Two number sum : why don't anybody do it this way

Question

I was looking for the solution to "two number sum problem" and I saw every body using two for loops and another way I saw was using a hash table

 def twoSumHashing(num_arr, pair_sum):
    sums = []
    hashTable = {}

    for i in range(len(num_arr)):
        complement = pair_sum - num_arr[i]
        if complement in hashTable:
            print("Pair with sum", pair_sum,"is: (", num_arr[i],",",complement,")")
        hashTable[num_arr[i]] = num_arr[i]

# Driver Code
num_arr = [4, 5, 1, 8]
pair_sum = 9    
  
# Calling function
twoSumHashing(num_arr, pair_sum)

But why don't nobody discuss about this solution

def two_num_sum(array, target):
    for num in array:
        match = target - num
        if match in array:
            return [match, num]
                 
    return "no result found" 

when using a hash table we have to store values into the hash table. But here there is no need for that. 1)Does that affect the time complexity of the solution? 2)looking up a value in hash table is easy compared to array, but if the values are huge in number, does storing them in a hash table take more space?

Answer 1

First, the second function you provide as a solution is not correct and does not return a complete list of answers.

Second, as a Pythonist, it's better to say dictionary instead of the hash table. A Python dictionary is one of the implementations of a hash table.

Anyhow, regarding the other questions that you asked:

• Using two for-loops is a brute-force approach and usually is not an optimized approach in real. Dictionaries are way faster than lists in Python. So, for the sake of time complexity, dictionaries are the winner.

• From the point of view of space complexity, using dictionaries for sure takes more memory allocation, but with current hardware, it is not an essential issue for billions of numbers. It depends on your situation, whether the speed is crucial to you or the amount of memory.