DSA Session 5 ( New Way to Approach ):-

We have a problem with the Statement of Sum of n Natural Numbers.

So let's take it like a game, we have a Starting score or first score = 0

Then we have levels & the final score

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

First Score + Level = Final Score & (final score = first score of next level)

Level + 1 = Next Level,

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So this is a pattern forming here.

Now the Algorithm or Pseudo code for this will be:-

First Score = 0
Final Level = 5
Repeat Below things again & again, till reach 5th level :-

    Whatever the score we have plus current level that 
    give me final score

    Go to next level -> +1 -> to next level

Output => answer will be final score you got.

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Converting it into code:-

firstScore = 0
finalLevel = 5
currentLevel = 1

while currentLevel <= finalLevel:
    finalScore = finalScore + currentLevel
    currentLevel = currentLevel + 1

return finalScore

Now this has a time complexity of #O(1)

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If we Put all this into Function then it will be:-

def gameSum():

    firstScore = 0    #O(1)
    finalLevel = 5    #O(1)
    currentLevel = 1    #O(1)

    while currentLevel <= finalLevel :
        finalScore = finalScore + currentLevel    #O(4)
        currentLevel = currentLevel + 1    #O(4)

return finalScore

Now if we replace finalLevel=4 with finalLevel=n

& def gameSum() to gameSum(n),
then it will have a time complexity of #O(n)

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so we can see that for the same problem, we have two-time complexities.

Algo 1 --> #O(n)

Algo 2 --> #O(1)