ho to implement Sets in matlab
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hey everybody,, how to use Matlab in the set. problem: A = {1,2}, A ^ 2 = {(1,1), (1,2), (2,2) (2,1)};
how to find A ^ 100 by using Matlab?
2 个评论
John BG
2017-9-1
In this question the operation A^2 means
% find all combinations with repetition.
Since A is defined containing 2 digits only, A^100 is the same as asking
% find all combinations with repetition of 100 bits
100 bits are 30 digits in binary.
Walter Roberson
2017-9-2
Slight rephrasing there: Numbers of 100 binary digits require just over 30 decimal digits.
采纳的回答
Walter Roberson
2017-9-1
P = 100;
A = uint8([1, 2]); %if your stored values exceed 255 then change the uint8 to suit
lenA = length(A);
if lenA <= intmax('uint8')
sstype = 'uint8';
elseif lenA <= intmax('uint16')
sstype = 'uint16';
elseif lenA <= intmax('uint64')
sstype = 'uint64';
else
error('A is too large to be able to subscript into. How did you even manage to create it??');
end
num_AP = lenA^P;
try
AP = zeros(num_AP, P, class(A));
catch
whoA = whos('A');
bytes_per_entry = whoA.bytes ./ lenA;
A_bytes_required = num_AP * P * bytes_per_entry;
error('You need to install more memory; you need at least %g bytes of memory', A_bytes_required);
end
T = zeros(1, P, sstype);
for J = 1 : num_AP
AP(J,:) = A(T+1);
for K = P : -1 : 1
if T(K) ~= lenA - 1
T(K) = T(K) + 1;
break;
else
T(K) = 0;
end
end
end
On my system, the maximum that can be constructed is for P = 28, which needs about 6.7 gigabytes.
As far as I know, there are no implementations of the x64 architecture that have more than 48 memory pins. In the case where A is a matrix with only 2 elements, that would give a maximum of P = 42, because 2^43 * 43 entries * 1 byte/entry > 2^48 bytes. However, I wrote the code assuming that you have access to a classified computer with memory capacities exceeding 2*10^9 times as much information stored on Earth as of 2013. (Don't tell me if I am wrong -- I am not authorized to know.)
The code was designed to reduce the memory requirements, not for efficiency.
2 个评论
yogi yaspranika
2017-9-2
编辑：yogi yaspranika
2017-9-2
Walter Roberson
2017-9-2
MATLAB does not have a set data structure. It has array data structures and it has cell array data structures. In my code, each row of AP is one of the members of A^P, where A^P is understood to be ordered P-tuples.
If you were using sets then the only solutions would be:
A^0 = {} %the empty set
A^1 = {}, {1}, {2}
A^2 = {}, {1}, {2}, {1, 2}
A^(numel(A)+1) and higher are identical to A^(numel(A)) because, for example, {1, 2, 1} as a set is the same as {1, 2} and {2, 1}: by definition sets are unordered and have no duplicates.
更多回答（2 个）
How many elements will this set have? Do you want to store 2^100 * 2 elements? A double needs 8 byte and Matlab uses about 100 bytes overhead for each vector. Then you need about:
1267650600228229401496703205376 * (2 * 8 + 100) Byte
147e15 PetaByte. This will let the solar system explode due to the required energy consumption.
So please tell us, which problem you actually want to solve. It is very easy to calculate a specific element and there cannot be any use in storing such a huge array.
2 个评论
John D'Errico
2017-9-1
"how to find A^100 by using Matlab?"
Answer: you don't. You find a better (i.e., doable) way to solve the problem.
Mahi
2022-10-29
0 个投票
If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38,
find n ( X ∩ Y ).
1 个评论
Steven Lord
2022-10-29
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