Algorithm Paradigms

1. Divide and Conquer

• Break down a problem into smaller sub-problems
• Solve each sub-problem recursively
• Combine the solutions to the sub-problems to solve the original problem
• Examples: Merge Sort, Quick Sort, Binary Search

2. Dynamic Programming

• Break down a problem into smaller sub-problems
• Solve each sub-problem only once and store the solution
• Use the stored solutions to solve larger problems
• Examples: Fibonacci Series, Longest Common Subsequence, Shortest Path Problems

3. Greedy Algorithm

• Make the locally optimal choice at each step
• Hope that the local choices will lead to a global optimum solution
• Examples: Huffman Coding, Activity Selection Problem, Fractional Knapsack Problem

4. Backtracking

• Explore all possible solutions by recursively adding choices
• Backtrack when a dead end is reached
• Examples: N-Queens Problem, Sudoku, Maze Solving

5. Brute Force

• Try all possible solutions
• Check each solution to see if it satisfies the problem constraints
• Examples: Finding the maximum or minimum value in an array, Checking if a string is a palindrome

6. Recursive Algorithm

• Solve a problem by breaking it down into smaller instances of the same problem
• Use recursive function calls to solve the problem
• Examples: Factorial, Fibonacci Series, Tree Traversal