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bbkzr31

  • one year ago

Need help with a discrete math problem.

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  1. bbkzr31
    • one year ago
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  2. zimmah
    • one year 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. bbkzr31
    • one year 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. bbkzr31
    • one year ago
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    Anyone know if this is how you do it, or is there a faster way?

  5. amscasey
    • one year ago
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    Sorry, this is WAY above my level of math :/ wish i could be more help

  6. bbkzr31
    • one year ago
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    @amistre64 Do you know if I am doing this right?

  7. amistre64
    • one year ago
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    it looks like a recurrsion alright

  8. bbkzr31
    • one year ago
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    Yeah, that is what it is.

  9. amistre64
    • one year 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
    • one year 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. bbkzr31
    • one year 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. bbkzr31
    • one year 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
    • one year ago
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    if you can determine a pattern :) but ive never really tried for a multivariable

  14. zimmah
    • one year ago
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    Oh that makes sense. It's like programming an if-then-else loop

  15. amistre64
    • one year ago
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    yep

  16. bbkzr31
    • one year 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. zimmah
    • one year ago
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    Having never seen anything like this I was like put what in what now? Lol

  18. zimmah
    • one year ago
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    Ye, that would be faster I guess

  19. bbkzr31
    • one year ago
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    Alrighty thanks for the help guys! I'm gonna hit up some python :D

  20. bbkzr31
    • one year 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. bbkzr31
    • one year ago
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    And, I don't think it is working quite right yet.

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

  23. bbkzr31
    • one year ago
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    oops, missed an A in the return

  24. bbkzr31
    • one year 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. bbkzr31
    • one year ago
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    lol

  26. bbkzr31
    • one year ago
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    I think one of the hardest parts will be getting it to output the results correctly

  27. bbkzr31
    • one year ago
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    Any luck with excel? I'm gonna switch to C++ to try to get the output working right.

  28. bbkzr31
    • one year 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. bbkzr31
    • one year 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. bbkzr31
    • one year 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
    • one year 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
    • one year ago
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    which i will most likely leave as 2^16

  33. bbkzr31
    • one year ago
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    So the stops working?

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

  35. myininaya
    • one year ago
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    what do you mean stops working?

  36. bbkzr31
    • one year 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
    • one year ago
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    pattern not a problem i was referring to your problem/question

  38. bbkzr31
    • one year ago
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    oh I get it now, lol.

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

  40. bbkzr31
    • one year 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
    • one year ago
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    You said you got 0. That is what I got too.

  42. myininaya
    • one year 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
    • one year ago
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    Is this what you were looking for?

  44. bbkzr31
    • one year 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. bbkzr31
    • one year ago
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    Thanks so much for all the help though! Really appreciate it.

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

  47. myininaya
    • one year ago
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    And A(1,0)=0

  48. bbkzr31
    • one year ago
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    so b will eventually get to 2^16?

  49. myininaya
    • one year ago
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    yep.

  50. bbkzr31
    • one year ago
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    and then it will be 0. I get it now, thank you so much :D

  51. myininaya
    • one year ago
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    Like because we keep subtracting 1 each time.

  52. myininaya
    • one year 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
    • one year 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
    • one year ago
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    we keep subtracting 1 from the n before.

  55. bbkzr31
    • one year ago
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    right right, exactly, until n becomes 0, then according to the second formula A(3,4) == 0

  56. bbkzr31
    • one year 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
    • one year 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. bbkzr31
    • one year 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. bbkzr31
    • one year 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
    • one year ago
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    He didn't say a human couldn't do it though right?

  61. bbkzr31
    • one year ago
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    No, he said it was possible to do by hand, but not with an algorithm.

  62. myininaya
    • one year 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
    • one year ago
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    So the answer is still 0

  64. myininaya
    • one year 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
    • one year 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. bbkzr31
    • one year 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
    • one year 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. bbkzr31
    • one year ago
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    Hmm, well I'll stick with that then. Perhaps my teacher is wrong. :D

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

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

  71. bbkzr31
    • one year ago
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    Yeah, but I got 0 with the program I wrote.

  72. myininaya
    • one year ago
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    So the answer you are saying is not zero?

  73. bbkzr31
    • one year ago
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    Which is just a simple recursive function.

  74. bbkzr31
    • one year ago
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    That is what I was led to believe by my fellow students and teacher.

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

  76. bbkzr31
    • one year 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
    • one year 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
    • one year ago
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    I just want to see if I agree with your algorithm.

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

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

  81. myininaya
    • one year ago
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    or

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

  83. myininaya
    • one year ago
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    maybe we can check another one.

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

  85. myininaya
    • one year ago
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    darn that is long. lol.

  86. bbkzr31
    • one year ago
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    haha, yeah. Runs for around 15 seconds.

  87. bbkzr31
    • one year ago
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    that is probably like a 100th of the output there. lol

  88. myininaya
    • one year ago
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    is the answer always 0 when n>m?

  89. bbkzr31
    • one year 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. bbkzr31
    • one year ago
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    For 2 and 3

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  91. myininaya
    • one year 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. bbkzr31
    • one year ago
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    Yep

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

  94. bbkzr31
    • one year ago
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    Yeah, computer seems to be doing it right.

  95. bbkzr31
    • one year ago
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    Well I guess it is very possible that my teacher was wrong, idk.

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

  97. bbkzr31
    • one year 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
    • one year 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. bbkzr31
    • one year ago
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    Hard to tell, do you have time to look at one more thing really really quick?

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

  101. bbkzr31
    • one year ago
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    http://openstudy.com/study#/updates/5276cbf2e4b0275c53855b4a Alright, thanks, wish I could give you another medal :/

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