Shuffle array in C

Question

I\'m looking for a function in ANSI C that would randomize an array just like PHP\'s shuffle() does. Is there such a function or do I have to write it on my own

Answer 1

I’ll just echo Neil Butterworth’s answer, and point out some trouble with your first idea:

You suggested,

Iterate through the array for, say, 100 times and exchange a random index with another random index

Make this rigorous. I'll assume the existence of randn(int n), a wrapper around some RNG, producing numbers evenly distributed in [0, n-1], and swap(int a[], size_t i, size_t j),

swap(int a[], size_t i, size_t j) {
  int temp = a[i]; a[i] = a[j]; a[j] = temp;
}

which swaps a[i] and a[j]. Now let’s implement your suggestion:

void silly_shuffle(size_t n, int a[n]) {
    for (size_t i = 0; i < n; i++)
        swap(a, randn(n), randn(n)); // swap two random elements
}

Notice that this is not any better than this simpler (but still wrong) version:

void bad_shuffle(size_t n, int a[n]) {
    for (size_t i = 0; i < n; i++)
        swap(a, i, randn(n));
}

Well, what’s wrong? Consider how many permutations these functions give you: With n (or 2×n for silly_shuffle) random selections in [0, n-1], the code will “fairly” select one of n² (or 2×n²) ways to shuffle the deck. The trouble is that there are n! = n×(n-1)×⋯×2×1 possible arrangements of the array, and neither n² nor 2×n² is a multiple of n!, proving that some permutations are more likely than others.

The Fisher-Yates shuffle is actually equivalent to your second suggestion, only with some optimizations that change (performance = 0, complexity = serious) to (performance = very good, complexity = pretty simple). (Actually, I’m not sure that a faster or simpler correct version exists.)

void fisher_yates_shuffle(size_t n, int a[n]) {
    for (size_t i = 0; i < n; i++)
        swap(a, i, i+randn(n-1-i)); // swap element with random later element
}

ETA: See also this post on Coding Horror.