11-17-2025, 01:18 PM
Thread 3 — Advanced Algorithmic Thinking
Divide-and-Conquer, Dynamic Programming & Greedy Strategies
Mastering the Core Strategies Behind Computer Science
Advanced algorithmic thinking isn’t about memorising code — it’s about
learning the mental frameworks that power efficient problem-solving.
In this thread, we explore the three most important algorithmic paradigms
used in programming, data science, AI, and computational mathematics.
1. Divide-and-Conquer — Solving Big Problems by Breaking Them Apart
Divide-and-conquer works by splitting a large problem into smaller
subproblems, solving each independently, and combining their results.
Examples include:
• Merge Sort
• Quick Sort
• Binary Search
• Fast Fourier Transform (FFT)
Why it works:
By reducing the size of the problem at each stage, algorithms often reach
logarithmic or near-linear efficiency.
Core structure:
1. Divide
2. Recurse
3. Combine
2. Dynamic Programming — When Subproblems Reoccur
Dynamic Programming (DP) is used when a problem can be broken down into
overlapping subproblems — meaning the same work would be repeated
multiple times unless results are stored.
Common examples:
• Fibonacci sequence
• Shortest paths (Dijkstra, Bellman-Ford variations)
• Knapsack optimisation
• Sequence alignment in bioinformatics
Why it works:
DP saves previous results in a table (memoisation or tabulation), turning
exponential brute-force problems into efficient polynomial-time solutions.
Key ideas:
• Optimal substructure
• Overlapping subproblems
• Storing results to avoid recomputation
3. Greedy Algorithms — Choosing the Best Option at Each Step
Greedy algorithms build a solution step by step, always choosing what
looks like the "best" immediate option, without reconsidering earlier
choices.
Examples:
• Huffman coding
• Activity selection
• Minimum spanning trees (Prim’s, Kruskal’s)
• Making change (when currency is canonical)
Why it works:
Greedy strategies are extremely fast — often O(n log n) or better — because
they avoid exploring multiple paths.
However:
They only work when the problem exhibits the greedy-choice property —
meaning local optimisation leads to global optimisation.
When this isn’t true, greedy methods fail.
4. When to Use Each Strategy
Divide-and-conquer
• Recursive structure
• Independent subproblems
• Combining results is easy
Dynamic programming
• Overlapping subproblems
• Need for optimal solutions
• State transitions can be defined
Greedy algorithms
• Local choices reveal global optimum
• Need for speed
• Structure is simple (matroids, trees, intervals)
Choosing the right paradigm is one of the most important skills in
computational thinking.
5. Practical Examples That Show the Difference
Shortest Path Problem:
• Greedy → Dijkstra’s uses the best next choice
• DP → Floyd–Warshall uses stored subpaths
• Divide-and-Conquer → can be used for spatial partitioning
String Problems:
• DP → Edit distance, longest common subsequence
• Divide-and-Conquer → Efficient parallel string operations
• Greedy → Lexicographically smallest string construction
Seeing the same problem through multiple paradigms is the key to mastery.
Final Thoughts
These three paradigms form the backbone of modern algorithm design.
From AI models to scientific simulations, efficient systems rely on
these strategies to handle complexity, scale computation, and extract
structure from difficult problems.
Members who understand these approaches will find that even the most
challenging programming tasks become manageable, predictable, and
surprisingly elegant.
Divide-and-Conquer, Dynamic Programming & Greedy Strategies
Mastering the Core Strategies Behind Computer Science
Advanced algorithmic thinking isn’t about memorising code — it’s about
learning the mental frameworks that power efficient problem-solving.
In this thread, we explore the three most important algorithmic paradigms
used in programming, data science, AI, and computational mathematics.
1. Divide-and-Conquer — Solving Big Problems by Breaking Them Apart
Divide-and-conquer works by splitting a large problem into smaller
subproblems, solving each independently, and combining their results.
Examples include:
• Merge Sort
• Quick Sort
• Binary Search
• Fast Fourier Transform (FFT)
Why it works:
By reducing the size of the problem at each stage, algorithms often reach
logarithmic or near-linear efficiency.
Core structure:
1. Divide
2. Recurse
3. Combine
2. Dynamic Programming — When Subproblems Reoccur
Dynamic Programming (DP) is used when a problem can be broken down into
overlapping subproblems — meaning the same work would be repeated
multiple times unless results are stored.
Common examples:
• Fibonacci sequence
• Shortest paths (Dijkstra, Bellman-Ford variations)
• Knapsack optimisation
• Sequence alignment in bioinformatics
Why it works:
DP saves previous results in a table (memoisation or tabulation), turning
exponential brute-force problems into efficient polynomial-time solutions.
Key ideas:
• Optimal substructure
• Overlapping subproblems
• Storing results to avoid recomputation
3. Greedy Algorithms — Choosing the Best Option at Each Step
Greedy algorithms build a solution step by step, always choosing what
looks like the "best" immediate option, without reconsidering earlier
choices.
Examples:
• Huffman coding
• Activity selection
• Minimum spanning trees (Prim’s, Kruskal’s)
• Making change (when currency is canonical)
Why it works:
Greedy strategies are extremely fast — often O(n log n) or better — because
they avoid exploring multiple paths.
However:
They only work when the problem exhibits the greedy-choice property —
meaning local optimisation leads to global optimisation.
When this isn’t true, greedy methods fail.
4. When to Use Each Strategy
Divide-and-conquer
• Recursive structure
• Independent subproblems
• Combining results is easy
Dynamic programming
• Overlapping subproblems
• Need for optimal solutions
• State transitions can be defined
Greedy algorithms
• Local choices reveal global optimum
• Need for speed
• Structure is simple (matroids, trees, intervals)
Choosing the right paradigm is one of the most important skills in
computational thinking.
5. Practical Examples That Show the Difference
Shortest Path Problem:
• Greedy → Dijkstra’s uses the best next choice
• DP → Floyd–Warshall uses stored subpaths
• Divide-and-Conquer → can be used for spatial partitioning
String Problems:
• DP → Edit distance, longest common subsequence
• Divide-and-Conquer → Efficient parallel string operations
• Greedy → Lexicographically smallest string construction
Seeing the same problem through multiple paradigms is the key to mastery.
Final Thoughts
These three paradigms form the backbone of modern algorithm design.
From AI models to scientific simulations, efficient systems rely on
these strategies to handle complexity, scale computation, and extract
structure from difficult problems.
Members who understand these approaches will find that even the most
challenging programming tasks become manageable, predictable, and
surprisingly elegant.