Question

a. Find an algorithm for solving the following problem: Given a positive

integer n, find the list of positive integers whose product is the largest

among all the lists of positive integers whose sum is n. For example, if

n is 4, the desired list is 2, 2 because 2 × 2 is larger than 1 × 1 × 1 × 1,

2 × 1 × 1, and 3 × 1. If n is 5, the desired list is 2, 3.

b. What is the desired list if n 2001?

Answer 1

1. Accept the value for n, check if it is positive I.e. if n > 0

2. Now we need to store the elements into an array whose sum is n, so that is done using for loop as follows,

for(i=1;i<n;i++)

{

element[i]=n-i;

}

3. Now we need to store the products of these elements, so lets use the array product[], as follows

for(i=1;i<n;i++)

{

product[i] = element[i]*i;

}

4. Now we have the products of all the elements, we just need to find the maximum from this array

5. Lets assume first product is maximum, and proceed as follows

max=product[1];

for(i=2;i<n;i++)

{

if(product[i]>max)

max=product[i];

}

6. Print this value of max as the desired list.

display("The desired list is %d",max);

b. 1001as 1001*1000 is the biggest I.e.1,001,000