I have to create a nested loop of for statement which goes to the level 51 to solve the equation which is a summation of 51 variables whose value varies from value1 to value 6

I have to create a nested loop of for statement which goes to the level 51 to solve the equation which is a summation of 51 variables whose value varies from value1 to value 6.

As in :

ANS = A1+A2+A3+A4+.......A51.

Value of each of these variables A1 to A51 varies from X1 to X6 (total 6 no. values).

The total no. of times the loop has to run is very high number i.e. 6^51.

Due to this the time taken is very high.

Any method to reduce the time of solving ?

Answer 1

[Jaimin]

Hi Ninad Pimpalkhare,

As described, you need to construct a nested loop structure with 51 levels to solve an equation that sums 51 variables (A1 to A51), each of which can assume one of six possible values (ranging from value1 to value6). This setup leads to a total of 6^51 iterations.

To optimize this issue, we can use a Dynamic Programming approach. By storing each repetitive result in memory, we can significantly reduce the number of repetitive calculations.

Here, I have attached a sample program related to your issue.

function result = sum_combinations(n, values)
    memo = containers.Map('KeyType', 'char', 'ValueType', 'double');
    
    function total_sum = helper(level, current_sum)
        if level == n
            total_sum = current_sum;
            return;
        end
        
        key = [num2str(level), '_', num2str(current_sum)];
        if isKey(memo, key)
            total_sum = memo(key);
            return;
        end
        
        total_sum = 0;
        for i = 1:length(values)
            total_sum = total_sum + helper(level + 1, current_sum + values(i));
        end
        
        memo(key) = total_sum;
    end

    result = helper(0, 0);
end

values = [1, 2, 3, 4, 5, 6];  % replace with actual values
n = 51; % Count of variables
result = sum_combinations(n, values);
disp(['The result is: ', num2str(result)]);

The result is: 8.656692481647626e+41

Here, I have attached some resources related to Dynamic Programming in MATLAB.

https://www.mathworks.com/matlabcentral/fileexchange/86573-dynamic-programming-for-matlab

I hope this will help solve your issue.