Fastest way to check if an array is sorted

Question

Considering there is an array returned from a function which is of very large size.

What will be the fastest approach to test if the array is sorted?

A simplest approach will be:

/// <summary>
/// Determines if int array is sorted from 0 -> Max
/// </summary>
public static bool IsSorted(int[] arr)
{
for (int i = 1; i < arr.Length; i++)
{
    if (arr[i - 1] > arr[i])
    {
    return false;
    }
}
return true;
}

Answer 1

You will have to visit each element of the array to see if anything is unsorted.

Your O(n) approach is about as fast as it gets, without any special knowledge about the likely state of the array.

Your code specifically tests if the array is sorted with smaller values at lower indices . If that is not what you intend, your if becomes slightly more complex. Your code comment does suggest that is what you're after.

If you were to have special knowledge of the probable state (say, you know it's generally sorted but new data might be added to the end), you can optimize the order in which you visit array elements to allow the test to fail faster when the array is unsorted.

You can leverage knowledge of the hardware architecture to check multiple parts of the array in parallel by partitioning the array, first comparing the boundaries of the partition (fail fast check) and then running one array partition per core on a separate thread (no more than 1 thread per CPU core). Note though that if a array partition is much smaller than the size of a cache line, the threads will tend to compete with each other for access to the memory containing the array. Multithreading will only be very efficient for fairly large arrays.

Answer 2

Faster approach, platform target: Any CPU, Prefer 32-bit.
A sorted array with 512 elements: ~25% faster.

static bool isSorted(int[] a)
{
    int j = a.Length - 1;
    if (j < 1) return true;
    int ai = a[0], i = 1;
    while (i <= j && ai <= (ai = a[i])) i++;
    return i > j;
}

Target: x64, same array: ~40% faster.

static bool isSorted(int[] a)
{
    int i = a.Length - 1;
    if (i <= 0) return true;
    if ((i & 1) > 0) { if (a[i] < a[i - 1]) return false; i--; }
    for (int ai = a[i]; i > 0; i -= 2)
        if (ai < (ai = a[i - 1]) || ai < (ai = a[i - 2])) return false;
    return a[0] <= a[1];
}

Forgot one, marginally slower than my first code block.

static bool isSorted(int[] a)
{
    int i = a.Length - 1; if (i < 1) return true;
    int ai = a[i--]; while (i >= 0 && ai >= (ai = a[i])) i--;
    return i < 0;
}

Measuring it (see greybeard's comment).

using System;                                  //  ????????? DEBUG ?????????
using sw = System.Diagnostics.Stopwatch;       //  static bool abc()    
class Program                                  //  {   // a <= b <= c ?  
{                                              //      int a=4,b=7,c=9;  
    static void Main()                         //      int i = 1;  
    {                                          //      if (a <= (a = b))  
        //abc();                               //      {  
        int i = 512;                           //          i++;  
        int[] a = new int[i--];                //          if (a <= (a = c))
        while (i > 0) a[i] = i--;              //          {    
        sw sw = sw.StartNew();                 //              i++;  
        for (i = 10000000; i > 0; i--)         //          }  
            isSorted(a);                       //      }  
        sw.Stop();                             //      return i > 2;  
        Console.Write(sw.ElapsedMilliseconds); //  }  
        Console.Read();                        //  static bool ABC();
    }                                          //  {
                                               //      int[]a={4,7,9};    
    static bool isSorted(int[] a) // OP Cannon //      int i=1,j=2,ai=a[0]; 
    {                                          //  L0: if(i<=j)    
        for (int i = 1; i < a.Length; i++)     //        if(ai<=(ai=a[i]))  
            if (a[i - 1] > a[i]) return false; //          {i++;goto L0;}  
        return true;                           //      return i > j;  
    }                                          //  }  
}

Target: x64. Four cores/threads. A sorted array with 100,000 elements: ~55%.

static readonly object _locker = new object();
static bool isSorted(int[] a)  // a.Length > 3
{
    bool b = true;
    Parallel.For(0, 4, k =>
    {
        int i = 0, j = a.Length, ai = 0;
        if (k == 0) { j /= 4; ai = a[0]; }                        // 0 1
        if (k == 1) { j /= 2; i = j / 2; ai = a[i]; }             // 1 2
        if (k == 2) { i = j - 1; ai = a[i]; j = j / 2 + j / 4; }  // 4 3
        if (k == 3) { i = j - j / 4; ai = a[i]; j = j / 2; }      // 3 2
        if (k < 2)
            while (b && i <= j)
            {
                if (ai <= (ai = a[i + 1]) && ai <= (ai = a[i + 2])) i += 2;
                else lock (_locker) b = false;
            }
        else
            while (b && i >= j)
            {
                if (ai >= (ai = a[i - 1]) && ai >= (ai = a[i - 2])) i -= 2;
                else lock (_locker) b = false;
            }
    });
    return b;
}

1,000,000 items?

if (k < 2)
    while (b && i < j)
        if (ai <= (ai = a[i + 1]) && ai <= (ai = a[i + 2]) &&
            ai <= (ai = a[i + 3]) && ai <= (ai = a[i + 4])) i += 4;
        else lock (_locker) b = false;
else
    while (b && i > j)
        if (ai >= (ai = a[i - 1]) && ai >= (ai = a[i - 2]) &&
            ai >= (ai = a[i - 3]) && ai >= (ai = a[i - 4])) i -= 4;
        else lock (_locker) b = false;

Let's forget percentages.
Original: 0.77 ns/item, now: 0.22 ns/item.
2,000,000 items? Four cores: 4 times faster.

Answer 3

Linq solution.

public static bool IsSorted<T>(IEnumerable<T> list) where T:IComparable<T>
{
    var y = list.First();
    return list.Skip(1).All(x =>
    {
        bool b = y.CompareTo(x) < 0;
        y = x;
        return b;
    });
}

Answer 4

Here is my version of the function IsSorted

public static bool IsSorted(int[] arr)
{               
    int last = arr.Length - 1;
    if (last < 1) return true;

    int i = 0;

    while(i < last && arr[i] <= arr[i + 1])
        i++;

    return i == last;
}

While this function is a bit faster than in the question, it will do fewer assignments and comparisons than anything has been posted so far. In the worst case, it does 2n+1 comparisons. It still can be improved if you can make a reasonable assumption about the nature of the data like minimum data size or array contains even number of elements.

Answer 5

The only improvement i can think of is check both ends of the array at the same time, this little change will do it in half time...

public static bool IsSorted(int[] arr)
{
int l = arr.Length;
for (int i = 1; i < l/2 + 1 ; i++)
{
    if (arr[i - 1] > arr[i] || arr[l-i] < arr[l-i-1])
    {
    return false;
    }
}
return true;
}

Answer 6

This is what I came up with and find works better particularly with greater sized arrays. The function is recursive and will be called for the very first time, say in a while loop like this

while( isSorted( yourArray, 0 )

The if statement checks if the bounds of the array have been reached.

The else if statement will call itself recursively and break at any time when the condition becomes false

 public static bool IsSorted(int[] arr, int index)
    {
        if (index >= arr.Length - 1)
        {
            return true;
        }
        else if ((arr[index] <= arr[ index + 1]) && IsSorted(arr, index + 1))
        {
            return true;
        }
        else
        {
            return false;
        }
    }

Answer 7

If the order doesn't matter(descending or ascending).

private bool IsSorted<T>(T[] values) where T:IComparable<T>
{
    if (values == null || values.Length == 0) return true;

    int sortOrder = 0;

    for (int i = 0; i < values.Length - 1; i++)
    {
        int newSortOrder = values[i].CompareTo(values[i + 1]);

        if (sortOrder == 0) sortOrder = newSortOrder;

        if (newSortOrder != 0 && sortOrder != newSortOrder) return false;
    }

    return true;
}

Answer 8

The question that comes to my mind is "why"?

Is it to avoid re-sorting an already-sorted list? If yes, just use Timsort (standard in Python and Java). It's quite good at taking advantage of an array/list being already sorted, or almost sorted. Despite how good Timsort is at this, it's better to not sort inside a loop.

Another alternative is to use a datastructure that is innately sorted, like a treap, red-black tree or AVL tree. These are good alternatives to sorting inside a loop.

Answer 9

This might not be the fastest but it's the complete solution. Every value with index lower than i is checked against the current value at i . This is written in php but can easily be translated into c# or javascript

for ($i = 1; $i < $tot; $i++) {
        for ($j = 0; $j <= $i; $j++) {
            //Check all previous values with indexes lower than $i
            if ($chekASCSort[$i - $j] > $chekASCSort[$i]) {
                return false;
            }
        }
    }