## Automatically add words if Duplicate Post Titles

i have two post duplicate Post Titles: “Love Story”.

i want code Automatically add a random words if Duplicate Post Titles, like post 2 duplicate Titles ==> auto change post 2 titles like: “Love Story Two”.

and if user up post 3, duplicate Titles again => auto add random words in post titles like : “Love story three”.

thanks a lot

## Induction on strings (words)

Given is an alphabet Σ = { 0, 1, 2 } and a function cross to calculate the cross sum of a word.

cross : Σ* → N with:

cross(w)= 0 when w = ε

        cross(v) + x when w = vx with x ∈ Σ 

Prove by Induction on words that ∀w ∈ Σ*. cross(w) <= 2*|w|

I can prove that the statement holds for ε

Base case: cross(ε) = 0 <= 2 * |ε| = 0

How can I show that the statement holds in the inductive step?

## Given a string S and a set of words D, find the longest word in D that is a subsequence of S

I’m trying to improve my code and algorithm to find out the longest word from a dictionary occurring as the sub-sequence in the given string.

Example : For example, given the input of S = “abppplee” and D = {“able”, “ale”, “apple”, “bale”, “kangaroo”} the correct output would be “apple”.

Currently my algorithm compares each character of the dictionary-word with the given-word and advances to next char in dictionary-word on finding a match and so on till either the dictionary-word is iterated over completely(which means the word is a valid sub-sequence) or the given word is iterated over completely(which means not a valid string).

Being a beginner to c++ and algorithms in general, my methods and logic could be further improved. So kindly suggest if any improvements in the algorithm or code which can improve the performance. Thanks.

#include <iostream> #include <string> #include <tuple> #include <vector>  class StringManipulater {   public:   StringManipulater(const std::string& p) : given_string_{p} {}   std::string given_string_;   std::tuple<std::string, typename std::string::size_type> current_longest_ = {       "", 0};    const std::string&& FindLongestSubSeq(const std::vector<std::string>& dict)   {     // flag determines whether current word is present in given_string input     bool flag;      // iterate through each of the dict-words     for (const std::string& word : dict) {       flag = false;       auto word_len = word.size();        // fair optimization : only consider current word if its       // length is greater than previous one       if (word_len > std::get<1>(this->current_longest_)) {         // iterate through the letters in both given string and current word         // to be compared         for (typename std::string::size_type i = 0, j = 0; j < word_len; ++i) {           // no need to go further checking if we have iterated over given           // string           if (i == this->given_string_.size()) break;            // compare each letter of both words           if (word[j] == given_string_[i]) {             flag = true;             // advance to next charcter in the dictionary word             ++j;           }           else {             // if the char couldn't be found             flag = false;           }         }  // end of comparison loop         if (flag) {           std::get<0>(this->current_longest_) = word;           std::get<1>(this->current_longest_) = word_len;         }       }  // top if     }    // end of iteration of dictionary words     return std::move(std::get<0>(this->current_longest_));   } };  int main() {   StringManipulater s_manip{"abppplee"};   std::cout << "Longest subsequence = "             << s_manip.FindLongestSubSeq(                    {"able", "ale", "apple", "bale", "kangaroo"})             << "\n";   return 0; } 

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