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bbkzr31
 2 years ago
Need help with a discrete math problem.
bbkzr31
 2 years ago
Need help with a discrete math problem.

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zimmah
 2 years ago
Best ResponseYou've already chosen the best response.0I'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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0So 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Anyone know if this is how you do it, or is there a faster way?

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

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64 Do you know if I am doing this right?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0it looks like a recurrsion alright

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, that is what it is.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0A( 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 ....

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0multivariables seem to be a pain to do by hand, might help to program a simple loop for it

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Well 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Makes sense though, the way this one is going, I bet the A(3,4) will be really long, haha.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0if you can determine a pattern :) but ive never really tried for a multivariable

zimmah
 2 years ago
Best ResponseYou've already chosen the best response.0Oh that makes sense. It's like programming an ifthenelse loop

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Well I guess I could do a simple program that outputs each step and then just copy the results to the paper.

zimmah
 2 years ago
Best ResponseYou've already chosen the best response.0Having never seen anything like this I was like put what in what now? Lol

zimmah
 2 years ago
Best ResponseYou've already chosen the best response.0Ye, that would be faster I guess

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Alrighty thanks for the help guys! I'm gonna hit up some python :D

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Well 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)

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0And, I don't think it is working quite right yet.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0yeah, i was trying to do it in excel ... its tricky at best

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0oops, missed an A in the return

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Here 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 )

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0I think one of the hardest parts will be getting it to output the results correctly

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Any luck with excel? I'm gonna switch to C++ to try to get the output working right.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0So 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; }

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Here 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0That 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. :/

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1which i will most likely leave as 2^16

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1what do you mean stops working?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0So how would I use this pattern in finding a solution? mistyped, you said you found a problem earlier.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1pattern not a problem i was referring to your problem/question

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1wow yeah it looks like A(3,4) might take longer to find.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Ah right, so we would need a separate pattern for A(3,4) determined by some of the output?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1You said you got 0. That is what I got too.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1A(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.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Is this what you were looking for?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Yes I think so, just trying to get my head around it. I think once I look at it for a bit I will understand.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks so much for all the help though! Really appreciate it.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Like A(something bigger than 1,0)=0 eventually A(1,k) will be A(1,0)

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0so b will eventually get to 2^16?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0and then it will be 0. I get it now, thank you so much :D

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Like because we keep subtracting 1 each time.

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

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1we keep subtracting 1 from the n before.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0right right, exactly, until n becomes 0, then according to the second formula A(3,4) == 0

bbkzr31
 2 years ago
Best 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?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Well 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?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1He didn't say a human couldn't do it though right?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0No, he said it was possible to do by hand, but not with an algorithm.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Just because a computer doesn't have the space to use an algorithm to compute doesn't mean we don't have the space.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1So the answer is still 0

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.12^16 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Right, so there isn't some sort of pattern we could figure out to get the answer without the steps?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm, well I'll stick with that then. Perhaps my teacher is wrong. :D

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1What? You said your teacher said it was possible for a human I thought.

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

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, but I got 0 with the program I wrote.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1So the answer you are saying is not zero?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Which is just a simple recursive function.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0That is what I was led to believe by my fellow students and teacher.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1So the teacher said the answer isn't 0 and does exist.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0No, 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.

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1I just want to see if I agree with your algorithm.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Is that it above? The final draft of your program?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1maybe you are accidentally getting 0. lol. i don't know.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1like you did get the right answer with A(3,3)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1maybe we can check another one.

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1darn that is long. lol.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0haha, yeah. Runs for around 15 seconds.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0that is probably like a 100th of the output there. lol

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1is the answer always 0 when n>m?

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0No, for m = 1 and n = 2 I get A(1, 2) = A(0, A(1, 1) Answer: 4

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1A(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)?

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

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, computer seems to be doing it right.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Well I guess it is very possible that my teacher was wrong, idk.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1I don't know. There is a possibility I'm wrong. There is always a chance for that.

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Well there is a lot less possibility that you are wrong then I am wrong, so I guess I'll stick with that. :P

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

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0Hard to tell, do you have time to look at one more thing really really quick?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1ok i will look no guarantees I will be able to help but i certainly will try

bbkzr31
 2 years ago
Best ResponseYou've already chosen the best response.0http://openstudy.com/study#/updates/5276cbf2e4b0275c53855b4a Alright, thanks, wish I could give you another medal :/
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