Codevs 2,055 Collection Division

"Title description"

For a set of contiguous integers from 1 to N (1<=n<=39), divided into two sub-sets, the sum of the numbers of each set is equal.

For example, if n=3, for {A-D} can be divided into two sub-sets, all of their numbers are equal: {3} and {a}

This is the only kind of division (the Interchange collection location is considered the same partitioning scheme and therefore does not increase the total number of partitioning schemes).

If the n=7, there are four ways to divide the set {1,2,3,4,5,6,7}, each subset of the subsets of each of the numbers and is equal:

{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}

Input

A positive integer n,1<=n<=39

Output

A number that divides the number of methods in the collection.

"Sample Input"

7

"Sample Output"

4

"Problem-solving ideas"

This is a backpack-type DP, for the kind of scheme, F[I,J] represents the number of the first I number of the scheme of J

Positive push: f[i,j]:=f[i-1,j]+f[i-1,j-i];

Initial conditions: f[1,1]:=1; F[1,0]:=1;

Backward (F[i,j] means the value of I~n is J)

F[i,j]:=f[i+1,j]+f[i+1,j-i];

Initial conditions: f[n,n]:=1; F[n,0]:=1;

1  ProgramT2;2 varN,sum,i,j:longint;3F:Array[1.. the,0.. -] ofLongint;4 begin5 read (n);6Sum:= (n+1) *nDiv 2;7     ifSumMoD 2=1  Then//Special Award8     begin9Write0);Ten Halt; One     End; ASum:=sumDiv 2; -f[1,1]:=1;//The method for taking the number 1 from the first 1 numbers is 1, the same as -f[1,0]:=1; the  -      fori:=2  toN-1  Do//default n in another array -          forj:=0  to(i+1) *iDiv 2  Do -         begin +f[i,j]:=f[i-1, j]; -             ifj-i>=0  Thenf[i,j]:=f[i,j]+f[i-1, j-i];//Anti-border +         End; AWriteln (f[n-1, sum]); at End.

Codevs 2,055 Collection Division