Algorithms are an important problem-solving strategy in cognition. They emphasise careful, step-by-step procedures that prioritise accuracy over speed, helping explain when humans can reliably solve problems—and when limited time or mental resources interfere.

What an Algorithm Is (and Why It Matters)

An algorithm is a methodical procedure for solving a problem that, if followed correctly, will produce a solution.

Algorithms matter in psychology because they illustrate controlled processing: deliberate, effortful thinking that relies on attention and working memory. They contrast with faster approaches that may be less reliable, showing how people trade speed for certainty.

Core Features of Algorithmic Problem-Solving

Systematic search

Algorithms work by organising the search through possible answers so that options are not skipped randomly.

This diagram shows the output of a breadth-first search (BFS): nodes are explored in a fixed, rule-governed order (level by level from the start). It’s a clear example of algorithmic problem-solving because the procedure systematically checks possibilities and keeps track of what has been explored to avoid missing options. Source

• Follow a defined sequence (first, second, third…)

• Apply consistent rules to each option

• Keep track of what has already been tried to avoid repetition

Exhaustiveness and guarantees

A key advantage is that algorithms can be exhaustive.

• If the algorithm is correctly designed and applied, it can guarantee a correct answer

• Guarantees are most realistic in well-defined problems (clear rules, clear goal, limited answer set)

Verification built in

Algorithms often include a way to check whether a candidate answer satisfies the goal conditions.

• The solver compares the attempted solution to the problem’s rules/constraints

• This reduces reliance on “gut feeling” and increases accuracy

When People Use Algorithms

Humans are most likely to use algorithms when:

• The task is rule-based (e.g., formal logic, structured puzzles, clear procedures)

• Accuracy is more important than speed (high-stakes settings)

• The person has sufficient time, motivation, and cognitive resources

• The steps have been practised enough to be applied consistently

Algorithms can also be taught directly (e.g., explicit procedures), which helps explain why instruction can improve performance on certain problem types.

Cognitive Costs and Limits

Algorithmic thinking is reliable but demanding.

Time cost

• Testing possibilities one-by-one can be slow, especially if there are many possibilities (large problem space)

This figure contrasts a balanced binary search tree (many options eliminated quickly) with an unbalanced tree (a near-linear chain). The comparison illustrates why algorithmic procedures can vary dramatically in time cost depending on the structure of the problem space, even when the rule for each step is consistent. Source

Mental effort

• Requires sustained attention and resistance to distraction

• Places demands on working memory (holding steps, rules, and intermediate results)

Real-world constraints

Even when an algorithm exists, people may not use it because:

• They feel pressured to respond quickly

• They lack the knowledge of the correct procedure

• The problem space is too large to search fully within realistic limits

Key AP Psychology Takeaways

• Algorithms solve problems by systematically trying possible solutions, favouring accuracy and rule-following.

• They are most effective in well-defined tasks and least practical when time, attention, or problem size makes exhaustive search unrealistic.

• Understanding algorithms helps explain why some problems are solved reliably through procedure, while others strain cognitive resources.