Shuffling

Shuffling is a procedure used to randomize an array.

The key property is that each item should have an equal probability to end up in any index.

Solution

The recommended (simple) algorithm is the Fisher–Yates shuffle. Its time complexity is O(n). It can even be done inplace.

You go from 0 - (n-1) and at each index i pick a random number between 0 - n-i and move the element at the result into the i + thisRandomNumberth location in the array.

Maintains Key Property

It maintains that key property as:

Probablility any item makes it to the first position
= 1/n

Probablility any item makes it into the second position 
=  didn't make it into the first * makes it into the second
=  (n-1)/(n) * 1/(n-1) = 1/n   

... so on

Has complexity O(n)

Remember random number generation / assiging an item to an array is O(1), so its just n iteration of O(1)

Code

function shuffleInPlace<T>(array: T[]): T[] {
  // if it's 1 or 0 items, just return
  if (array.length <= 1) return array;

  // For each index in array
  for (let i = 0; i < array.length; i++) {

    // choose a random not-yet-placed item to place there
    // must be an item AFTER the current item, because the stuff
    // before has all already been placed
    const randomChoiceIndex = getRandom(i, array.length - 1);

    // place our random choice in the spot by swapping
    [array[i], array[randomChoiceIndex]] = [array[randomChoiceIndex], array[i]];
  }

  return array;
}

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