6. Input Size and Running Time
Efficiency in algorithm performance is evaluated based on input size and basic operations to compute running time functions. Worst-case analysis provides an upper bound on resource consumption while understanding input characteristics is crucial for algorithm design. Average case analysis, although appealing, presents challenges in estimation, rendering worst-case analysis a practical focus in algorithm evaluation.
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What we have learnt
- The running time of an algorithm depends on the size of the input.
- Worst-case the analysis is essential to determine the maximum time an algorithm may take.
- Input size can vary depending on the nature of the problem and can be defined in terms of properties such as number of digits in arithmetic operations.
Key Concepts
- -- Input Size
- The measure of the amount of space needed to represent the problem's distribution, typically correlated with the number of elements such as in an array.
- -- Worst Case Analysis
- An evaluation of the maximum time an algorithm can take, based on the least favorable input condition.
- -- Average Case Analysis
- An assessment of the expected time taken by an algorithm when inputs are distributed uniformly, often difficult to compute accurately.
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