Question

MATLAB Question:

TASK 5 12 MARKS -L06N] The rounded-square-root (RSR) of a positive integer n is defined as the square root of n rounded to the nearest integer. Adapting Heron's method to integer arithmetic allows the rounded-square-root of n to be calculated as follows. Let d be the number of digits of number n d-1 If d is odd, then Xo = 2 × 107- If d is even, then Xo-7 × 107- where xo is the starting guess for the rounded-square-root of n. The proceeding guess is calculated using the current guess as: where x and [xl (notice the ticks at the top and bottom of the brackets) represent the floor and ceiling of x, respectively. This pattern repeats such that, +1箭! r2 + Hence, the general equation is Xi + Naming x as xi and xi1 as xi1, the equation is given as xi1-floor((xi+ceil(n/xi)/2). For the next iteration, x becomes x#1 and x#1 is recalculated using this new xi. Repeat this process until x 1. Write a function named numdigs that takes n as an input, and outputs the number of digits d Hint: convert the number to a string and take the length of the string. Write a script that calculates the RSR value for a positive integer n. It is strongly recommended that you perform several iterations of this process by hand to obtain a deeper understanding of the changes in variables required. As a check, below is a table of n, corresponding RSR and number of iterations taken. 2. RSR 35 37 75 Iterations taken 1234 1337 5678 3. Modify your script such that it calculates the RSR values for all 4-digit numbers (i.e. n-1000:9999) You may want to make a copy of your code in step 2 as a backup.

Answer 1

%%%%%FUNCTION FOR PART A

function d = numdigs(n)
d = strlength(string(n));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%SCRIPT FOR PART 2

n=input('Enter a positive integer: ');
d = numdigs(n);
if rem(d,2)==0
    x0=7*10^((d-2)/2);
else
    x0=7*10^((d-1)/2);
end
xi=1/x0;
xi1=x0;
while xi~=xi1
    xi=xi1;
    xi1=floor((xi+ceil(n/xi))/2);
end
fprintf('RSR value: %d\n',xi1)
       

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%SCRIPT FOR PART 3

RSR=zeros(1,length(1000:9999));
for n=1000:9999
    d = numdigs(n);
    if rem(d,2)==0
        x0=7*10^((d-2)/2);
    else
        x0=7*10^((d-1)/2);
    end
    xi=1/x0;
    xi1=x0;
    while xi~=xi1
        xi=xi1;
        xi1=floor((xi+ceil(n/xi))/2);
    end
    RSR(n-999)=xi1;
end

Command Window >>RSR calc Enter a positive integer 1234 RSR value: 35 RSR calc Enter a positive integer: 1337 RSR value: 37 RSR calc Enter a positive integer: 5678 RSR value: 75