Pigeonhole Sort – Python

Last Updated : 03 Mar, 2025

Pigeonhole Sort is a sorting algorithm that is suitable for sorting lists of elements where the number of elements and the number of possible key values are approximately the same. It requires O(n + Range) time where n is number of elements in input array and ‘Range’ is number of possible values in array.

Pigeonhole Sort Algorithm

Find minimum and maximum values in array. Let the minimum and maximum values be ‘min’ and ‘max’ respectively. Also find range as ‘max-min-1’.
Set up an array of initially empty “pigeonholes” the same size as of the range.
Visit each element of the array and then put each element in its pigeonhole. An element arr[i] is put in hole at index arr[i] – min.
Start the loop all over the pigeonhole array in order and put the elements from non- empty holes back into the original array.

Implementation:

def pigeonhole_sort(a):
    # size of range of values in the list
    # (ie, number of pigeonholes we need)
    my_min = min(a)
    my_max = max(a)
    size = my_max - my_min + 1

    # our list of pigeonholes
    holes = [0] * size

    # Populate the pigeonholes.
    for x in a:
        assert type(x) is int, "integers only please"
        holes[x - my_min] += 1

    # Put the elements back into the array in order.
    i = 0
    for count in range(size):
        while holes[count] > 0:
            holes[count] -= 1
            a[i] = count + my_min
            i += 1
            

a = [8, 3, 2, 7, 4, 6, 8]
print("Sorted order is : ", end =" ")

pigeonhole_sort(a)
        
for i in range(0, len(a)):
    print(a[i], end =" ")

Output

Sorted order is :  2 3 4 6 7 8 8

Time Complexity:

The overall time complexity is O(n + k), where n is the number of elements in the input list and k is the range of values in the list (i.e., the difference between the maximum and minimum values).
In cases where k is much larger than n, the time complexity can approach O(k). If k is small (i.e., the range of values is not large), the algorithm performs well.

Space Complexity:

The overall space complexity of pigeonhole sort is O(n + k), where n is the number of elements and k is the range of values in the input list. The extra space required is for the pigeonholes list, which grows with the range of the numbers.