Sum a number in different ways.

Applications Programming
1

Hello, I need some help to correct my algorithm steps to sum a number. I am confused... please input some steps

Example:
Let's say a number 5.
Now we can get a list of numbers: 1, 2, 3, 4 (less than 5 in sorted order).
so the sum could be: 1+4; 2+3 ( 1+1+1+1+1 or 1+2+2 is not a solution).

Example2: number=7, soultion=1+6; 1+2+4; 2+5; 3+4

My Algorithm Steps:
num=n
start_num=1
ending_num=num-1
arr= @(1 to num-1)

result = first_element + next_element

if result = num then print the first_element + next_element;
 else result = result + third_element

print " all solutions ":
2

one way could be:

n=$1
printf "solutions="
    for (( i=1; i<=n/2; i++ )) 
    do 
    printf "$i+`expr $n - $i`; "
    done
printf "\n"