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anonymous

  • 2 years ago

Need help with a discrete math problem.

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  1. anonymous
    • 2 years ago
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  2. anonymous
    • 2 years ago
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    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.

  3. anonymous
    • 2 years ago
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    So if I started filling in the bottom formula for A(3, 3) A(3-1, A(3,3-1)) A(2, A(3,2)) Plug the A(3,2) back into the formula: A(2, A(3-1, A(3, 2-1))) 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(2-1, A(2, 2-1))) A(2, A(1, A(2, 1))) Use the third formula again: A(2, A(1, 2)) A(2, A(1-1,A(1, 2-1))) 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.

  4. anonymous
    • 2 years ago
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    Anyone know if this is how you do it, or is there a faster way?

  5. anonymous
    • 2 years ago
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    Sorry, this is WAY above my level of math :/ wish i could be more help

  6. anonymous
    • 2 years ago
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    @amistre64 Do you know if I am doing this right?

  7. amistre64
    • 2 years ago
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    it looks like a recurrsion alright

  8. anonymous
    • 2 years ago
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    Yeah, that is what it is.

  9. amistre64
    • 2 years ago
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    A( m-1, A(m,n-1) ) ; 3,3 A(m,n) = A( 3-1, A(3,3-1) ) 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 ....

  10. amistre64
    • 2 years ago
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    multivariables seem to be a pain to do by hand, might help to program a simple loop for it

  11. anonymous
    • 2 years ago
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    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.

  12. anonymous
    • 2 years ago
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    Makes sense though, the way this one is going, I bet the A(3,4) will be really long, haha.

  13. amistre64
    • 2 years ago
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    if you can determine a pattern :) but ive never really tried for a multivariable

  14. anonymous
    • 2 years ago
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    Oh that makes sense. It's like programming an if-then-else loop

  15. amistre64
    • 2 years ago
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    yep

  16. anonymous
    • 2 years ago
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    Well I guess I could do a simple program that outputs each step and then just copy the results to the paper.

  17. anonymous
    • 2 years ago
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    Having never seen anything like this I was like put what in what now? Lol

  18. anonymous
    • 2 years ago
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    Ye, that would be faster I guess

  19. anonymous
    • 2 years ago
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    Alrighty thanks for the help guys! I'm gonna hit up some python :D

  20. anonymous
    • 2 years ago
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    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)

  21. anonymous
    • 2 years ago
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    And, I don't think it is working quite right yet.

  22. amistre64
    • 2 years ago
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    yeah, i was trying to do it in excel ... its tricky at best

  23. anonymous
    • 2 years ago
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    oops, missed an A in the return

  24. anonymous
    • 2 years ago
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    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 )

  25. anonymous
    • 2 years ago
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    lol

  26. anonymous
    • 2 years ago
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    I think one of the hardest parts will be getting it to output the results correctly

  27. anonymous
    • 2 years ago
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    Any luck with excel? I'm gonna switch to C++ to try to get the output working right.

  28. anonymous
    • 2 years ago
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    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", m-1, m , n-1); } 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; }

  29. anonymous
    • 2 years ago
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    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.

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  30. anonymous
    • 2 years ago
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    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. :/

  31. myininaya
    • 2 years ago
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    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.

  32. myininaya
    • 2 years ago
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    which i will most likely leave as 2^16

  33. anonymous
    • 2 years ago
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    So the stops working?

  34. myininaya
    • 2 years ago
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    I seen 2^n*A(1,16-n)

  35. myininaya
    • 2 years ago
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    what do you mean stops working?

  36. anonymous
    • 2 years ago
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    So how would I use this pattern in finding a solution? mistyped, you said you found a problem earlier.

  37. myininaya
    • 2 years ago
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    pattern not a problem i was referring to your problem/question

  38. anonymous
    • 2 years ago
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    oh I get it now, lol.

  39. myininaya
    • 2 years ago
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    wow yeah it looks like A(3,4) might take longer to find.

  40. anonymous
    • 2 years ago
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    Ah right, so we would need a separate pattern for A(3,4) determined by some of the output?

  41. myininaya
    • 2 years ago
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    You said you got 0. That is what I got too.

  42. myininaya
    • 2 years ago
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    A(3,4) =A(2,A(3,3)) =A(2,2^16) =A(1,A(2,2^16-1)) ------------------ Let's look at A(2,2^16-1) A(2,2^16-1)=A(1,A(2,2^16-2)) There is like a pattern going on we have A(2,2^16-b) 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.

  43. myininaya
    • 2 years ago
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    Is this what you were looking for?

  44. anonymous
    • 2 years ago
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    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.

  45. anonymous
    • 2 years ago
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    Thanks so much for all the help though! Really appreciate it.

  46. myininaya
    • 2 years ago
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    Like A(something bigger than 1,0)=0 eventually A(1,k) will be A(1,0)

  47. myininaya
    • 2 years ago
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    And A(1,0)=0

  48. anonymous
    • 2 years ago
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    so b will eventually get to 2^16?

  49. myininaya
    • 2 years ago
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    yep.

  50. anonymous
    • 2 years ago
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    and then it will be 0. I get it now, thank you so much :D

  51. myininaya
    • 2 years ago
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    Like because we keep subtracting 1 each time.

  52. myininaya
    • 2 years ago
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    I'm not doing all those steps. It is impossible to do all those steps. You have to look for a pattern.

  53. myininaya
    • 2 years ago
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    n=2^16 n-1=2^16-1 (n-1)-1=n-2=2^16-2 (n-2)-1=n-3=2^16-3 ....

  54. myininaya
    • 2 years ago
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    we keep subtracting 1 from the n before.

  55. anonymous
    • 2 years ago
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    right right, exactly, until n becomes 0, then according to the second formula A(3,4) == 0

  56. anonymous
    • 2 years ago
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    @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?

  57. myininaya
    • 2 years ago
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    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?

  58. anonymous
    • 2 years ago
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    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.

  59. anonymous
    • 2 years ago
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    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.

  60. myininaya
    • 2 years ago
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    He didn't say a human couldn't do it though right?

  61. anonymous
    • 2 years ago
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    No, he said it was possible to do by hand, but not with an algorithm.

  62. myininaya
    • 2 years ago
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    Just because a computer doesn't have the space to use an algorithm to compute doesn't mean we don't have the space.

  63. myininaya
    • 2 years ago
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    So the answer is still 0

  64. myininaya
    • 2 years ago
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    n=2^16 n-1=2^16-1 (n-1)-1=n-2=2^16-2 (n-2)-1=n-3=2^16-3 remember when I wrote this?

  65. myininaya
    • 2 years ago
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    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.

  66. anonymous
    • 2 years ago
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    Right, so there isn't some sort of pattern we could figure out to get the answer without the steps?

  67. myininaya
    • 2 years ago
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    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.

  68. anonymous
    • 2 years ago
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    Hmm, well I'll stick with that then. Perhaps my teacher is wrong. :D

  69. myininaya
    • 2 years ago
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    What? You said your teacher said it was possible for a human I thought.

  70. myininaya
    • 2 years ago
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    "No, he said it was possible to do by hand, but not with an algorithm."

  71. anonymous
    • 2 years ago
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    Yeah, but I got 0 with the program I wrote.

  72. myininaya
    • 2 years ago
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    So the answer you are saying is not zero?

  73. anonymous
    • 2 years ago
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    Which is just a simple recursive function.

  74. anonymous
    • 2 years ago
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    That is what I was led to believe by my fellow students and teacher.

  75. myininaya
    • 2 years ago
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    So the teacher said the answer isn't 0 and does exist.

  76. anonymous
    • 2 years ago
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    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.

  77. myininaya
    • 2 years ago
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    Can you copy it here? What you put in as the algorithm into your computer? I will try to follow it.

  78. myininaya
    • 2 years ago
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    I just want to see if I agree with your algorithm.

  79. myininaya
    • 2 years ago
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    Is that it above? The final draft of your program?

  80. myininaya
    • 2 years ago
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    maybe you are accidentally getting 0. lol. i don't know.

  81. myininaya
    • 2 years ago
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    or

  82. myininaya
    • 2 years ago
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    like you did get the right answer with A(3,3)

  83. myininaya
    • 2 years ago
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    maybe we can check another one.

  84. myininaya
    • 2 years ago
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    Let's look at A(2,5) Use program and let's do it by hand.

  85. myininaya
    • 2 years ago
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    darn that is long. lol.

  86. anonymous
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    haha, yeah. Runs for around 15 seconds.

  87. anonymous
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    that is probably like a 100th of the output there. lol

  88. myininaya
    • 2 years ago
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    is the answer always 0 when n>m?

  89. anonymous
    • 2 years ago
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    No, for m = 1 and n = 2 I get A(1, 2) = A(0, A(1, 1) Answer: 4

  90. anonymous
    • 2 years ago
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    For 2 and 3

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  91. myininaya
    • 2 years ago
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    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)?

  92. anonymous
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    Yep

  93. myininaya
    • 2 years ago
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    hmmm... I get 16 by hand for A(2,3)

  94. anonymous
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    Yeah, computer seems to be doing it right.

  95. anonymous
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    Well I guess it is very possible that my teacher was wrong, idk.

  96. myininaya
    • 2 years ago
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    I don't know. There is a possibility I'm wrong. There is always a chance for that.

  97. anonymous
    • 2 years ago
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    Well there is a lot less possibility that you are wrong then I am wrong, so I guess I'll stick with that. :P

  98. myininaya
    • 2 years ago
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    I don't see anything wrong with your program. Maybe for most computers the algorithm will run too long. Not sure.

  99. anonymous
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    Hard to tell, do you have time to look at one more thing really really quick?

  100. myininaya
    • 2 years ago
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    ok i will look no guarantees I will be able to help but i certainly will try

  101. anonymous
    • 2 years ago
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    http://openstudy.com/study#/updates/5276cbf2e4b0275c53855b4a Alright, thanks, wish I could give you another medal :/

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