Why is fishing the most useful shuffling algorithm?

Question

Could you say that the most up-to-date version of the fishing nursery is the most unbiased shuffling algorithm? How would you explain that each element in an array has a probability that 1 / n is in its original location?

Answer 1

Given the ideal pseudo-random number generator ( Mersenne Twister is very close), the Fisher-Yates algorithm is completely unbiased in that each permutation has an equal probability of occurrence. This is easy to prove using induction. The Fisher-Jace algorithm can be written recursively as follows (in the pseudocode of Python syntax):

def fisherYatesShuffle(array):
    if len(array) < 2:
        return

    firstElementIndex = uniform(0, len(array))
    swap(array[0], array[firstElementIndex])
    fisherYatesShuffle(array[1:])

firstElementIndex. , .

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Answer 2

(Modern, aka "Knuth" ) Fisher-Yates shuffle -

• O (n) O (1) O (0)
• unbiased ( )
• / , , .

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