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When analyzing the runtime of Euclid's algorithm, it turns out that the inputs requiring the most steps are two successive Fibonacci numbers, and the worst case runtime is O(n), where n is the number of digits in the input (see Big O). |
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When analyzing the runtime of this version of Euclid's algorithm, it turns out that the inputs requiring the most steps are two successive Fibonacci numbers, and the worst case requires O(n) divisions, where n is the number of digits in the input (see Big O). |
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The following code shows a Javascript implementation of Euclid's original version shown under algorithm. |
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Euclid originally formulated the problem geometrically, as the problem of finding a common "measure" for two line lengths, and his algorithm proceeded by repeated subtraction of the shorter from the longer segment. This is illustrated in the following Javascript implementation which should work in most web browsers. |
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{a = a - b} |
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{a = a - b} |
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Can be readily used in most browsers. |
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