programming to find out all possible combination of numbers a,b,c,d in which 0<a<b<c<d<90.
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all possible combination of numbers a,b,c,d in which 0<a<b<c<d<90.
2 个评论
Guillaume
2015-8-26
You have to clarify what you mean by numbers. There is of course an infinity of numbers between 0 and 90. Do you mean integers?
UJJWAL BARMAN
2015-8-26
采纳的回答
Isn't this simply four for loop?
for a = 1:86
for b = a+1:87
for c = b+1:88
for d = c+1:89
%do whatever you want with a,b,c,d
end
end
end
end
3 个评论
Walter Roberson
2015-8-26
That only deals with integers. The past questions of the poster suggest that the poster intends to test all possible double precision numbers over that range, in order to attempt to find the solution to a set of simultaneous equations in 4 unknowns. (If the simultaneous equations have not changed since the earlier postings, my tests suggest that there are no solutions in the target range.)
UJJWAL BARMAN
2015-9-4
Walter Roberson
2015-9-4
Be specific about how you want them output. Do you want them all displayed? If so then is a list of 4 numbers per line acceptable? Do you need every line to include the text 'a=' and ',b=' and so on? Do you want a variable that contains a something-by-4 array where each line is an a, b, c, d selection?
更多回答（4 个）
Walter Roberson
2015-8-26
1 个投票
There will be 4636033603912859644 choices for "a" alone, for a total of 19247532396881346240525890574203961674141911582083171582958740223586992125 combinations. That is roughly the cube of the number of fundamental particles in the observable universe, so there is no known means for recording all of those combinations.
8 个评论
Guillaume
2015-8-26
Am I missing something? Even if you remove the ordering relationship, all combinations of four integers between 1 and 89 is only 89^4 = 62742241 combinations.
Walter Roberson
2015-8-26
You are assuming integers. I, though, have answered several questions from the same poster in which the poster has been trying to find four angles in the range 0 to 90 which satisfy a particular set of simultaneous equations. (My investigations at the time suggested firmly that there were no real-valued solutions in that range -- though there were solutions if at least one or more of the angles was allowed to exceed that range.)
Guillaume
2015-8-26
Oh yes, if it's not integer, then of course the question makes no sense.
John D'Errico
2015-8-26
Well, you cannot really say there is no known means. Simply listing the combinations in theory is adequate. It just might take a wee bit more time than most people are willing to invest.
Walter Roberson
2015-8-26
There isn't enough energy in the universe to be able to output them all on any known display.
Walter Roberson
2015-8-27
[A,B,C,D] = ndgrid(1:86, 2:87, 3:88, 4:89);
ABCD = [A(:), B(:), C(:), D(:)];
idx = ABCD(:,1) < ABCD(:,2);
ABCD = ABCD(idx,:);
idx = ABCD(:,2) < ABCD(:,3);
ABCD = ABCD(idx,:);
idx = ABCD(:,3) < ABCD(:,4);
ABCD = ABCD(idx,:);
Now ABCD will be an N x 4 array in which column 1 corresponds to an A value, column 2 to a B value, column 3 to a C value, column 4 to a D value.
UJJWAL BARMAN
2015-8-27
Walter Roberson
2015-8-27
A = ABCD(:, 1); B = ABCD(:, 2);
etc. The 5th solution would be A(5),B(5),C(5),D(5)
You asked for all of the solutions and this is all of the solutions. Millions of them.
Kelly Kearney
2015-8-27
For just the integers:
tmp = nchoosek(1:89,4);
a = tmp(:,1);
b = tmp(:,2);
c = tmp(:,3);
d = tmp(:,4);
The nchoosek function automatically sorts its results, so you don't have to worry about the inequality check. You could use the same function to test non-integers, too, though as everyone has pointed out the size of your arrays will quickly get out of control as you increase resolution.
1 个评论
Roger Stafford
2015-9-4
Kelly's answer using 'nchoosek' is the best one, Ujjwal, and you should accept it. It will give you 89!/4!/85! = 2,441,626 possible combinations.
Note however that he misstates things a bit where he asserts that 'nchoosek' sorts the results. It does not. It actually uses the same order as was present in the received vector argument, which in the case of 1:89 would happen to be sorted.
UJJWAL BARMAN
2015-9-4
0 个投票
1 个评论
Guillaume
2015-9-4
Please use comments rather than answering your own question with another question.
To solve your problem, simply move the save after the end of the last loop and save aa, bb, etc. instead of a, b, etc.
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