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Given a string of digits, we need to find the count of even substrings in it. Let's see an example.Inputnum = "1234"Output6The even substrings that can be formed from the given string are2 12 4 34 234 1234AlgorithmInitialise the string with digits.Initialise the count to 0.Iterate over the string.Get the current digit by subtracting the char 0 from the current char digit.Check whether the digit is even or not.If the current digit is even, then add it's index plus 1 to the count.Return the count.ImplementationFollowing is the implementation of the above algorithm in C++#include using namespace std; int getEvenSubstringsCount(char str[]) ... Read More
A Grammar that makes more than one Leftmost Derivation (or Rightmost Derivation) for the similar sentence is called Ambiguous Grammar.Example − Verify whether the following Grammar is Ambiguous or Not.E → E+E|E $\ast$ E|idSolutionFor string id + id * id, there exist two parse trees.E ⇒lm $\underline{E}$+E ⇒ id+ $\underline{E}$⇒ id+$\underline{E}$ $\ast$ E⇒ id+id $\ast$ $\underline{E}$⇒ id+id $\ast$ idE ⇒lm $\underline{E}$ $\ast$ E⇒ $\underline{E}$+E $\ast$ E⇒ id+ $\underline{E}$ $\ast$ E⇒ id+id $\ast$ $\underline{E}$⇒ id+id $\ast$ idSo, the same string is generated using two different leftmost derivations. Each is having a different parse tree.∴ Two different parse trees exist for string id + id ... Read More
Derivations mean replacing a given string’s non-terminal by the right-hand side of the production rule. The sequence of applications of rules that makes the completed string of terminals from the starting symbol is known as derivation.It can derive terminal strings, beginning with the start symbol, by repeatedly replacing a variable with some production. The language of CFG is a set of terminal symbols we can derive so. This language is called context Free Language.Derivations are denoted by ⇒.For example, consider a Grammar.G=({S}, {a, b}, P, S), where, P contains following productions −P={S→aSa |bSb | ∈}In the above, S may be ... Read More
Grammar − It is a set of rules which checks whether a string belongs to a particular language a not.A program consists of various strings of characters. But, every string is not a proper or meaningful string. So, to identify valid strings in a language, some rules should be specified to check whether the string is valid or not. These rules are nothing but make Grammar.Example − In English Language, Grammar checks whether the string of characters is acceptable or not, i.e., checks whether nouns, verbs, adverbs, etc. are in the proper sequence.Context-Free GrammarIt is a notation used to specify ... Read More
Lexical Analysis is the first step of the compiler which reads the source code one character at a time and transforms it into an array of tokens. The token is a meaningful collection of characters in a program. These tokens can be keywords including do, if, while etc. and identifiers including x, num, count, etc. and operator symbols including >, >=, +, etc., and punctuation symbols including parenthesis or commas. The output of the lexical analyzer phase passes to the next phase called syntax analyzer or parser.The syntax analyser or parser is also known as parsing phase. It takes tokens ... Read More
Minimizing means reducing the number of states in DFA. We have to detect those states of DFA whose presence or absence in DFA does not affect language accepted by DFA. These states can be eliminated from DFA.Algorithm: Minimization of DFAInput − DFA D1 with a set of states Q with a set of final states F.Output − DFA D2 which accepts the same language as D1 and having a minimum number of states as possible.MethodMake a partition 'π' of a set of states with two subsets −Final state 'F'Non-Final States 'Q-F'∴ π={F, Q−F}To apply the following procedure to make πnew ... Read More
You are given the result of the preorder traversal. You need to find the number of elements that are smaller than the root.The first element in the preorder traversal is the root of the BST. Let's see an example.Inputpreorder_result = [5, 4, 2, 1, 7, 6, 8, 9]Output3 There are three elements that are less than the root. The root is 5.AlgorithmInitialise the preorder result in an array.Store the first element i.e.., root of the BST in a variable.Write a loop that iterates from the 2nd element of the preorder result.Compare every element with the root.If the current element is ... Read More
Yes, we can convert a NFA into DFA. For every NFA there exists an equivalent DFA. The equivalence is defined in terms of languages acceptance. Since NFA is nothing but a finite automata in which zero, one or more transitions on an input symbols are permitted. It can always construct finite automata which will simulate all moves of DFA on a particular input symbol in parallel, then get a finite automata in which there will be exactly one transition on every input symbol. Here, corresponding to a NFA there exist a DFA. To construct DFA equivalent to NFA, it should ... Read More
You are given a number and subarray lower and upper bound indexes. You need to count a number of elements that are less than or equal to the given number. Let's see an example.Inputarr = [1, 2, 3, 4, 5, 6, 7, 8] k = 4 lower = 0 upper = 5Output4There are 4 elements between the index 0 and 5 that are less than or equal to 4.AlgorithmInitialise the array, number, and subarray indexes.Initialise the count to 0.Write a loop that iterates from the lower index of the subarray to the upper index of the subarray.If the current element ... Read More
A Regular Expression is a representation of Tokens. But, to recognize a token, it can need a token Recognizer, which is nothing but a Finite Automata (NFA). So, it can convert Regular Expression into NFA.Algorithm for the conversion of Regular Expression to NFAInput − A Regular Expression ROutput − NFA accepting language denoted by RMethodFor ε, NFA isFor a NFA isFor a + b, or a | b NFA isFor ab, NFA isFor a*, NFA isExample1 − Draw NFA for the Regular Expression a(a+b)*abSolutionExample2 − Draw NFA for a + b + abSolutionExample3 − Draw NFA for letter (letter+digit)*SolutionExample4 − ... Read More