I was trying to better understand in a common Java shuffle deck of cards algorithm, this piece of code:

// Random for remaining positions. int r = i + rand.nextInt(52 - i);

Why is it necessary to “pad” or add `i`

index to the resultant random number? It looks like as you iterate and add `i`

, by subtracting `i`

, you keep the max possible range of random numbers consistent from 0 to 51, but why not just do:

int r = rand.nextInt(52);

*Full code:*

// Function which shuffle and print the array public static void shuffle(int card[], int n) { Random rand = new Random(); for (int i = 0; i < n; i++) { // Random for remaining positions. int r = i + rand.nextInt(52 - i); //swapping the elements int temp = card[r]; card[r] = card[i]; card[i] = temp; } }

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## Answer

The Fisherâ€“Yates shuffle works as follows:

- Take a random element from the array, and swap it into first place
- Take a random element from
*remaining*values, and swap it into second place - Take a random element from
*remaining*values, and swap it into third place *and so on*

It is the “*remaining* values” part you’re asking about.

E.g. after 10 iterations, you have swapped 10 random values into the first 10 positions of the array, so for the next iteration you need a random position in range 10-end, hence the offset of 10 from a random range of 10 less than full range, aka `i + rand.nextInt(52 - i)`

.

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