# Fisher–Yates shuffling algorithm

This is a simple implementation of one of the best shuffling algorithms out there. The Fisher-Yates shuffling algorithm is unbiased (every permutation is equally likely), runs in linear time, and requires constant space.

The algorithm logic is quite simple: start from one of the ends of the array and pick one random element from the unsorted part of the array (including the current element) and swap it with the current element until the opposite end is reached. This is my implementation of the abovementioned algorithm in Java.

public static void shuffle(List<?> list) {
for (int i = list.size() - 1; i > 0; i--) {
int index = (int) (Math.random() * (i + 1));
Collections.swap(list, i, index);
}
}


With Java you can use Collections.shuffle(List) which is usually a Fisher–Yates implementation.

## Random permutations

It should be clear without saying, but this algorithm can be used to generate random permutations of the elements of a list (that’s what shuffling means). If you are looking for all permutations in random order without repetition, you could use either Heap’s algorithm or Narayana Pandita’s algorithm and shuffle the resulting permutation list with Fisher–Yates.