Zero Sum
[Credit: ACM Programming Contest, adapted]
- Consider the sequence of digits from 1 through N (where N <= 9) in increasing order:
- 1 2 3 4 5 ... N
-
- Your job is to write a program that will calculate the sums and differences of the numbers and find all the sequences of length N that will procude a ZERO sum. Output all the numbers and insert either a (+) for ddition or a (-) for subtraction or a ( ) [blank or null] to run the digits together.
-
- Eg.
Input
- 7
- Output
- 1 + 2 - 3 + 4 - 5 - 6 + 7 = 0
- 1 + 2 - 3 - 4 + 5 + 6 - 7 = 0
- 1 - 2 + 3 + 4 - 5 + 6 - 7 = 0
- 1 - 2 - 3 - 4 - 5 + 6 + 7 = 0
- 1 - 23 + 4 + 5 + 6 + 7 = 0
- 1 - 23 - 45 + 67 = 0