Huge Addition

Matlab. This was an interesting assignment in the Matlab course I took before. Its inputs and output could be very large, in fact, larger than representable number in Matlab. Solution can show its output with full digits even if it is more than 16 digits.

For example;

input 1 = ‘392819655968612702353430868739406976733152178677243’

input 2 = ‘800648666501228076207488540123’

Question: Write function called huge_add that adds together two positive integers of any length specified as char vectors using decimal notation. The single output argument is the result and it is a char vector as well. The inputs and output must contain digits only; no commas, spaces or any other characters are allowed. If any of these assumptions are violated by the input, the function returns the number -1. Hint: you cannot use any of the built-in numerical data types of MATLAB to do the calculation since the function needs to work for numbers that are larger than what can be represented as a number in MATLAB.

Solution: After checking if the inputs are char or not, char inputs were converted to double and passed to the calculation stage. I wrote an function inside called “calculator” for addition creating a char vector by taking care of any carries. In the final stage, this function is called after the input sizes are compared and zeros are added to close the digit gap between the inputs.

answer = ‘392819655968612702354231517405908204809359667217366’

function output = test_huge_add
tic
char1 = '392819655968612702353430868739406976733152178677243';   %input 1
char2 = '800648666501228076207488540123';                        %input 2

 %Checking Stage for the Inputs 

if ~ischar(char1) || ~ischar(char2)
    output = -1;
    return
end

number1 = str2num(char1);
number2 = str2num(char2);

if length(number1) ~=1 || length(number2) ~=1
    output = -1;
    return
end  
if number1 < 0 || fix(number1) ~= number1 
    output = -1;
    return
end    
if number2 < 0 || fix(number2) ~= number2 
    output = -1;
    return
end   

 %Calculating Stage

function calculator()
new_char_vector = '';
    carry = 0;
    for i = length(char1):-1:1
        x = str2num(char1(i)) + str2num(char2(i)) + carry;
        carry = 0;
        if x < 10
            x = num2str(x);
            new_char_vector = [x new_char_vector];
            x = str2num(x);
        end 
        if x >= 10
            remainder = mod(x,10);
            remainder = num2str(remainder);
            new_char_vector = [remainder new_char_vector];
            remainder = str2num(remainder);
            carry = carry + 1;
        end
    end 
    if carry == 1                       %if there is carry at last addition
        new_char_vector = ['1' new_char_vector];
    end    
    output = new_char_vector;
end

 %Final Stage - checking which input is bigger and finalising the array

if length(char1) == length(char2)       %if both digit numbers are equal
    calculator();                       %calling the function
end

if length(char1) > length(char2)        %if the first number digit is bigger
    d = length(char1) - length(char2);  %difference between digits
    for j = 1:d                       
        char2 = ['0' char2];            %adding zeros to the new char vector              
    end    
    calculator();                       
end

if length(char1) < length(char2)        %if the second number digit is bigger
    d = length(char2) - length(char1);  %difference between digits
    for j = 1:d                       
        char1 = ['0' char1];            %adding zeros to the new char vector              
    end    
   calculator();
end
toc
end

function output = test_huge_add

tic

char1 = '392819655968612702353430868739406976733152178677243'; %input 1

char2 = '800648666501228076207488540123'; %input 2

%Checking Stage for the Inputs

if ~ischar(char1) || ~ischar(char2)

output = -1;

return

end

number1 = str2num(char1);

number2 = str2num(char2);

if length(number1) ~=1 || length(number2) ~=1

output = -1;

return

end

if number1 < 0 || fix(number1) ~= number1

output = -1;

return

end

if number2 < 0 || fix(number2) ~= number2

output = -1;

return

end

%Calculating Stage

function calculator()

new_char_vector = '';

carry = 0;

for i = length(char1):-1:1

x = str2num(char1(i)) + str2num(char2(i)) + carry;

carry = 0;

if x < 10

x = num2str(x);

new_char_vector = [x new_char_vector];

x = str2num(x);

end

if x >= 10

remainder = mod(x,10);

remainder = num2str(remainder);

new_char_vector = [remainder new_char_vector];

remainder = str2num(remainder);

carry = carry + 1;

end

if carry == 1 %if there is carry at last addition

new_char_vector = ['1' new_char_vector];

end

output = new_char_vector;

end

%Final Stage - checking which input is bigger and finalising the array

if length(char1) == length(char2) %if both digit numbers are equal

calculator(); %calling the function

end

if length(char1) > length(char2) %if the first number digit is bigger

d = length(char1) - length(char2); %difference between digits

for j = 1:d

char2 = ['0' char2]; %adding zeros to the new char vector

end

calculator();

end

if length(char1) < length(char2) %if the second number digit is bigger

d = length(char2) - length(char1); %difference between digits

for j = 1:d

char1 = ['0' char1]; %adding zeros to the new char vector

end

calculator();

end

toc

end