Here is a probabilistic approach. The algorithm is:
10) Select a random char from the input string.
20) Try to insert the selected char in a random position in the output string.
30) If it can't be inserted because of proximity with the same char, go to 10.
40) Remove the selected char from the input string and go to 10.
50) Continue until there are no more chars in the input string, or the failed attempts are too many.
public static string ShuffleNoSameAdjacent(string input, Random random = null)
{
if (input == null) return null;
if (random == null) random = new Random();
string output = "";
int maxAttempts = input.Length * input.Length * 2;
int attempts = 0;
while (input.Length > 0)
{
while (attempts < maxAttempts)
{
int inputPos = random.Next(0, input.Length);
var outputPos = random.Next(0, output.Length + 1);
var c = input[inputPos];
if (outputPos > 0 && output[outputPos - 1] == c)
{
attempts++; continue;
}
if (outputPos < output.Length && output[outputPos] == c)
{
attempts++; continue;
}
input = input.Remove(inputPos, 1);
output = output.Insert(outputPos, c.ToString());
break;
}
if (attempts >= maxAttempts) throw new InvalidOperationException(
$"Shuffle failed to complete after {attempts} attempts.");
}
return output;
}
Not suitable for strings longer than 1,000 chars!
Update: And here is a more complicated deterministic approach. The algorithm is:
- Group the elements and sort the groups by length.
- Create three empty piles of elements.
- Insert each group to a separate pile, inserting always the largest group to the smallest pile, so that the piles differ in length as little as possible.
- Check that there is no pile with more than half the total elements, in which case satisfying the condition of not having same adjacent elements is impossible.
- Shuffle the piles.
- Start yielding elements from the piles, selecting a different pile each time.
- When the piles that are eligible for selection are more than one, select randomly, weighting by the size of each pile. Piles containing near half of the remaining elements should be much preferred. For example if the remaining elements are 100 and the two eligible piles have 49 and 40 elements respectively, then the first pile should be 10 times more preferable than the second (because 50 - 49 = 1 and 50 - 40 = 10).
public static IEnumerable<T> ShuffleNoSameAdjacent<T>(IEnumerable<T> source,
Random random = null, IEqualityComparer<T> comparer = null)
{
if (source == null) yield break;
if (random == null) random = new Random();
if (comparer == null) comparer = EqualityComparer<T>.Default;
var grouped = source
.GroupBy(i => i, comparer)
.OrderByDescending(g => g.Count());
var piles = Enumerable.Range(0, 3).Select(i => new Pile<T>()).ToArray();
foreach (var group in grouped)
{
GetSmallestPile().AddRange(group);
}
int totalCount = piles.Select(e => e.Count).Sum();
if (piles.Any(pile => pile.Count > (totalCount + 1) / 2))
{
throw new InvalidOperationException("Shuffle is impossible.");
}
piles.ForEach(pile => Shuffle(pile));
Pile<T> previouslySelectedPile = null;
while (totalCount > 0)
{
var selectedPile = GetRandomPile_WeightedByLength();
yield return selectedPile[selectedPile.Count - 1];
selectedPile.RemoveAt(selectedPile.Count - 1);
totalCount--;
previouslySelectedPile = selectedPile;
}
List<T> GetSmallestPile()
{
List<T> smallestPile = null;
int smallestCount = Int32.MaxValue;
foreach (var pile in piles)
{
if (pile.Count < smallestCount)
{
smallestPile = pile;
smallestCount = pile.Count;
}
}
return smallestPile;
}
void Shuffle(List<T> pile)
{
for (int i = 0; i < pile.Count; i++)
{
int j = random.Next(i, pile.Count);
if (i == j) continue;
var temp = pile[i];
pile[i] = pile[j];
pile[j] = temp;
}
}
Pile<T> GetRandomPile_WeightedByLength()
{
var eligiblePiles = piles
.Where(pile => pile.Count > 0 && pile != previouslySelectedPile)
.ToArray();
Debug.Assert(eligiblePiles.Length > 0, "No eligible pile.");
eligiblePiles.ForEach(pile =>
{
pile.Proximity = ((totalCount + 1) / 2) - pile.Count;
pile.Score = 1;
});
Debug.Assert(eligiblePiles.All(pile => pile.Proximity >= 0),
"A pile has negative proximity.");
foreach (var pile in eligiblePiles)
{
foreach (var otherPile in eligiblePiles)
{
if (otherPile == pile) continue;
pile.Score *= otherPile.Proximity;
}
}
var sumScore = eligiblePiles.Select(p => p.Score).Sum();
while (sumScore > Int32.MaxValue)
{
eligiblePiles.ForEach(pile => pile.Score /= 100);
sumScore = eligiblePiles.Select(p => p.Score).Sum();
}
if (sumScore == 0)
{
return eligiblePiles[random.Next(0, eligiblePiles.Length)];
}
var randomScore = random.Next(0, (int)sumScore);
int accumulatedScore = 0;
foreach (var pile in eligiblePiles)
{
accumulatedScore += (int)pile.Score;
if (randomScore < accumulatedScore) return pile;
}
Debug.Fail("Could not select a pile randomly by weight.");
return null;
}
}
private class Pile<T> : List<T>
{
public int Proximity { get; set; }
public long Score { get; set; }
}
This implementation can suffle millions of elements. I am not completely convinced that the quality of the suffling is as perfect as the previous probabilistic implementation, but should be close.
