Hi! I'm Manish. I was wondering what to do in this COVID-19 pandemic, to stay a bit productive and then the phrase **100 Days Of Code** striked me while surfing the internet and I decided to take up the challenge.

To begin with that, I have enolled for the email subscription by **Daily Coding Problems**. The team at DCP sends us an email with one coding problem a day and I believed that it would be the right thing for the challenge. To add to that, I have decided to share my experience on solving the question too and start writing on **dev**.

The Question On Day #1:

```
Given a list of numbers and a number `k`, return whether any two numbers from the list add up to `k`.
For example, given `[10, 15, 3, 7]` and `k` of `17`, return true since `10 + 7` is `17`.
```

## My First Approach

- Input the given numbers into a list and and the sum to check in a variable.
- Traverse through the list and for each element at index
*i*, check if there exists a complementary number starting from the index*i*in the list. - If there exists atleast one such number print "pair exists" and exit the loop by marking a flag.
- After the cursor exits the loop adn if the flag is still unmarked, print "pair doesn't exist".

**Python Code**

```
l=[10,15,3,7]
k=17
flag=0
for i in range(len(l)-1):
if (k-l[i]) in l[i+1:]:
#slicing to prevent additional checks
print("pair exists")
flag=1
break
if flag==0:
print("pair doesn't exist")
```

**Points To Note:**

- The check for the complementary number is only done for the sliced list from i+1 to len(l), since the previous number pairs are already checked in the iterations before.
- The last element of the list is thus skipped from being checked for a complementary number.

**Time Complexity Of The Above Solution**

The traversal through the list takes a time of O(n) where n is the length of list. For each element, there is an another check withinoperator which again takes a time complexity of O(n-i) for a list in python ref.

*The total time complexity for the solution will result in a time complexity of O(n^2).*

## Better Approach

An approach better to the above solution is to convert the list into a set first, does making the *in operator* efficient to use.

The time complexity of using the in operator on a set is O(1) on average and O(n) in the worst case.

**Python Code**

```
l=[10,15,3,7]
k=17
s=set(l) #converting list l into a set and storing it in s
flag=0
for i in s:
if (k-i) in s:
print("pair exists")
flag=1
break
if flag==0:
print("pair doesn't exist")
```

**Time Complexity Of The Above Solution**

The conversion from list to a set takes a time of O(n) where n is the length of list. Hence, the total time complexity for the above solution is O(n)+O(nx1)

[O(nx1) on average and O(nxn) in the worst case for the loop and condition check using in operator on the set s].

**Thus the total time complexity on average results to O(n) and O(n^2) in the worst case scenario.**

This question helped me in understanding the time complexities of individual data structure operations in python. I would love to hear from my fellow developers and take suggestions on improving the above logic. I am a pretty newbie to solving such questions, please consider it. I also request you to drop suggestions to improve my article readability or understanding.

*Thanks and cheers:)*

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