CODEWITHSUNDEEP
python
Reyer Eryer
Reyer Eryer

Reputation: 189

Summing consecutive third numbers in python

How would I solve this?

The program should contain the definition for the function sumTri(cutOff). The function adds Tri numbers into the sum.

Tri numbers are every third number: 1, 4, 7, 10, .... The function adds consecutive Tri numbers 1, 4, 7, ... into the sum so long as the Tri number is less than the cutOff. The function returns the sum of these numbers.

Upvotes: 0

Views: 309

Answers (2)

John La Rooy
John La Rooy

Reputation: 304127

This sequence is related to triangular numbers

Here is one that is O(1)

def sumTri(cutoff):
    n = (cutoff+1)//3
    return (3*n-1)*n//2

Upvotes: 4

Igor Chubin
Igor Chubin

Reputation: 64563

It's simple:

def sumTri(cutOff):
  return sum(range(1,cutOff,3))

Or, when you need it lowlevel:

def sumTri(cutOff):
  sum = 0
  tri = 1
  while tri < cutOff:
    sum += tri
    tri += 3
  return sum

I'll try to explain both soultions a little bit.

In the first case you use two "highlevel" functions of Python, that make all work for you: sum and range. The range(a,b,c) function generates a list of numbers from a to b with the step c between. E.g.:

In [1]: range(1,10,3)
Out[1]: [1, 4, 7]

In [2]: range(1,22,3)
Out[2]: [1, 4, 7, 10, 13, 16, 19]

You must note here that range generates numbers until the number in the list is less than b, not less-or-equal. Exactly what you need for your task.

And sum obviously calculates and returns the sum of the numbers in the list that it has as its argument:

In [3]: sum([1])
Out[3]: 1

In [4]: sum([1,2])
Out[4]: 3

In [5]: sum([1,2,3])
Out[5]: 6

Now you need just to combine these two functions:

return sum(range(1,cutOff,3))

The second solution is more "lowlevel" and "algorithmic". You use no special python functions here and do everything yourself.

You use two variable to calculate the sum:

  • sum -- the variable where you store your sum
  • tri -- the variable with the current value of number that you add step by step

When you write something like:

a = a + 5

that means: "Now I want a to be equal to what a was before plus 5" or "increase a by 5". You can write it shorter:

a += 5

These two forms are equivalent.

But you need not simple add something. You need to do it for many times until something is happened. In python you do it using while:

while someting-is-true:
  do-something

Every time while checks the something-is-true condition, and when it's True, it makes commands that are under while (indented) i.e. do-something.

Now you know all necessary to write the solution:

def sumTri(cutOff):
  sum = 0                      # we start the sum from 0
  tri = 1                      # and the first number to add is 1
  while tri < cutOff:          # next number to add < cutOff?
    sum += tri                 # than add it to sum
    tri += 3                   # and increase the number by 3
  return sum                   # now you have the result, return it

That was the function that makes the job. Now you can use the function. How you do this?

def sumTri(cutOff):
  ...

# anywhere in you program:
# presuming a is the cutOff
print sumTri(a)

when you want to run the function and use its result you just write function_name(args).

Upvotes: 5

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