What is the method for discovering the recurrence equation of an algorithm?

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The method for discovering the recurrence equation of an algorithm typically involves analyzing the algorithm to see how many basic operations it performs and how many times it performs them. This analysis can often be done using a technique called "recursion tree" or "substitution method". Once the number of operations and their frequency are determined, a recurrence equation can be derived that represents the running time of the algorithm in terms of its input size. The recurrence equation can then be solved using various techniques, such as iteration or the master theorem, to determine the asymptotic behavior of the algorithm.