Amortized Analysis

Amortized analysis is a mathematical technique employed in the realm of computer science and algorithm analysis. It offers a more refined and comprehensive approach to evaluating the time complexity of algorithms that involve a sequence of operations, especially those with variable costs.

Especially useful for data structures changes their size and structure dynamically. Example including dynamic arrays, hash tables, self-balancing binary search trees, and splay trees.

Types of Amortized Analysis

• Aggregate Analysis

  Aggregate analysis is the simplest method of amortized analysis. It involves determining the total cost of a sequence of operations and then dividing this cost by the number of operations to determine the amortized cost.

• Accounting Method

  This method involves assigning “credits” and “debits” to different operations in a way that the total credits always cover the total cost of the operations. The goal is to distribute the cost of expensive operations across multiple operations, making the average cost more predictable.

• Potential Method

  The potential method defines a “potential function” that represents the stored energy in a data structure after each operation. Changes in potential are used to offset the actual cost of operations, ensuring that the amortized cost remains relatively constant.

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