2) Coding exercises. Write pseudocode segments in the style of Cheney and Kincai

Question

2) Coding exercises. Write pseudocode segments in the style of Cheney and Kincaid to solve the following problems: a) Assuming an integer variable n has already been initialized, output the integer prime numbers between 2 and n, inclusive. Y ou may assume that the value initialized in n is greater than 2. Make use of a special arithmetic operator, the modulo operator %, in your pseudocode. The modulo operator results in the remainder of an integer division operation. For example, 7 % 3-1, 10 % 4-2, and 12 % 6-0.

Explanation / Answer

(a)

for i ranges from 2 to n //we will check each i from 2 to n if it is a prime no or not

isPrime = True //initialising isPrime to true

for j ranges from 2 to i-1 //we will check from 2 to i-1 whether i has a factor

if (i%j=0) then //if i%j=0, it means j is a factor of i

isPrime=false //we assign false to isPrime

exit inner loop //and exit the inner loop

endif

endfor

if(isPrime = true) then //we will check if isPrime is true

print i is a prime number //if it is true, then i is a prime number

else

print i is not a prime number //otherwise i is not a prime number

endif

endfor

(b)

1. initialise rp to 1 and rn to 2 //this is to make sure the loop runs for atleast one time

2. while (mod(rn - rp) > 0.000001) do //condition to if check |rn - rp|> 0.000001

rp=rn //assigning new rn to rp

rn = ( rp + x/rp )/2 //assign the value to rn according to formula

endwhile

3. print rn //this rn is the approximate square root of x

(c)

1. Initialise mean and sigma to 0 //initialising mean and sigma to 0

2. for i in range 1 to 100 //iterating over all the array numbers

mean=mean + x[i] //adding all array numbers to mean

endfor

3. mean = mean/100 //dividing mean by 100 as mean = sum/n

4. for i in range 1 to 100 //iterating over all array numbers

sigma = sigma + (x[i]-mean) * (x[i]-mean) //adding (x[i]-mean)2 to sigma for each i

endfor

5. sigma = sigma / n // completing the formula for sigma

6. print sigma and mean //printing sigma and mean

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