What are the four types of algorithms?

Algorithms can be classified into several types based on their approach to solving problems. While there are many ways to categorize algorithms, four fundamental types are commonly discussed:

1. Divide and Conquer Algorithms

• What It Does: Breaks the problem into smaller subproblems, solves each subproblem recursively, and combines the results to solve the original problem.
• Key Features:
  • Problem is divided into smaller, manageable parts.
  • Each subproblem is solved independently.
  • Solutions are merged to form the final result.
• Examples:
  • Merge Sort: Divides an array into halves, sorts them recursively, and merges the sorted halves.
  • Quick Sort: Partitions the array around a pivot and sorts each partition.
  • Binary Search: Divides the search space in half repeatedly to find the target.
• Applications: Sorting, searching, computational geometry.

2. Greedy Algorithms

• What It Does: Builds the solution step by step by choosing the locally optimal option at each step, aiming for a global optimum.
• Key Features:
  • No backtracking.
  • Decisions are made based on current information without considering future consequences.
• Examples:
  • Huffman Coding: Constructs an optimal binary tree for data compression.
  • Dijkstra’s Algorithm: Finds the shortest path in a graph with non-negative weights.
  • Activity Selection: Selects the maximum number of activities that don’t overlap.
• Applications: Resource allocation, scheduling, optimization problems.

3. Dynamic Programming Algorithms

• What It Does: Solves problems by breaking them into overlapping subproblems, solving each subproblem only once, and storing the results for reuse (memoization).
• Key Features:
  • Optimal substructure: The solution to the larger problem depends on solutions to its smaller subproblems.
  • Overlapping subproblems: Subproblems are solved multiple times.
• Examples:
  • Knapsack Problem: Determines the maximum value that can be achieved within a weight limit.
  • Longest Common Subsequence: Finds the length of the longest subsequence common to two strings.
  • Fibonacci Sequence: Computes Fibonacci numbers efficiently using memoization.
• Applications: Optimization problems, text analysis, bioinformatics.

4. Backtracking Algorithms

• What It Does: Explores all possible solutions to a problem by incrementally building a solution and abandoning paths that fail to satisfy the constraints.
• Key Features:
  • Uses recursion to explore solutions.
  • Prunes invalid or suboptimal paths early.
• Examples:
  • N-Queens Problem: Places N queens on a chessboard such that no two queens threaten each other.
  • Sudoku Solver: Fills in a Sudoku grid by testing possible numbers and backtracking when rules are violated.
  • Subset Sum Problem: Determines if a subset of numbers adds up to a given value.
• Applications: Constraint satisfaction problems, combinatorial problems.

Summary of the Four Types

How to Choose the Right Algorithm

1. Problem Type: Does the problem involve optimization, constraints, or recursion?
2. Input Size: Is the problem large and needs efficient solutions?
3. Constraints: Does the problem require all solutions or just one optimal solution?

Suggested Resources

• Grokking Data Structures & Algorithms for Coding Interviews (Learn More): Covers the implementation and application of these algorithm types. - Grokking the Coding Interview: Patterns for Coding Questions (Learn More): Focuses on patterns, including divide and conquer, dynamic programming, and more. - Mastering the 20 Coding Patterns (Explore): Highlights patterns and their use cases, helping you recognize the type of algorithm required.

These four types of algorithms are fundamental to solving a wide range of computational problems and are essential knowledge for technical interviews and software development.