使用字典对 O(n) 中的数组进行排序？

Question

Assuming you have an array of numbers that need to be sorted and the following two conditions are true:

1. A low standard deviation
2. Memory isn't a constraint

How about using dictionary to sort this in O(n), below is the python code:

def sortArray(nums: List[int]) -> List[int]:

    # dictionary to store all the numbers in the array as key and number of occurrences as value
    d = {} 
    
    # Keep a track of upper and lower bound of array
    max_num = nums[0]
    min_num = nums[0]
    
    for e in nums:
        if e>max:
            max=e
        if e<min:
            min=e
            
        try:
        #increment the value for "e" if it exists in dictionary
            d[e]=d[e]+1  
        except:
        #add a new key "e"
            d[e]=1 
    
    a=[]
    for i in range(min_num,max_num+1):
        try:
            for j in range(0,d[i]):
                # add the element in new array for d[i] times
                a.append(i)
        except:
            continue
            
    return a

Given the 2 conditions,Are there any scenarios where this code would not work in O(n)? Is there something wrong with this approach?

Answer 1

It is not possible to tell the exact complexity of this procedure because the running time depends on the range of the values, among others.

If this range is fixed, the final double loop adds an element N times. Hence O(N), if the hash table guarantees an O(N) complexity.

But for unbounded N, a fixed range does not make much sense, and it should grow with N. Hence the complexity will be of order O(M(N) + N), where M(N) is the size of the range.

It is also worth to note that the append operation does not necessarily feature constant time cost per element.