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<p>On one hand, <strong>it's difficult to eliminate interference from the testing environment</strong>. Hardware configurations can affect algorithm performance. For example, algorithm <code>A</code> might run faster than <code>B</code> on one computer, but the opposite result may occur on another computer with different configurations. This means we would need to test on a variety of machines to calculate average efficiency, which is impractical.</p>
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<p>On the other hand, <strong>conducting a full test is very resource-intensive</strong>. As the volume of input data changes, the efficiency of the algorithms may vary. For example, with smaller data volumes, algorithm <code>A</code> might run faster than <code>B</code>, but the opposite might be true with larger data volumes. Therefore, to draw convincing conclusions, we need to test a wide range of input data sizes, which requires significant computational resources.</p>
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<h2 id="212-theoretical-estimation">2.1.2 Theoretical estimation<a class="headerlink" href="#212-theoretical-estimation" title="Permanent link">¶</a></h2>
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<p>Due to the significant limitations of actual testing, we can consider evaluating algorithm efficiency solely through calculations. This estimation method is known as "asymptotic complexity analysis," or simply "complexity analysis."</p>
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<p>Due to the significant limitations of actual testing, we can consider evaluating algorithm efficiency solely through calculations. This estimation method is known as <u>asymptotic complexity analysis</u>, or simply <u>complexity analysis</u>.</p>
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<p>Complexity analysis reflects the relationship between the time and space resources required for algorithm execution and the size of the input data. <strong>It describes the trend of growth in the time and space required by the algorithm as the size of the input data increases</strong>. This definition might sound complex, but we can break it down into three key points to understand it better.</p>
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<ul>
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<li>"Time and space resources" correspond to "time complexity" and "space complexity," respectively.</li>
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<li>"Time and space resources" correspond to <u>time complexity</u> and <u>space complexity</u>, respectively.</li>
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<li>"As the size of input data increases" means that complexity reflects the relationship between algorithm efficiency and the volume of input data.</li>
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<li>"The trend of growth in time and space" indicates that complexity analysis focuses not on the specific values of runtime or space occupied but on the "rate" at which time or space grows.</li>
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</ul>
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