.

Here is a simple guide to the main categories of problems in algorithm design, with clear examples and when to use them.

1. Searching Problems

Searching problems aim to find an element inside a collection.

🔍 Example

Find whether the number 23 exists in a list.

Common Algorithms

  • Linear Search

  • Binary Search

Used In

Search bars, phone contacts, database lookups.

2. Sorting Problems

Sorting problems involve arranging data in ascending or descending order.

🔍Example

Sort the list: [9, 4, 2, 7, 1]

Common Algorithms

  • Bubble Sort

  • Selection Sort

  • Insertion Sort

  • Merge Sort

  • Quick Sort

  • Heap Sort

Used In

Ranking, scheduling, database indexing.

3. Optimization Problems

These problems require finding the best possible solution under specific rules or constraints.

🔍 Examples

  • Shortest path between cities

  • Maximize profit in Knapsack

  • Minimum cost of connecting networks

Used In

Transportation, logistics, networking.

4. Numerical Problems

Numerical problems are based on mathematics and number theory.

🔍 Examples

  • Computing the GCD

  • Prime factorization

  • Fibonacci numbers

  • Root finding

Used In

Cryptography, simulations, mathematics applications.

5. String Processing Problems

These involve working with text, patterns, and characters.

🔍 Examples

  • Check if a string is palindrome

  • Count vowels

  • Pattern matching (KMP, Rabin–Karp)

  • Finding longest repeating substring

Used In

Search engines, bioinformatics, compilers.

6. Graph Problems

Graph problems involve nodes and edges representing connections.

🔍 Examples

  • Shortest path (Dijkstra)

  • Minimum spanning tree (Kruskal, Prim)

  • Cycle detection

  • DFS, BFS

Used In

Social networks, GPS, computer networks.

7. Dynamic Programming Problems

Dynamic programming (DP) solves problems by breaking them into smaller overlapping subproblems.

🔍 Examples

  • 0/1 Knapsack

  • Longest Increasing Subsequence

  • Matrix Chain Multiplication

  • DP Fibonacci

Used In

Game theory, resource optimization, AI.

8. Backtracking Problems

Backtracking tries all possibilities but prunes wrong choices early.

🔍 Examples

  • N-Queens

  • Sudoku solver

  • Maze solving

  • Permutation generation

Used In

Puzzle solving, constraint satisfaction problems.

9. Greedy Problems

Greedy problems follow a strategy of taking the locally best choice at every step.

🔍 Examples

  • Activity selection

  • Fractional knapsack

  • Huffman coding

  • MST algorithms (Kruskal/Prim)

Used In

Compression, scheduling, optimization.

10. Divide and Conquer Problems

These problems break a large task into smaller parts, solve them, and combine the results.

🔍 Examples

  • Merge sort

  • Quick sort

  • Binary search

  • Closest pair (DC method)

Used In

Sorting, searching, computational geometry.

11. Geometric Problems (Computational Geometry)

Geometric problems involve points, shapes, distances, and spatial relationships.

🔍 Examples

  • Closest pair of points

  • Convex hull

  • Line segment intersection

  • Point inside polygon

  • Area/perimeter of shapes

Used In

Graphics, robotics, maps, GIS, gaming.

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