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, resembling quantity idea, geometry, algebra, astronomy, magnetism, and many others. Even immediately, a variety of mathematical and scientific ideas are named after him. One such idea is the Gaussian Addition, which we are going to discover immediately!

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 fascinating instance of considering exterior the field relatively than engaging in duties in a predetermined manner.

When Carl Gauss was a baby, his trainer gave him a activity so as to add the numbers from 1 to 100. Now such a activity, completed 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 activity completed. He understood that the addition of numbers from 1 to 100 is similar as addition of fifty pairs that may 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 full of 5050 will be simply calculated with none tedious calculations.

Carl Gauss was clever; he was in a position to provide you with a sensible method to calculate the sum, however let’s be trustworthy. None of us are that sensible :P. Whereas we wouldn’t have the brains of Gauss, we absolutely do have the benefit of programming and computer systems that do complicated calculations for us. Allow us to code the above downside in Python.

Code

Allow us to remedy 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 we now 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 we now have specified ’11’ because the quantity at which the sequence stops. It’s 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 wish to print the variable numbers, we gained’t get an inventory of those numbers within the specific sequence. Nonetheless, we are going to get a spread datatype. It’s because the vary datatype doesn’t retailer the sequence within the laptop’s reminiscence the way in which an inventory shops its gadgets. We can’t equate the vary of numbers with an inventory.

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

For Loop

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

Now, since we’re iterating over the vary we now have outlined earlier, which in our case could be from 1 to 100, with the default step of 1 (we are able to 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 complete that may retailer the sum of the sequence of numbers after each iteration. The worth of complete will probably be 0 initially, and will probably be elevated with each iteration. So within the first iteration, once we are looping from 1 to 100, the full will probably be 1. Within the second iteration, will probably be 1 + 2 = 3. Within the third iteration, will probably be 3 + 3 = 6, and so forth.

We’ll print the worth complete on the finish. See, it quantities to 5050, the identical worth as Gauss.

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

Whereas loop

One other method to do the above activity is through the use of Python whereas loop. The whereas loop works till a specific situation turns into false. In our case, we should initialize a variable i, give it the beginning worth of 1 and increment it by 1 solely, in order that it loops via the checklist till it reaches 101. At i = 101, the whereas loop’s situation will develop into false, and so it would cease. The worth complete will probably be printed.

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

Conclusion

On this quick article, we used the vary operate as a faster method to overcome our activity 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 had been in a position to give us the proper end result.

Nonetheless, as will 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 when it comes to 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 look ahead to your feedback!