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An example string would be "abcbpbcbp" where the "Old" palindrome is "bcbpbcb" and the Center is on the second "c". The MirroredCenter is the first "c" and it has a longest palindrome of "bcb". The longest palindrome at the Center on the second "c" has to be at least that long and, in this case, is longer.
In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation.It can produce either a postfix notation string, also known as reverse Polish notation (RPN), or an abstract syntax tree (AST). [1]
The algorithm that is presented here does not need an explicit stack; instead, it uses recursive calls to implement the stack. The algorithm is not a pure operator-precedence parser like the Dijkstra shunting yard algorithm. It assumes that the primary nonterminal is parsed in a separate subroutine, like in a recursive descent parser.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
The reverse of a string is a string with the same symbols but in reverse order. For example, if s = abc (where a, b, and c are symbols of the alphabet), then the reverse of s is cba. A string that is the reverse of itself (e.g., s = madam) is called a palindrome, which also includes the empty string and all strings of length 1.
The recursive calls modify the initial elements and a rule is needed at each iteration to select which will be exchanged with the last. Heap's method says that this choice can be made by the parity of the number of elements operated on at this step.
Finally, the parser reads a '$' (end of input symbol) from the input stream, which means that according to the action table (the current state is 3) the parser accepts the input string. The rule numbers that will then have been written to the output stream will be [5, 3, 5, 2] which is indeed a rightmost derivation of the string "1 + 1" in reverse.
For function that manipulate strings, modern object-oriented languages, like C# and Java have immutable strings and return a copy (in newly allocated dynamic memory), while others, like C manipulate the original string unless the programmer copies data to a new string.