Implementing the Gaussian Problem in Python

Carl Gauss was a German mathematician and astronomer, often known as the “Prince of Arithmetic”. He’s widely known for his contributions within the fields of science and arithmetic, reminiscent of quantity concept, geometry, algebra, astronomy, magnetism, and many others. Even as we speak, various mathematical and scientific ideas are named after him. One such idea is the Gaussian Addition, which we are going to discover as we speak!

It’s not information, however the act of studying, not possession however the act of getting there, which grants the best enjoyment.

– Carl Friedrich Gauss

Gaussian Addition

The Gaussian Addition Problem is an attention-grabbing instance of considering exterior the field reasonably than engaging in duties in a predetermined manner.

When Carl Gauss was a toddler, his trainer gave him a process so as to add the numbers from 1 to 100. Now such a process, finished one step at a time, including the primary 2 numbers, then the following, then the following, would have taken hours.

However Carl Gauss got here up with a faster and smarter method to get his process finished. He understood that the addition of numbers from 1 to 100 is identical as addition of fifty pairs that will sum to 101, that’s, the primary and the final 1 + 100 = 101, equally the second and the second final 2 + 99 = 101, the n^th and the n^th final merchandise within the collection would all quantity to 101, and 50 such pairs could be made. This implies the whole of 5050 may be simply calculated with none tedious calculations.

Carl Gauss was clever; he was capable of provide you with a wise method to calculate the sum, however let’s be sincere. None of us are that good :P. Whereas we would not have the brains of Gauss, we absolutely do have the benefit of programming and computer systems that do advanced calculations for us. Allow us to code the above downside in Python.

Code

Allow us to resolve the Gaussian Problem whereas understanding the Python built-ins for use:

Vary

The very first thing we have to perceive is the Python vary operate. This operate is used to create a sequence of numbers that can be utilized later in different capabilities, such because the for loop.

The syntax for the vary operate is as follows.

vary = (quantity at which sequence begins, quantity at which sequence stops, step)

Suppose now we have to generate a sequence of numbers from 1 to 10, with a step or distinction of 1, so we are going to use this vary operate as follows:

numbers = vary(1,11)
for i in numbers:
    print(i)

Discover that now we have specified ’11’ because the quantity at which the sequence stops. It is because, in accordance with the syntax, the final quantity could be inside the vary, that’s, within the instance above, lower than 11 = 10.

If we need to print the variable numbers, we received’t get a listing of those numbers within the specific sequence. Nevertheless, we are going to get a spread datatype. It is because the vary datatype doesn’t retailer the sequence within the laptop’s reminiscence the best way a listing shops its gadgets. We can not equate the vary of numbers with a listing.

numbers = vary(1,11)
print(numbers)

For Loop

Subsequent, we have to iterate by way of these numbers. Python loops are our go-to for any form of iteration. On this tutorial, we are going to be taught concerning the two loops and obtain the above end result utilizing each of them.

Now, since we’re iterating over the vary now we have outlined earlier, which in our case could be from 1 to 100, with the default step of 1 (we will omit mentioning that), we are going to use the for loop and supply it with this vary. However first, we are going to outline a variable known as whole that may retailer the sum of the sequence of numbers after each iteration. The worth of whole can be 0 initially, and can be elevated with each iteration. So within the first iteration, once we are looping from 1 to 100, the whole can be 1. Within the second iteration, it will likely be 1 + 2 = 3. Within the third iteration, it will likely be 3 + 3 = 6, and so forth.

We are going to print the worth whole on the finish. See, it quantities to 5050, the identical worth as Gauss.

numbers = vary(1,101)
whole = 0
for i in numbers:
    whole = whole + i
print("Whole: ", whole)

Whereas loop

One other method to do the above process is through the use of Python whereas loop. The whereas loop works till a selected situation turns into false. In our case, we must initialize a variable i, give it the beginning worth of 1 and increment it by 1 solely, in order that it loops by way of the record till it reaches 101. At i = 101, the whereas loop’s situation will grow to be false, and so it’s going to cease. The worth whole can be printed.

numbers = vary(1,101)
whole = 0
i = 1
whereas i in numbers:
    whole = whole + i
    i = i + 1
print("Whole: ", whole)

Conclusion

On this brief article, we used the vary operate as a faster method to overcome our process of defining numbers from 1 to 100. We then used each the for and the whereas loops to resolve the issue of addition, and each have been capable of give us the proper end result.

Nevertheless, as may be seen in such selections, one method works higher than the opposite. What do you suppose has been higher in fixing the Gaussian Problem, the whereas loop or the for loop? Assume by way of complexity, time, reminiscence used, and readability. Clearly, one is healthier than the opposite. Do share which one you suppose is healthier than the opposite and why. I’ll sit up for your feedback!