Class Name: Partitions
Method Name: getKthPartition
Parameters: int,int
Returns: int[]
A nice order partition of positive integer n is a nonincreasing ordered
sequence of positive integers that sum to n. For example, {6,2,1} is a nice
order partition of 9 and {10,3,3,2} is a nice order partition of 18 and {3} is
a nice order partition of 3.
Nice order partitions are ordered based on the following rule:
Partition A is before partition B if and only if there exists a positive
integer x such that
A1 = B1 and A2 = B2 and . . . and A(x1) = B(x1) and Ax > Bx
where Pn is the nth integer in partition P (the i integers in the partition are
numbered 1 to i).
For example the partition {6,3,2,1} is before the partition {6,3,1,1,1} in the
ordered list of nice order partitions of 12.
Implement a class Partitions which contains a method getKthPartition. The
method inputs two ints, n and k. The method returns the kth unique nice order
partition of n, using the ordering rule above. k=1 refers to the first
partition (Start counting at 1, not 0). The partition is returned as an int[]
of the elements in the partition, where the element with index 0 of the int[]
is the first Integer in the partition, index 1 is the second, etc...
If k is larger than the number of partitions, the method should return an empty
instance of an int[] object.
The method signature is:
public int[] getKthPartition(int n, int k);
n and k satisfy:
0 < n < 21
0 < k < 1001
Note:
The solution must run in under 6 seconds on TopCoder's tester.
Examples:
*If n=5 and k=2, the partitions, in order, are:
{5}
{4,1}
{3,2}
{3,1,1}
{2,2,1}
{2,1,1,1}
{1,1,1,1,1}
The 2nd one is {4,1} and the method should return {4,1} as an int[].
*If n=10 and k=7, the method should return {7,1,1,1}
