Programming Puzzle 1 - Simple Loop

[G Gabriel]

Re: Programming Puzzle 1 - Simple Loop

So, on to a more realistic solution, one that complies with the spirit rather than the letter of the rules.
My first instinct was to:
1-identify the first even number
2-Loop stepping by 2 adding the values until reach the top value.
I ended up with 100 loops. That's embarrassing! a hundred loop to solve a simple puzzle like this? There got to be a better way.
There is..
One that uses a 20 loops or few more.
Here it is:
P.S.: To best read the introduction in case your screen rsolution is different from mine, copy/paste it into Word and read it in Word.

'Introduction:
'The object is to sum all even values between 2 given numbers
'Since these 2 numbers are provided in the puzzle, meaning I could hard-code these values which makes everything a lot simpler and faster but just in case the intent was to solve for any numbers not just the ones provided in the puzzle, the script is written so that you can substitute these number at will and get the correct result.
'
'Let me first start with the logic behind the script.
'To add all even values between 2 given numbers, you identify the first even number, then add 2 to it and add the new number to the previous one and so on..
'That's the standard way of thinking.. by doing that you will have to loop as many times as there are even values..
'That's too many loops and too expensive..
'
'Let's look at the puzzle from a different perspective..
'
'In the example provided, the first even number is 102.
'Let's call this number a base.
'Every subsequent number is 2 points more than the one before..
'Let's get away from this line of thinking.
'A different way to think about is:
'You have a base number, then
'Every subsequent number has one more 2 than the one before, i.e.:
'The base number is 102
'The one after has one more 2 than the base: 104
'The one after has two more 2's than the base: 106
'The one after has three more 2's than the base: 108
'and so on..
'
'Now if I strip the base of its 2, then we could re-state the above as follows:
'Instead of the base, I am going to have new figure, will call it the "denominator" which is the base stripped off its 2, i.e. 102-2=100
'
'Now the first even value (the base, 102) has one 2 more than the denominator and
'The second even value (104)  has two 2's more than the denominator
'The third even value (106) has three 2's more than the denominator
'and so on..
'
'so now I could deal with 2 sets of values:
'The first set, we will call it the "Denominator-cluster" is basically made up of the even values stripped off their 2's. meaning, they are all 100
'
'The second set, we will call it the "Two-cluster" is made up of those 2's that are above and beyond the denominator. This is a series made up as one 2, two 2's, three 2's... ten 2's.
'
'Now I am going to break up all the even values between 101 and 302 into 10 clusters.
'As you can see, the "Denominator-clusters" will each have 10 equal values. the first cluster will have 10 equal values each of 100. If I loop through these clusters and step increment each cluster by 20 (10 2's), the second cluster will have 10 equal values of 120 each, the third cluster will have 10 equal values of 140 each.. and so on.
'
'To this cluster, I need to add the cluster of 2's. I need to calculate this cluster only once and add it to each one of the "denominator-clusters" and then add all the clusters together which gives me the final total sum.
'
'To add the cluster of 2's, I could hard-code that:
'2+4+6+8...+20=110
'But once again, if the intent of the puzzle is to be able to substitute for other values, I will use a loop to add these incrementing 2's, which means I will loop 10 times to calculate the cluster of 2's then loop another 10 times to calculate the "denominator-clusters" and in each loop I am adding each one of the to the previous total plus the sum of the cluster of 2's so at the end of the last loop. After that I will find the orphan values, the ones that were not included in the clusters and add those to the total which gives me the grand total.
'Now why did I choose 10 clusters?
'That produces the "optimal" number of loops in this scenario:
'If you increase the size of the cluster to reduce their number and thus the number of looping through them, you will increase the number of 2's and the number of their loops.
'How to arrive at the optimal cluster size?
'That's for another day another post, but regardless, any number of clusters will beat the standard looping method.

Here is the script:

'For further explanations, please read the Introduction section
option strict
dim bottom_num as n
dim top_num as n
dim denominator as n
dim span as n 'the span between the bottom and top numbers
dim values_num as n
dim i as n 'to be used as a counter
dim twos as n'this will add the 2's that are above and beyond the denominator values
dim vtotal as n=0
dim trail_num as n'number of orphan values not in the clusters
dim trail_values as n'the actual value of the orphan
dim loop_num as n'how many times we looped so far
dim last_even as n'this is the value of top-most even number in the series
bottom_num=101
top_num=302
span=top_num-bottom_num
values_num=int(span/2)+1 'This is how many even number in the span between the bottom and top numbers. The 1 is added to make it all inclusive, i.e. including the bottom as well as the top numbers
trail_num=mod(values_num,10)
denominator=bottom_num-if(mod(bottom_num,2)=0,0,1)
'First will add the "Two-cluster"
for i=1 to 10
	twos=twos+i*2
next i
loop_num=i
'Now we will iterate over the "denominator-clusterss" , each cluster will have a denomiator value of 20 more the one before
for i=1 to 10
vtotal=vtotal+(denominator+20*(i-1))*10+twos
next i
loop_num=loop_num+i
'Now we will add the trailing numbers, those that were not included in the 10 clusters
'Find the last even number:
last_even=if(mod(top_num,2)=0,top_num,top_num-1)
for i= 1 to trail_num step-1
	trail_values=trail_values+last_even
	last_even=last_even-2
next
loop_num=loop_num+1	
vtotal=vtotal+trail_values
msgbox("The sum total of all even numbers is: "+vtotal+" "+"and the number of loops is: "+loop_num)

[G Gabriel]

Re: Programming Puzzle 1 - Simple Loop

Just came across this part of the message board. Not sure whose idea it is to have a section for "Puzzles"..but I think it's a pretty good idea..
On to the first puzzle..don't have time to scan over any others..nor to scan over the responses, but this puzzle, clearly, can be solved without any loops whatsoever, rather with one simple expression. But if I do that then I am in violation of the rules.
For those who might be interested, here is the expression:

vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2

Where vtotal is the sum of all even values, start is the bottom value and end is the top value, all inclusive.

If I want to be de facto in compliance with the rules, I could be a slick, clever, irritating smart alec, which I do not want to be, but again, for those who might be interest, I will use a single loop that does nothing and I will have my lawyer sue and demand the ultimate prize arguing that I am in full compliance with the rules the way they were written and offered.
Here is the smart alec script:

option strict
dim start as n'this is the bottom value
dim end as n'this is the top value
dim i as n 'to be used as a counter in the loop
dim vtotal as n
start=101 
end = 302
'Now we will use the same expression provided in the previous example and add a dummy loop
for i=1 to 1
vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2
next
msgbox("The total sum is: "+vtotal+"  and the script used 1 loop")

'The same could be done using while..end while loop

option strict
dim start as n'this is the bottom value
dim end as n'this is the top value
dim i as n 'to be used as a counter in the loop
dim vtotal as n
start=101 
end = 302

while i<=1
vtotal=int((end-start)/2)+1+(int((end-start)/2)+1)*if(mod(start,2)=0,start-2,int(start/2)*2)+(int((end-start)/2)+1)^2
i=i+1
end while
msgbox("The total sum is: "+vtotal+"  and the script used 1 loop")

There is only one loop, about as few as you can get unless I hire the real smart alec lawyer who will argue for my original expression to be the ultimate winner as it has zero loops!! But I don't think the panel of judges will buy that.

As you can see, even if the judges accept the logic of zero loops or one loop, still I wont get any prizes since I am still in violation of the rules since I didn't explain how and why does that expression work, and I wont.. To understand this expression, you have to mentally translate this math puzzle into a geometric one..to explain that is a bit time consuming and outside the parameters of this puzzle, so we will move on to a more realistic solution, which I will start in a new post and and ask you to please ignore this post as a side show that may or may not have any redeeming value.

[Tom Cone Jr]

Re: Programming Puzzle 1 - Simple Loop

Very nice, Thomas.

The message board left justifies your script. That makes it harder to read scripts because we lose the indents.

To preserve the indents prepare your reply using the "Go Advanced" button, and then encapsulate your code with CODE tags, like this:

option strict

dim target_num as n = 0 'used to determine if number is even
dim i as n = 0
dim result as n = 0 'result adds the total of the even numbers
dim num_loops as n = 0 'counts the number of interations

for i = 302 to 101 step-2
	num_loops = num_loops + 1
	target_num = i
	if mod(target_num,2)= 0 then
		result=result+target_num
	end if
next i

ui_msg_box("Program Puzzle One","The answeres are Sum = "+ alltrim(str(result))+" Loops = "+alltrim(str(num_loops)))

end

The # button on the advanced editor toolbar will do this for you. Just select the text to be encapsulated, and click #.

Also, when you develop a solution to the next puzzle, I suggest you learn how to "export" your script as a text file, and then simply attach it to a reply here. If you use the script export tool in Alpha Five the text file will be specially formatted to work with Alpha's import tool. This makes it easier for us to study your code and run it on our machines. We just import your previously exported script. To get to the export (and import) tools, save your script to the Code page of the A5 control panel. Then right click the script name. Choose Export off the drop down list (context menu).

Welcome to the board!

[Tom Reese]

Re: Programming Puzzle 1 - Simple Loop

As I am very new to xbasic my version to puzzle 1 is simple, but I believe it gets the job done.
Would appreciate any comments that may be needed or helpful.

Now to see if I can find Puzzle 2.

'Date Created: 09-Nov-2011 05:23:03 PM
'Last Updated: 10-Nov-2011 08:12:35 AM
'Created By : T. E. Reese
'Updated By : T. E. Reese
option strict

dim target_num as n = 0 'used to determine if number is even
dim i as n = 0
dim result as n = 0 'result adds the total of the even numbers
dim num_loops as n = 0 'counts the number of interations

for i = 302 to 101 step-2
num_loops = num_loops + 1
target_num = i
if mod(target_num,2)= 0 then
result=result+target_num
end if
next i

ui_msg_box("Program Puzzle One","The answeres are Sum = "+ alltrim(str(result))+" Loops = "+alltrim(str(num_loops)))

end

[The Mage]

Re: Programming Puzzle 1 - Simple Loop

OPTION strict

dim first as N		'Starting number
dim last as N		'Ending number
dim total as N		'For final total
dim count as N		'To count the number of times this code is run, but it won't be that important as you will see.

count = 0		'Starting counter at 0

first = 102		'Starting point
last = 302		'Ending point

total = ( ( first + last ) * ( last - first ) ) / 4
			'By adding in the first and last numbers I am figuring out a standard number for the math
			'and by subtracting the last and first from eachother, I am counting the total of the 
			'numbers between the first and last.  Since I am adding in both first and last numbers,
			'I only need to figure in half of those numbers, and since only even numbers are counted,
			'I need only half of those numbers still.  So I divide the total by 4.  
			'logically it should have divided the (last-first) before being multiplied, but the result is the same.

count = count + 1	'Adding to the counter

			'Results:
ui_msg_box( " Total" , total ,UI_ATTENTION_SYMBOL )	

			'Number of times the formula had to be run:
ui_msg_box( "Times Run" , count , UI_ATTENTION_SYMBOL )

Admittedly I am cheating here by not using a loop.

[Tom Cone Jr]

Re: Programming Puzzle 1 - Simple Loop

Jeb, good try. Prof. Ignatious Pickypicky has several comments for your elucidation (his word, not mine!)

1) The pound symbol on the "Next" line throws an error. It doesn't belong.

2) The message box fails to display because the variables "message" and "message2" haven't been declared,
and OPTION STRICT is on.

3) The professor's eyes aren't what they used to be. Consider formatting your scripts so they're easier
to read. (Example below to give you some ideas).

4) It's not necessary to comment every line. Some things will always be obvious when you come back to
the script years later. Others will not. The latter is what must be documented / commented.

5) It's customary to indent lines inside a code block / loop structure.

OPTION strict		

'recommend DIMing all vars at the top
dim sum as N		'defining sum variable as Number. Sum will be used to get the 
			'total sum of the even number through the range.
dim qx as N		'defining qx variable as Number. QX will be used as the loop.
dim lnum as N		'defining lnum variable as Number. Lnum will be used to get the 
			'total times the loop was done.
dim qx as N		'loop counter (index)
dim message as C 	'text string for message box
dim message2 as C	'ditto


sum=0		'giving the sum variable a value of zero.
lnum=0		'giving the lnum variable a value of zero.

for qx = 102 to 302 step 2	'starting the loop. Stating loop is is going to be 
				'ran from 102 to 302. 'Step 2' defines the number 
				'to increase by after each loop.

	sum=sum+qx	'equation that gets the value for each loop cycle(each QX) and 
			'eventually will add them together.

	lnum=lnum+1	'equation that sets the first loop to 1. The second loop to 2. 
			'The third loop to 3, etc.

next	'goes to next part of loop(next QX).

dim message as C
dim message2 as C

'assigning the total sum message for the pop up message.
message="The sum of the even numbers through the range 102-302 is: "+ltrim(str(sum))

'assigning the total lnum or total times the loop was done, for the pop up message.
message2="The number of times the code was iterated through the loop was: "+ltrim(str(lnum))

ui_msg_box("Jeb's Calculation",message +crlf()+message2)	'message box that gives 
					'the results of the calculation. LNUM and SUM

.

[jeb richardson]

Re: Programming Puzzle 1 - Simple Loop

OPTION strict
dim sum as N
'defining sum variable as Number. Sum will be used to get the total sum of the even number through the range.
dim qx as N
'defining qx variable as Number. QX will be used as the loop.
dim lnum as N
'defining lnum variable as Number. Lnum will be used to get the total times the loop was done.
sum=0
lnum=0
FOR qx = 102 TO 302 step 2
	'starting the loop. Stating loop is is going to be ran from 102 to 302. 'Step 2' defines the number to increase by after each loop.
	sum=sum+qx
	'equation that gets the value for each loop cycle(each QX) and eventually will add them together.
	lnum=lnum+1
	'equation that sets the first loop to 1. The second loop to 2. The third loop to 3, etc.
next
'goes to next part of loop(next QX).
message="The sum of the even numbers through the range 102-302 is: "+sum
message2="The number of times the code was iterated through the loop was: "+lnum
ui_msg_box("Jeb's Calculation",message +crlf()+message2)

[Mbuso]

Re: Programming Puzzle 1 - Simple Loop

thanx pmanandhar.
interesting to read your work since you have a taste for math, and background in cpp, as seen in flyPuzzle :-)

[pmanandhar]

Re: Programming Puzzle 1 - Simple Loop

CALocklin - Its not that difficult and you definitely have the ability (maybe not time). It took me a while to figure out the logic and formula. I saw Mbuso's logic too and its way easier than the way I was doing. His logic was to get the start and end numbers to be even. Then, get the average (easy to calculate), and times no. of even numbers which is (N+1)/2.. That's it.. brilliant..
I was also thinking similiar but the question wanted to calcuate from 101 -302. So wanted the input to be starting -odd and ending- even numbers. I did it for adding odd numbers which made little complications.

[Mbuso]

Re: Programming Puzzle 1 - Simple Loop

...Very clever, grasshopper!...

*blushing* ...

with a slight modification the same can be applied to calculate sum of equal contributions made in to investment or loan repayment. Which indeed, can also be done the snaky route (loop:-)

[Tom Cone Jr]

Re: Programming Puzzle 1 - Simple Loop

Mbuso,

Very nice! Thinking outside the box. Your solution does not use a loop, but is ingenious nevertheless. In your algorithm you adjust the end points of the number range, then compute both the number of "even" terms and the avg over the entire range. Multiplying them together you get the sum. Very clever, grasshopper! Prof. Pickypicky will be watching you closely, too!

[Mbuso]

Re: Programming Puzzle 1 - Simple Loop

upon a realisation that my input attracts no response other than anonymous respondents through email and private messages. No harm in posting another version, yet in attempt to contribution in a speedier progress for a would be alpha fellow.

regards,

[CALocklin]

Re: Programming Puzzle 1 - Simple Loop

Nice job Pratik! When I posted my original solution I was pretty sure there had to be some way to do it without any iterations but didn't have the time to work it out. And seeing your solution - probably not the ability either.

[Tom Cone Jr]

Re: Programming Puzzle 1 - Simple Loop

Pratik,

I was mostly pulling your leg. Trying to be facetious. No mathematical proof is necessary. Thanks for contributing to this thread. I look forward to your answers on other puzzles in the future. -- tom

[pmanandhar]

Re: Programming Puzzle 1 - Simple Loop

hey tom,
I am new to this forum and don't know what you and your "Prof. Pickypicky" is talking about. Maybe I'm little careless that even in my classes I rarely got an A (instead A- or B+) even though I get the job done. I don't know what proof are you asking and i don't know how to proof ?? I am good in math so I just took some time and came up with this formula. Now if you are interested as how I came up with this formula then I can explain but still its little complicated to explain. you can try using different values in n1 and n2 several times. That works so is that considered "proof"??