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November 14th Subset Sums

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November 14th Subset Sums Empty November 14th Subset Sums

Post  Eddie Fri Nov 14, 2008 11:16 pm

Subset Sums
JRM

For many sets of consecutive integers from 1 through N (1 <= N <= 39), one can partition the set into two sets whose sums are identical.

For example, if N=3, one can partition the set {1, 2, 3} in one way so that the sums of both subsets are identical:

* {3} and {1,2}

This counts as a single partitioning (i.e., reversing the order counts as the same partitioning and thus does not increase the count of partitions).

If N=7, there are four ways to partition the set {1, 2, 3, ... 7} so that each partition has the same sum:

* {1,6,7} and {2,3,4,5}
* {2,5,7} and {1,3,4,6}
* {3,4,7} and {1,2,5,6}
* {1,2,4,7} and {3,5,6}

Given N, your program should print the number of ways a set containing the integers from 1 through N can be partitioned into two sets whose sums are identical. Print 0 if there are no such ways.

Your program must calculate the answer, not look it up from a table.
PROGRAM NAME: subset
INPUT FORMAT
The input file contains a single line with a single integer representing N, as above.
SAMPLE INPUT (file subset.in)

7

OUTPUT FORMAT

The output file contains a single line with a single integer that tells how many same-sum partitions can be made from the set {1, 2, ..., N}. The output file should contain 0 if there are no ways to make a same-sum partition.
SAMPLE OUTPUT (file subset.out)

4

Spoiler:

Eddie
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November 14th Subset Sums Empty Re: November 14th Subset Sums

Post  a13x Mon Nov 24, 2008 10:01 pm

still don't get it completely, but since when does anyone have to understand how something works to use it?

a13x
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