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Algorithmic thinking is a problem-solving strategy that involves breaking down complex problems into smaller, manageable parts, and representing them using abstract structures, such as trees, graphs, or other mathematical constructs. This approach is commonly used in computer science, mathematics, and engineering to develop efficient and effective solutions to real-world problems.

The term "algorithm" was first used by the 9th-century Persian mathematician Muhammad ibn Musa al-Khwarizmi, who introduced the concept of using a series of steps to solve mathematical problems. Over time, the term evolved to encompass a broad range of computational and mathematical techniques for automating decision-making and problem-solving processes.

Algorithmic thinking involves several key components, including:

1. Declarative problem definition: Clearly defining the problem to be solved, including the input, output, and constraints.

2. Abstract data structure representation: Representing the problem as a mathematical structure, such as a graph or tree, to facilitate analysis and solution development.

3. Recursive or iterative solution development: Breaking down the problem into smaller sub-problems, and using recursive or iterative techniques to find a solution.

4. Proof and verification: Verifying the correctness of the solution, and ensuring that it meets the specified problem constraints.

Algorithmic thinking is a fundamental aspect of many fields, including artificial intelligence, data analysis, computer graphics, and software engineering. By breaking down complex problems into smaller, more manageable parts, algorithmic thinking enables the development of efficient, effective, and scalable solutions.