Problem Statement
(<Var> or <Var>) and (<Var> or <Var>) and ... and (<Var> or <Var>)<Var> can be a capital letter, or '~'(not) followed by a capital letter. Each "(<Var> or <Var>)" is called a BLOCK. For example:
"(P or P) and (~R or P) and (Q or Q)" is a logical statement with 3 BLOCKs.A logical statement can be MADE TRUE if there is a way of assigning truth values to the capital letters used, such that the entire statement evaluates to true. The previous example can be MADE TRUE since setting P and Q to true, and R to either true or false will make the statement true. Given a logical statement as a String[] of blocks, you will determine the minimum number of blocks that have to be removed such that the statement can be MADE TRUE. For example:
statement = {"P or Q","~P or ~P"}
This corresponds to the statement "(P or Q) and (~P or ~P)".
This statement can already be MADE TRUE so your method would return 0.
statement = {"P or P","~P or ~P"}
This corresponds to the statement "(P or P) and (~P or ~P)".
Removing either block will enable this statement to be MADE TRUE.
Your method would return 1.
Create a class Logical that contains the method howMany, which takes a String[] statement, and returns an int that represents the minimum number of blocks that need to be removed such that the statement can be MADE TRUE.Definition
- Class:
- Logical
- Method:
- howMany
- Parameters:
- String[]
- Returns:
- int
- Method signature:
- int howMany(String[] statement)
- (be sure your method is public)
Constraints
- statment must contain between 1 and 10 elements inclusive
- Each element of statement must be of the form(quotes for clarity): " or " where can be either a capital letter ('A'-'Z'), or '~' followed by a capital letter
Examples
{"P or P","~R or P","Q or Q"}
Returns: 0
This was one of the examples stated in the problem. The statement can already be MADE TRUE by making P, and Q true and R either false or true.
{"P or Q","~P or ~P"}
Returns: 0
This example was also mentioned in the problem statement. Making P false and Q true will make this statement true thus the statement can be MADE TRUE as is.
{"P or P","~P or ~P"}
Returns: 1
As mentioned in the problem, this statement cannot be MADE TRUE. If we remove either block the statement can be MADE TRUE.
{"P or P","Q or Q","P or P","Q or Q","~P or ~Q","~P or ~Q"}
Returns: 2
This example shows that statements can be duplicated.
{"A or B","B or C","C or D","D or E","A or C","~C or ~C","~A or ~A","~C or ~A"}
Returns: 1
{"A or B","C or D","E or F","G or H","I or J","K or L","M or N","O or P","Q or R","S or T"}
Returns: 0
{"A or A","~B or ~B","C or C","~D or ~D"}
Returns: 0
{"A or A","~B or ~B","C or C","~D or ~D","B or ~A","~C or D"}
Returns: 2
{"A or A","~B or ~B","C or C","~D or ~D","B or ~A","~C or D","~A or ~C","B or ~C","B or D"}}
Returns: 2
{"Z or Z","Y or Y","~Z or ~Y","Z or Z","Y or Y","~Z or ~Y","Z or Z","Y or Y","~Z or ~Y"}
Returns: 3
{"Z or Z","Y or Y","~Z or ~Y","A or A","B or B","~A or ~B","~M or ~M","~N or ~N","M or N","M or ~M"}
Returns: 3
{"A or A","~A or ~A","A or A","~A or ~A","A or A","~A or ~A","A or A","~A or ~A","A or A","~A or ~A"}
Returns: 5
{"A or B","B or C","C or D","~D or ~D","~C or ~C","~B or ~B","~A or ~A"}
Returns: 2
{"A or B","B or C","C or D","~D or ~D","~C or ~C","~B or ~B","~A or ~A","D or E","~E or ~E","~A or ~E"}
Returns: 2
{"A or B","~A or ~A","~B or ~B","A or A","B or B","~A or ~B"}
Returns: 2
{"P or Q"}
Returns: 0