Bulgarian solitaire for creating a pattern

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CS on 2 Feb 2022
Answered: Steven Lord on 3 Feb 2022
Bulgarian solitaire is a game in which you start with a sequence of numbers that adds to k(k+1)/2 for some k. (This sum is 1 + 2 + … + k.) Think of each number in the sequence as representing a collection of pebbles. (For example, the sequence <6, 9> represents two piles containing 6 and 9 pebbles.) Form a new sequence by taking one pebble from each pile to form a new pebble. Thus for example, the sequence <6, 9> generates the sequence <2, 5, 8>, then <1, 3, 4, 7> etc. The sequence stops with <1, 2, 3, 4, 5> since this sequence remains unchanged after a move.
My question: Given a sequence, I want to write a program that takes such a sequence as input and displays all the sequences generated by moves of Bulgarian solitaire until the sequence <1, 2, …, k> is reached for some k.
Any help is greatly appreciated! Thanks!
CS on 3 Feb 2022
Here is what I have thus far:
% Bulgarian Solitaire
% Generate a random integer array whose elements total less than 46
array = randperm(45,1);
k = sum(array);
i = 2;
while k <= 45
array(i) = randperm(45,1);
k = sum(array);
i = i+1;
end
while k > 46
array(i) = 0;
k = sum(array);
i = i-1;
end
% Remove zeros from the initial array
value = find(array(:) == 0);
array(value) = [];
array = reshape(array, size(array,1), []);
% Sort array from smallest to largest
array = sort(array)
% Find the value of the largest element in the array
maxValue = max(array(:));
% Iterate the solitaire process
% If maxValue > 9, continue interation
count = 0;
if maxValue > 9
% Subtract one from each element of the array and increment counter
for i = 1:length(array)
array(i) = array(i) - 1;
count = count + 1;
i = i + 1;
end
% Increment array length by 1 and add the count value to the array
array(length(array) + 1) = count;
% Remove zeros from the array
value = find(array(:) == 0);
array(value) = [];
array = reshape(array, size(array,1), []);
% Find the value of the largest element in the array
maxValue = max(array(:));
% Sort array from smallest to largest
array = sort(array)
end
Any help is appreciated! Thanks!

Steven Lord on 3 Feb 2022
A couple suggestions:
% Bulgarian Solitaire
% Generate a random integer array whose elements total less than 46
array = randperm(45,1);
k = sum(array);
i = 2;
while k <= 45
array(i) = randperm(45,1);
k = sum(array);
i = i+1;
end
while k > 46
array(i) = 0;
k = sum(array);
i = i-1;
end
So you want a vector of integer values between 1 and 45 whose sum is less than 46? A simpler way to do this would be to generate a 45-element vector (a 45-element vector each element of which is 1 is the longest vector you could create that could satisfy your sum requirement.) Use cumsum to add up the first element, the first two elements, the first three elements, etc. Then find the last element in that cumulative sum that's less than 46 and truncate your array at that point, throwing away the later elements.
% Remove zeros from the initial array
value = find(array(:) == 0);
array(value) = [];
array = reshape(array, size(array,1), []);
% Sort array from smallest to largest
array = sort(array)
array = 30
% Find the value of the largest element in the array
maxValue = max(array(:));
There's no need to call max here. If you have an array that's been sorted from smallest to largest, which element is the largest?
% Iterate the solitaire process
% If maxValue > 9, continue interation
count = 0;
if maxValue > 9
% Subtract one from each element of the array and increment counter
for i = 1:length(array)
array(i) = array(i) - 1;
count = count + 1;
i = i + 1;
end
% Increment array length by 1 and add the count value to the array
array(length(array) + 1) = count;
% Remove zeros from the array
value = find(array(:) == 0);
array(value) = [];
array = reshape(array, size(array,1), []);
% Find the value of the largest element in the array
maxValue = max(array(:));
% Sort array from smallest to largest
array = sort(array)
end
array = 1×2
1 29
Your code above processes each element of your array one by one. One of the nice features about MATLAB is that you can operate on vectors or arrays in one command (for many operations.) Have a vector of values 1:5 and want to add to 1 each? You could loop through the elements or you could do it in one command, like where I create y below:
x = 1:5
x = 1×5
1 2 3 4 5
y = x + 1
y = 1×5
2 3 4 5 6
The size and length functions may be of use to you in determining how much larger the sum of elements in y is than the sum of elements in x.