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SRM2 Mar 2016
SRM 685

MultiplicationTable2Easy

Problem statement, definition, constraints, and public examples.

Problem Statement

Fox Ciel is creating a new binary operation.

The operation will be denoted $ and it will be defined on the finite set S = {0, 1, 2, ..., n-1}. I.e., for each ordered pair (i, j) of elements of S the operation (i $ j) will return some element of S.

For example, we can have S = {0, 1}, and we can define that (0 $ 0) = 0, (0 $ 1) = 1, (1 $ 0) = 0, and (1 $ 1) = 0.

Note that Ciel's operation is not necessarily symmetric. In other words, it is possible that for some i and j the operations (i $ j) and (j $ i) return two different values.

A nice concise description of the operation $ is its "multiplication table": a square table where in row i and column j we have the value (i $ j). You are given this "multiplication table" encoded as a int[] table with n^2 elements. For each valid i and j the operation (i $ j) returns the value table[i*n+j].

A subset T of S is called good if it has the following property: for any two elements i and j in T, (i $ j) is also in T.

You are given a int[] t. The elements of t form a subset of the set S. Return "Good" (quotes for clarity) if this subset is good. Otherwise, return "Not Good". Note that the return value is case-sensitive.

Definition

Class:
MultiplicationTable2Easy
Method:
isGoodSet
Parameters:
int[], int[]
Returns:
String
Method signature:
String isGoodSet(int[] table, int[] t)
(be sure your method is public)

Notes

  • You are not given the value of n explicitly. Instead, you can determine it as the square root of the number of elements in table.

Constraints

  • n will be between 2 and 50, inclusive.
  • table will contain exactly n*n elements.
  • Each element in table will be between 0 and n-1, inclusive.
  • t will contain between 1 and n elements, inclusive.
  • Each element in t will be between 0 and n-1, inclusive.
  • Elements in t will be distinct.

Examples

  1. {1, 1, 2, 3,
     1, 0, 2, 3,
     3, 3, 0, 3,
     2, 2, 2, 0}
    
    {1,0}
    Returns: "Good"
    We can verify: 0 $ 0 = 1 0 $ 1 = 1 1 $ 0 = 1 1 $ 1 = 0
  2. {1, 1, 2, 3,
     1, 0, 2, 3,
     3, 3, 0, 3,
     2, 2, 2, 0}
    {2, 3}
    Returns: "Not Good"
    Note that: 2 $ 2 = 0 but 0 is not in T, so it is not good.
  3. {1, 1, 2, 3,
     1, 0, 2, 3,
     3, 3, 0, 3,
     2, 2, 2, 0}
    
    {0,1,2,3}
    Returns: "Good"
  4. {1, 1, 2, 3,
     1, 0, 2, 3,
     3, 3, 0, 3,
     2, 2, 2, 0}
    
    {1}
    Returns: "Not Good"
  5. {2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2}
    {2,4,5}
    Returns: "Good"
  6. {2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2,
     2,2,2,2,2,2}
    {0,1,3,4,5}
    Returns: "Not Good"
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