Difference Between Algorithms and Heuristics

1. Algorithms

• A step-by-step, precise, and guaranteed method for solving a problem.

• Always produces the correct solution (if one exists).

• Often requires more time or computation because it explores all necessary steps.

Example:
Binary search, bubble sort, Dijkstra’s algorithm, long division, etc.

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2. Heuristics

• A rule-of-thumb, educated guess, or shortcut strategy.

• Not guaranteed to produce the correct or optimal solution.

• Trades accuracy for speed.

• Useful when problems are too complex or expensive to solve exactly.

Example:
Trial-and-error, greedy choices, “look for patterns”, “choose the most promising option first”.

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Key Differences 

Feature	Algorithm	Heuristic
Guarantee of correctness	✔ Yes	✖ No
Speed	Slower but exact	Faster but approximate
Approach	Systematic & complete	Flexible & intuitive
Use case	When accuracy is required	When speed is more important
Example	Dijkstra’s shortest path	A* using a heuristic estimate

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Example Where Heuristics Are Faster Than Algorithms

🎯 Problem:

Find a word in a dictionary of 100,000 words.

Using an Algorithm (Binary Search):

1. Look at the middle word.

2. Decide whether to go left/right.

3. Repeat until the word is found.

• Exact, guaranteed.

• Worst-case steps:

  $$\log_2(100,000) \approx 17 \text{ comparisons}$$
  

Using a Heuristic (“Jump to likely section”)

Suppose the word is “zebra”.

A human doesn’t start at the middle—they jump directly to the end of the dictionary because:

• Words starting with Z are always near the end.

• This is a heuristic based on knowledge of alphabetical order.

This can take only 1–2 steps, much faster than the full algorithm.

✔ Faster
✖ Not a formal algorithm