2.2.2 Subset Sums

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

{
ID: makeeca1
PROG: subset
LANG: PASCAL
}
program subset;
var n,i,j,v:longint;
    f:array[0..39,0..400]of longint;
begin
  assign(input,'subset.in');reset(input);
  assign(output,'subset.out');rewrite(output);
  readln(n);     close(input);
  v:=n*(n+1)>>1;
  if v and 1=1 then begin writeln(0); close(output);halt;end;
  v:=v>>1;
  f[1,1]:=1;f[1,0]:=1;
  for i:=2 to n do
    for j:=0 to v do
      if j-i>=0 then f[i,j]:=f[i-1,j]+f[i-1,j-i] else f[i,j]:=f[i-1,j];//Êý×Ö»®·Ö2
  writeln(f[n,v]>>1);
  close(output);
end.