Hey ppl,
I was browsing thro the topcoder sample problems and came up with this one. Plz suggest some good algorithm for this.
Problem Statement
Note: Please keep programs under 7000 characters in length. Thank you
Class Name: SquareDigits
Method Name: smallestResult
Parameters: int
Returns: int
Define the function S(x) as the sum of the squares of the digits of x.
For example: S(3)=3*3=9 and S(230)=2*2+3*3+0*0=13.
Define the set T(x) to be the set of unique numbers that are produced by
repeatedly applying S to x. That is: S(x), S(S(x)), S(S(S(x))), etc...
For example, repeatedly applying S to 37:
S(37)=3*3+7*7=58.
S(58)=5*5+8*8=89.
S(89)=145.
S(145)=42.
S(42)=20.
S(20)=4.
S(4)=16.
S(16)=37.
Note this sequence will repeat so we can stop calculating now and:
T(37)={58,89,145,42,20,4,16,37}.
However, note T(x) may not necessarily contain x.
Implement a class SquareDigits, which contains a method smallestResult. The
method takes an int, n, as a parameter and returns the smallest int, x, such
that T(x) contains n.
The method signature is (be sure your method is public):
int smallestResult(int n);
TopCoder will ensure n is non-negative and is between 0 and 199 inclusive.
Examples:
If n=0: S(0) = 0, so T(0)={0}, so the method should return 0.
If n=2: T(0) through T(10) do not contain the value 2. If x=11, however:
S(11)=1*1+1*1=2, so T(11) contains 2, and the method should return 11.
If n=10: T(0) through T(6) do not contain 10. If x=7:
S(7)=49.
S(49)=97.
S(97)=130.
S(130)=10.
S(10)=1.
and it starts to repeat...
so T(7) is {49,97,130,10,1}, which contains 10, and the method should return 7.
n=1 -> x=1
n=19 -> x=133
n=85 -> x=5
n=112 -> x=2666
Definition
Class: SquareDigits
Method: smallestResult
Parameters: int
Returns: int
Method signature: int smallestResult(int param0)
(be sure your method is public)
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