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Problem Solving Approaches

#technology#algorithms#problem-solving

Updated: 2026-09-24

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This note lists the main approaches you can reach for when an algorithmic problem does not give way at first. It opens with two reference articles on how to find a solution, then walks through nine strategies side by side. Brute force tries every option. Greedy takes the best local choice. Divide and conquer splits a problem and recombines the parts. Dynamic programming stores results it already computed. Backtracking and branch and bound explore choices and prune the bad ones. Graph algorithms and bit manipulation cover specific shapes of input. The last entry, machine learning, learns patterns from data instead of coding fixed rules. Read each one for its short description and its stated downside, then match it to the problem in front of you.

Table of Contents

References

Approaches

Brute Force

  • Try every possible option to find the right answer
  • Suitable when the data is small or no better method is known yet
  • Downside: slow on large data

Greedy

  • At each step, pick the best option available now without regard for the future
  • Applies when the problem can be solved in small steps and earlier choices do not much affect later ones
  • Note: it does not always produce the optimal result

Divide and Conquer

  • Split a large problem into smaller parts, solve each part, then combine the results
  • Useful when the problem can be split while preserving its nature and the results are easy to combine

Dynamic Programming

  • Store the results of steps already computed to avoid recomputation
  • Use when the problem has many repeated parts that can be broken into related subproblems

Backtracking

  • Try a choice; if it does not fit, go back and try another
  • Use when you want to find all solutions or there are many possibilities but the unreasonable ones can be pruned

Branch and Bound

  • Similar to backtracking but adds upper and lower bounds to prune unnecessary branches
  • Applies when you need an optimal solution and can determine the search range in advance

Graph Algorithms

  • Traverse vertices and edges to find the solution
  • Use when the problem can be modeled as a graph

Bit Manipulation

  • Use bit-level operations to process data faster
  • Useful when working with binary numbers or optimizing memory

Machine Learning Approach

  • Use data to learn the patterns instead of writing a fixed algorithm
  • Applies when the problem is too complex to write an algorithm for or when you need to predict from existing data

See also: Algorithm Development · Enumeration Problems · Learning Resources