algorithm to sum up a list of numbers for all combinations

Question

I have a list of numbers and I want to add up all the different combinations. For example:

• number as 1,4,7 and 13
• the output would be:

1+4=5
1+7=8
1+13=14
4+7=11
4+13=17
7+13=20
1+4+7=12
1+4+13=18
1+7+13=21
4+7+13=24
1+4+7+13=25

Is there a formula to calculate this with different numbers?

Answer 1

A simple way to do this is to create a bit set with as much bits as there are numbers. In your example 4.

Then count from 0001 to 1111 and sum each number that has a 1 on the set:

Numbers 1,4,7,13:

0001 = 13=13
0010 = 7=7
0011 = 7+13 = 20

1111 = 1+4+7+13 = 25