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.
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, 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{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.{1, 1, 2, 3, 1, 0, 2, 3, 3, 3, 0, 3, 2, 2, 2, 0}{0,1,2,3}Returns: "Good"
{1, 1, 2, 3, 1, 0, 2, 3, 3, 3, 0, 3, 2, 2, 2, 0}{1}Returns: "Not Good"
{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"
{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"
Back to all problems