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Binary Expression Tree
A binary expression tree is a specific kind of a binary tree used to represent expressions. Two common types of expressions that a binary expression tree can represent are algebraic and boolean. These trees can represent expressions that contain both unary and binary operators. Like any binary tree, each node of a binary expression tree has zero, one, or two children. This restricted structure simplifies the processing of expression trees. Construction of an expression tree Example The input in postfix notation is: a b + c d e + * * Since the first two symbols are operands, one-node trees are created and pointers to them are pushed onto a stack. For convenience the stack will grow from left to right. The next symbol is a '+'. It pops the two pointers to the trees, a new tree is formed, and a pointer to it is pushed onto the stack. Next, c, d, and e are read. A one-node tree is created for each and a pointer to the corresponding tree is pushed onto the stack. Conti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the ''left child'' and the ''right child''. That is, it is a ''k''-ary tree with . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. In ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Addition
Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), division. The addition of two Natural number, whole numbers results in the total or ''summation, sum'' of those values combined. For example, the adjacent image shows two columns of apples, one with three apples and the other with two apples, totaling to five apples. This observation is expressed as , which is read as "three plus two Equality (mathematics), equals five". Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers, and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as Euclidean vector, vec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parse Tree
A parse tree or parsing tree (also known as a derivation tree or concrete syntax tree) is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar. The term ''parse tree'' itself is used primarily in computational linguistics; in theoretical syntax, the term ''syntax tree'' is more common. Concrete syntax trees reflect the syntax of the input language, making them distinct from the abstract syntax trees used in computer programming. Unlike Reed-Kellogg sentence diagrams used for teaching grammar, parse trees do not use distinct symbol shapes for different types of constituents. Parse trees are usually constructed based on either the constituency relation of constituency grammars ( phrase structure grammars) or the dependency relation of dependency grammars. Parse trees may be generated for sentences in natural languages (see natural language processing), as well as during processing of computer languages, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form : A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). Regardless of which symbols surround it, the single nonterminal A on the left hand side can always be replaced by \alpha on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form \alpha A \beta \rightarrow \alpha \gamma \beta with A a nonterminal symbol and \alpha, \beta, and \gamma strings of terminal and/or nonterminal symbols. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, : \lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term (logic)
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variable symbols, and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation. For example, is a term built from the constant 1, the variable , and the binary function symbols and ; it is part of the atomic formula which evaluates to true for each real-numbered value of . Besides in logic, terms play important roles in universal algebra, and rewriting systems. Definition Given a set ''V'' of variable symbols, a set ''C'' of constant symbols and sets ''F''''n'' of ''n''-ary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Not
In logic, negation, also called the logical not or logical complement, is an operation (mathematics), operation that takes a Proposition (mathematics), proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \overline. It is interpreted intuitively as being true when P is false, and false when P is true. For example, if P is "Spot runs", then "not P" is "Spot does not run". An operand of a negation is called a ''negand'' or ''negatum''. Negation is a unary operation, unary logical connective. It may furthermore be applied not only to propositions, but also to notion (philosophy), notions, truth values, or interpretation (logic), semantic values more generally. In classical logic, negation is normally identified with the truth function that takes ''truth'' to ''falsity'' (and vice versa). In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition P is the proposition whose proofs are the re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Or
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language, English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula S \lor W , assuming that S abbreviates "it is sunny" and W abbreviates "it is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theory, proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous nonclassical logic, non- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical And
In logic, mathematics and linguistics, ''and'' (\wedge) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdot in which \wedge is the most modern and widely used. The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., A \land B is true if and only if A is true and B is true. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English " and"; * In programming languages, the short-circuit and control structure; * In set theory, intersection. * In lattice theory, logical conjunction ( greatest lower bound). Notation And is usually denoted by an infix operator: in mathematics and logic, it is denoted by a "wedge" \wedge (Unicode ), \& or \times; in electronics, \cdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Child Nodes
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leaf Nodes
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internal Node
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected Node (computer science), nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each paren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
