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Lexicographically Smallest String using All of the First K Letters of the Alphabet, with No Two Adjacent Characters Being the Same using C++
In the world of programming, solving string manipulation problems is a common and interesting challenge. A crucial problem faced is how to obtain a lexicographically smallest string utilizing only K letters from the alphabet while following additional constraints such as no matching adjacent characters. In this article, our aim is to delve into this issue and present an effective solution using C++ programming language. By detailing different methods employed in syntax and providing algorithmic details on a step-by-step basis, we can introduce innovative techniques aiming towards favorable results on distinct fronts. We provide complete executable code guides for each method aimed at easy implementation by users for practical purposes.
Syntax
Before exploring the algorithm and techniques, it's necessary to establish the syntax used in the code snippets that follow.
std::string findLexSmallestString(int n, int k);
In this syntax, n refers to the count of letters in alphabet, k denotes the number of letters utilized, and the function yields the lexico-graphically lowest string satisfying prescribed conditions.
Algorithm
To address and resolve the challenge of finding the lexicographically smallest string with no repetition amongst adjacent characters using only a maximum of K letters from the alphabet, a methodical approach has been crafted in form of an algorithm.
Initialize an empty string `ans` and an array/vector `used` to keep track of the used characters.
Start iterating from the first character of the alphabet.
Append the current character to `ans` and mark it as used.
If `ans` has more than one character and the last two characters are the same, find the next available character by iterating from the current character to 'n'.
If no available character is found, backtrack by removing the last character from `ans` and marking it as unused.
Repeat steps 3-5 until `ans` reaches length `k`.
Return `ans` as the lexicographically smallest string using all of the first K letters of the alphabet, where no two adjacent characters are the same.
Approach 1: Greedy Algorithm
In this approach, we will use a greedy strategy to construct the lexicographically smallest string. The same process emphasizes on careful consideration of each character in sequential order while ensuring that choices made throughout are focused on minimizing lexicographical value of overall output.
Example
#include <iostream>
#include <vector>
std::string findLexSmallestGreedy(int n, int k) {
std::string ans = "";
std::vector<bool> used(n, false);
for (int i = 0; i < n; i++) {
for (int j = 0; j < k; j++) {
if (!used[j]) {
if (ans.empty() || ans.back() != 'a' + j) {
ans += 'a' + j;
used[j] = true;
break;
}
}
}
}
return ans;
}
int main() {
int n = 5; // Assuming there are 5 letters in the alphabet
int k = 3; // Assuming 3 letters will be used
std::string result = findLexSmallestGreedy(n, k);
std::cout << "Lexicographically Smallest String: " << result << std::endl;
return 0;
}
Output
Lexicographically Smallest String: abc
Approach 2: Backtracking Algorithm
This strategy involves utilizing backtracking to exhaustively search through every combination of characters while ensuring that consecutive characters do not repeat. Thus by considering each character at each position we can find the lexicographically smallest string that satisfies the given constraints.
Example
#include <iostream>
#include <vector>
bool findLexSmallestBacktracking(int n, int k, std::vector<char>& ans, std::vector<bool>& used) {
if (ans.size() == k) {
return true;
}
for (int i = 0; i < n; i++) {
if (!used[i]) {
if (ans.empty() || ans.back() != 'a' + i) {
ans.push_back('a' + i);
used[i] = true;
if (findLexSmallestBacktracking(n, k, ans, used)) {
return true;
}
ans.pop_back();
used[i] = false;
}
}
}
return false;
}
std::string findLexSmallestStringBacktracking(int n, int k) {
std::vector<char> ans;
std::vector<bool> used(n, false);
if (findLexSmallestBacktracking(n, k, ans, used)) {
return std::string(ans.begin(), ans.end());
}
return "";
}
int main() {
int n = 22; // Assuming n = 22
int k = 4; // Assuming k = 4
std::string result = findLexSmallestStringBacktracking(n, k);
std::cout << "Lexicographically Smallest String: " << result << std::endl;
return 0;
}
Output
Lexicographically Smallest String: abcd
Conclusion
In this article, we explored the problem of finding the lexicographically smallest string using the first K letters of the alphabet, with the constraint that no two adjacent characters can be the same. We discussed the syntax and provided two distinct approaches to tackle this problem: the greedy algorithm and the backtracking algorithm. The greedy algorithm employs a strategy that minimizes the lexicographical value of the resulting string, while the backtracking algorithm explores all possible combinations to find the desired string. The provided C++ code samples demonstrated the implementation of each approach and allowed us to generate the lexicographically smallest string efficiently. Armed with this knowledge, you can now confidently solve similar string manipulation problems and optimize your code accordingly.
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