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zimmahBest ResponseYou've already chosen the best response.0
I'm not familiar with these type of problems, seems like you need to use the bottom formul a for both, but I don't know how to fill it in.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
So if I started filling in the bottom formula for A(3, 3) A(31, A(3,31)) A(2, A(3,2)) Plug the A(3,2) back into the formula: A(2, A(31, A(3, 21))) A(2, A(2, A(3, 1))) Now n = 1 so I can use the third formula to get A(3, 1) = 2 A(2, A(2, 2)) A(2, A(21, A(2, 21))) A(2, A(1, A(2, 1))) Use the third formula again: A(2, A(1, 2)) A(2, A(11,A(1, 21))) A(2, A(0, A(1, 1))) A(2, A(0, 2)) Use the first formula: A(2, 2n) A(2, 2(2) A(2, 4) A(1, A(2, 3)) A(1, A(1, A(2, 2))) A(1, A(1, A(1,A(2, 1)))) A(1, A(1, A(1, 2))) A(1, A(1, A(0, A(1, 1)))) A(1, A(1, A(0, 2))) A(1, A(1, 2(2))) A(1, A(1, 4)) A(1, A(0, A(1, 3))) A(1, A(0, A(0, A(1, 2)))) A(1, A(0, A(0, A(0, A(1, 1))))) A(1, A(0, A(0, A(0, 2)))) A(1, A(0, A(0, 4))) A(1, A(0, 8)) A(1, 16) A(0, A(1, 15)) A(0, A(0, A(1, 14)) lol, this is going to take a while.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Anyone know if this is how you do it, or is there a faster way?
 5 months ago

amscaseyBest ResponseYou've already chosen the best response.0
Sorry, this is WAY above my level of math :/ wish i could be more help
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
@amistre64 Do you know if I am doing this right?
 5 months ago

amistre64Best ResponseYou've already chosen the best response.0
it looks like a recurrsion alright
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Yeah, that is what it is.
 5 months ago

amistre64Best ResponseYou've already chosen the best response.0
A( m1, A(m,n1) ) ; 3,3 A(m,n) = A( 31, A(3,31) ) A(3,3) =A( 2, A(3,2) ) A(3,2) = A( 2, A(3,1) ) A(3,1) = 2 A(3,2) = A( 2, 2) = A( 1, A(2,1) ) A(3,2) = A( 0, 2 ) = 4 A(3,3) =A( 2, 4 ) etc ....
 5 months ago

amistre64Best ResponseYou've already chosen the best response.0
multivariables seem to be a pain to do by hand, might help to program a simple loop for it
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Well I have to show my work for the homework so I'll probably have to write it out. I guess it is basically just a lot of plugging in the numbers over and over again.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Makes sense though, the way this one is going, I bet the A(3,4) will be really long, haha.
 5 months ago

amistre64Best ResponseYou've already chosen the best response.0
if you can determine a pattern :) but ive never really tried for a multivariable
 5 months ago

zimmahBest ResponseYou've already chosen the best response.0
Oh that makes sense. It's like programming an ifthenelse loop
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Well I guess I could do a simple program that outputs each step and then just copy the results to the paper.
 5 months ago

zimmahBest ResponseYou've already chosen the best response.0
Having never seen anything like this I was like put what in what now? Lol
 5 months ago

zimmahBest ResponseYou've already chosen the best response.0
Ye, that would be faster I guess
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Alrighty thanks for the help guys! I'm gonna hit up some python :D
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Well I started on the program. I think it will take a little more work to get it to print all the steps. def A(m, n): print "(", m, ", " , n, ")" if m == 0: return (2*n) elif m >= 1 and n == 0: return 0 elif m >= 1 and n == 1: return 2 elif m >= 1 and n >= 2: return (m  1, A(m, n  1)) m = input('m: ') n = input('n: ') answer = A(m,n)
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
And, I don't think it is working quite right yet.
 5 months ago

amistre64Best ResponseYou've already chosen the best response.0
yeah, i was trying to do it in excel ... its tricky at best
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
oops, missed an A in the return
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Here is my output: ( 3 , 3 ) ( 3 , 2 ) ( 3 , 1 ) ( 2 , 2 ) ( 2 , 1 ) ( 1 , 2 ) ( 1 , 1 ) ( 0 , 2 ) ( 2 , 4 ) ( 2 , 3 ) ( 2 , 2 ) ( 2 , 1 ) ( 1 , 2 ) ( 1 , 1 ) ( 0 , 2 ) ( 1 , 4 ) ( 1 , 3 ) ( 1 , 2 ) ( 1 , 1 ) ( 0 , 2 ) ( 0 , 4 ) ( 0 , 8 ) ( 1 , 16 ) ( 1 , 15 ) ( 1 , 14 ) ( 1 , 13 ) ( 1 , 12 ) ( 1 , 11 ) ( 1 , 10 ) ( 1 , 9 ) ( 1 , 8 ) ( 1 , 7 ) ( 1 , 6 ) ( 1 , 5 ) ( 1 , 4 ) ( 1 , 3 ) ( 1 , 2 ) ( 1 , 1 ) ( 0 , 2 ) ( 0 , 4 ) ( 0 , 8 ) ( 0 , 16 ) ( 0 , 32 ) ( 0 , 64 ) ( 0 , 128 ) ( 0 , 256 ) ( 0 , 512 ) ( 0 , 1024 ) ( 0 , 2048 ) ( 0 , 4096 ) ( 0 , 8192 ) ( 0 , 16384 ) ( 0 , 32768 )
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
I think one of the hardest parts will be getting it to output the results correctly
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Any luck with excel? I'm gonna switch to C++ to try to get the output working right.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
So here is what I came up with. Ended up using C. #include <stdio.h> #include <stdlib.h> int m; int n; int answer; void PrintA(m,n) { printf("A(%d, %d) = ", m, n); printf("A(%d, A(%d, %d)\n", m1, m , n1); } int A(int m, int n) { if(m == 0) return (2*n); else if(m >= 1 && n == 0) return 0; else if(m >= 1 && n == 1) return 2; else if(m >= 1 && n >= 2) PrintA(m,n); return A(m  1, A(m, n  1)); } int main() { printf("m: "); scanf("%d", &m); printf("n: "); scanf("%d", &n); answer = A(m, n); printf("Answer: %d\n", answer); return 0; }
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Here is what I get for the first one. A(3,3) Obviously the answer is wrong, but all the steps up to the answer should be correct. So I can calculate the answer myself from the last step, which is 4 I think.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
That works fine, now the problem is when I try A(3, 4) although I get the answer to be 0, it outputs for about 30 seconds, so I get like 1000s of lines of output which would be a bit too much to write. lol. Anyway, I'm thinking there must be some way to recognize a pattern in order to get the answer. :/
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
So yeah I found a pattern for A(3,3) problem when I got to A(1,16) and got the computer output you got.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
which i will most likely leave as 2^16
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I seen 2^n*A(1,16n)
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
what do you mean stops working?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
So how would I use this pattern in finding a solution? mistyped, you said you found a problem earlier.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
pattern not a problem i was referring to your problem/question
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
wow yeah it looks like A(3,4) might take longer to find.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Ah right, so we would need a separate pattern for A(3,4) determined by some of the output?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
You said you got 0. That is what I got too.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
A(3,4) =A(2,A(3,3)) =A(2,2^16) =A(1,A(2,2^161))  Let's look at A(2,2^161) A(2,2^161)=A(1,A(2,2^162)) There is like a pattern going on we have A(2,2^16b) b keeps increasing eventually it will get to 2^16 Since this is happening in the n part of A then the output will be 0.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Is this what you were looking for?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Yes I think so, just trying to get my head around it. I think once I look at it for a bit I will understand.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Thanks so much for all the help though! Really appreciate it.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Like A(something bigger than 1,0)=0 eventually A(1,k) will be A(1,0)
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
so b will eventually get to 2^16?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
and then it will be 0. I get it now, thank you so much :D
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Like because we keep subtracting 1 each time.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I'm not doing all those steps. It is impossible to do all those steps. You have to look for a pattern.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
n=2^16 n1=2^161 (n1)1=n2=2^162 (n2)1=n3=2^163 ....
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
we keep subtracting 1 from the n before.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
right right, exactly, until n becomes 0, then according to the second formula A(3,4) == 0
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
@myininaya Hi there, could you look over this one more time. According to my teacher, it is impossible to find the second number for A(3,4) by using a computer algorithm. And the students in my class are saying the answer is a really big number and not 0. Like a lot bigger then the number for A(3,3) Do you have any idea where that would be coming from?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Well it looked like the pattern was going toward it being 0. I can look at it again. Did you explain your thinking to the teacher person? Like why did they say the thinking was wrong?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
The teacher hasn't looked at my work yet, he was just giving hints to help with the homework, and he said that this part cannot be done with a computer program because it will run out of memory and lose the answer.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
I don't really understand why that would happen, but I just want to make sure to get it right since other students are getting really large numbers.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
He didn't say a human couldn't do it though right?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
No, he said it was possible to do by hand, but not with an algorithm.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Just because a computer doesn't have the space to use an algorithm to compute doesn't mean we don't have the space.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
So the answer is still 0
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
n=2^16 n1=2^161 (n1)1=n2=2^162 (n2)1=n3=2^163 remember when I wrote this?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
2^16 steps is a lot. I don't know if it is too long for a computer or not. But it will actually take longer than 2^16 steps to compute.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Right, so there isn't some sort of pattern we could figure out to get the answer without the steps?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I said it would take longer than 2^16 because we did some other crap before to get there and we still have to do more stuff after that, but the pattern seems to be leading to the answer being zero.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Hmm, well I'll stick with that then. Perhaps my teacher is wrong. :D
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
What? You said your teacher said it was possible for a human I thought.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
"No, he said it was possible to do by hand, but not with an algorithm."
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Yeah, but I got 0 with the program I wrote.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
So the answer you are saying is not zero?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Which is just a simple recursive function.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
That is what I was led to believe by my fellow students and teacher.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
So the teacher said the answer isn't 0 and does exist.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
No, the teacher didn't say anything about the answer, just that it couldn't be done with a computer, and since I got the same number with I computer 0, as you got by hand, I figured it couldn't be right unless my teacher was wrong.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Can you copy it here? What you put in as the algorithm into your computer? I will try to follow it.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I just want to see if I agree with your algorithm.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Is that it above? The final draft of your program?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
maybe you are accidentally getting 0. lol. i don't know.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
like you did get the right answer with A(3,3)
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
maybe we can check another one.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
Let's look at A(2,5) Use program and let's do it by hand.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
darn that is long. lol.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
haha, yeah. Runs for around 15 seconds.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
that is probably like a 100th of the output there. lol
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
is the answer always 0 when n>m?
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
No, for m = 1 and n = 2 I get A(1, 2) = A(0, A(1, 1) Answer: 4
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
A(1,2)=A(0,A(1,1)) =A(0,2) =2n =2n=2(2) since n=2. okay.did you computer also get 4 for A(1,2)?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
hmmm... I get 16 by hand for A(2,3)
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Yeah, computer seems to be doing it right.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Well I guess it is very possible that my teacher was wrong, idk.
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I don't know. There is a possibility I'm wrong. There is always a chance for that.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Well there is a lot less possibility that you are wrong then I am wrong, so I guess I'll stick with that. :P
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
I don't see anything wrong with your program. Maybe for most computers the algorithm will run too long. Not sure.
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
Hard to tell, do you have time to look at one more thing really really quick?
 5 months ago

myininayaBest ResponseYou've already chosen the best response.1
ok i will look no guarantees I will be able to help but i certainly will try
 5 months ago

bbkzr31Best ResponseYou've already chosen the best response.0
http://openstudy.com/study#/updates/5276cbf2e4b0275c53855b4a Alright, thanks, wish I could give you another medal :/
 5 months ago
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