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Lecture

Algorithm Design: Time Complexity Analysis

Description

This lecture covers algorithms, pseudo-code, data inputs, outputs, internal variables, assignments, and instructions. It also discusses time complexity analysis using examples and notations like n², O(n), and f(n)=O(g(n)). The instructor demonstrates how to calculate the time an algorithm takes to execute for different input sizes.

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Related concepts (27)

Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

Instructions per cycle

In computer architecture, instructions per cycle (IPC), commonly called instructions per clock is one aspect of a processor's performance: the average number of instructions executed for each clock cycle. It is the multiplicative inverse of cycles per instruction. While early generations of CPUs carried out all the steps to execute an instruction sequentially, modern CPUs can do many things in parallel.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Instructions per second

Instructions per second (IPS) is a measure of a computer's processor speed. For complex instruction set computers (CISCs), different instructions take different amounts of time, so the value measured depends on the instruction mix; even for comparing processors in the same family the IPS measurement can be problematic. Many reported IPS values have represented "peak" execution rates on artificial instruction sequences with few branches and no cache contention, whereas realistic workloads typically lead to significantly lower IPS values.

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

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