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Computational complexity is a branch of computer science that studies the resources required for algorithms to solve problems, focusing on time and space as primary metrics. It categorizes problems based on their inherent difficulty and the efficiency of the best possible algorithms that solve them, providing a framework for understanding what can be computed feasibly.
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Time complexity is a computational concept that measures the amount of time an algorithm takes to complete as a function of the length of the input. It provides a high-level understanding of the efficiency of an algorithm, helping in the comparison and selection of algorithms based on performance criteria.
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Space complexity refers to the amount of working storage an algorithm needs, considering both the fixed part and the variable part that depends on the input size. It is crucial for evaluating the efficiency of algorithms, especially when dealing with large datasets or limited memory resources.
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Algorithm efficiency refers to the measure of the computational resources required by an algorithm to solve a problem, typically in terms of time and space complexity. It is crucial for optimizing performance, especially in large-scale applications where resource constraints are significant.
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Big O notation is a mathematical concept used in computer science to describe the upper bound of an algorithm's running time or space requirements in terms of input size. It provides a high-level understanding of the algorithm's efficiency and scalability, allowing for the comparison of different algorithms regardless of hardware or implementation specifics.
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Problem solving is the process of identifying a challenge or obstacle and developing effective strategies to overcome it, often involving critical thinking and decision-making skills. It requires a clear understanding of the problem, creative thinking to generate solutions, and the ability to implement and evaluate the chosen solution effectively.
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Resource allocation is the strategic distribution of available assets to various projects or departments to optimize efficiency and achieve organizational goals. It involves decision-making processes to ensure that limited resources are used effectively to maximize output and minimize waste.
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Scalability refers to the ability of a system, network, or process to handle a growing amount of work or its potential to accommodate growth. It is a critical factor in ensuring that systems can adapt to increased demands without compromising performance or efficiency.
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Gustafson's Law posits that the potential speedup of a parallel computing system is determined by the proportion of the problem that can be parallelized, rather than the fixed size of the problem. It emphasizes scalability, suggesting that as more processors are added, larger problems can be solved in the same amount of time, which contrasts with Amdahl's Law that focuses on fixed workloads.
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