Implementing the Gaussian Problem in Python

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

It isn’t data, 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 pondering exterior the field somewhat than engaging in duties in a predetermined method.

When Carl Gauss was a baby, his instructor 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 subsequent, then the subsequent, would have taken hours.

However Carl Gauss got here up with a faster and smarter technique to get his process finished. He understood that the addition of numbers from 1 to 100 is identical 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 can be made. This implies the full of 5050 could be simply calculated with none tedious calculations.

Carl Gauss was clever; he was capable of provide you with a sensible method to calculate the sum, however let’s be sincere. None of us are that good :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 drawback in Python.

Code

Allow us to clear up 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 features, 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’ll 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’s because, in accordance with the syntax, the final quantity can 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 explicit sequence. Nevertheless, we’ll get a variety 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 not equate the vary of numbers with an inventory.

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

For Loop

Subsequent, we have to iterate by means of these numbers. Python loops are our go-to for any type of iteration. On this tutorial, we’ll be taught in regards to the two loops and obtain the above consequence utilizing each of them.

Now, since we’re iterating over the vary now we have outlined earlier, which in our case can be from 1 to 100, with the default step of 1 (we will omit mentioning that), we’ll use the for loop and supply it with this vary. However first, we’ll outline a variable known as whole that can retailer the sum of the sequence of numbers after each iteration. The worth of whole shall be 0 initially, and shall be elevated with each iteration. So within the first iteration, once we are looping from 1 to 100, the full shall be 1. Within the second iteration, it is going to be 1 + 2 = 3. Within the third iteration, it is going to 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 technique to do the above process is by utilizing 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 means of the listing till it reaches 101. At i = 101, the whereas loop’s situation will change into false, and so it can cease. The worth whole shall 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 quick article, we used the vary operate as a faster technique to overcome our process of defining numbers from 1 to 100. We then used each the for and the whereas loops to unravel the issue of addition, and each had been capable of give us the right consequence.

Nevertheless, as could be seen in such selections, one method works higher than the opposite. What do you assume 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 assume is healthier than the opposite and why. I’ll sit up for your feedback!