Solving Alphabetical Strings Problem: A Step-by-Step Guide

In competitive programming, understanding how to leverage data structures effectively can be a game-changer. The 'Alphabetical Strings' problem, featured in Codeforces Round #731 (Div. 3), is a perfect example of this. This problem challenges you to determine whether a given string can be constructed by iteratively adding characters from 'a' to a certain point, either to the left or right of the existing string. In this detailed walkthrough, we will dissect the problem statement, explore the underlying logic, and demonstrate how a deque (double-ended queue) data structure can provide an elegant and efficient solution. Get ready to level up your problem-solving skills!

What is an Alphabetical String?

The 'Alphabetical Strings' problem

defines an alphabetical string as one that can be built using a specific algorithm. You start with an empty string, then iteratively add lowercase letters from 'a' up to a certain letter. At each step, you have the choice of adding the letter to the left or right end of the current string. The string's length, n, ranges from 1 to 26 (inclusive).

For instance, 'a', 'ba', 'ab', 'bac', and 'ihfcbadeg' are all alphabetical strings. Conversely, 'z', 'ayya', and 'dsdciba' are not. The challenge is: given a string, determine if it's alphabetical according to this definition.

This problem requires a deep understanding of string manipulation and algorithmic thinking. A key insight is to reverse the process and try to deconstruct the given string back to its origin – an empty string or the single character 'a'. This is where the deque data structure shines, allowing us to efficiently add and remove characters from both ends.

Breaking Down the Algorithm

The algorithm essentially provides a recipe for creating alphabetical strings. Understanding it is crucial for devising a solution to the problem. Here's a formal breakdown:

1. Initialization: Start with an empty string s.
2. Iteration: Repeat the following n times, where n is the desired length of the string:
   • Let c be the i-th lowercase letter of the Latin alphabet (starting from 'a').
   • Append c to either the left or right of the string s.

It’s important to note that the string must be composed of consecutive alphabetical characters starting from 'a'. That is, 'a', then 'b', then 'c', and so on, up to a certain limit.

Analyzing the constraints – a maximum string length of 26 – suggests that an efficient algorithm is possible. Exhaustive search might be too computationally expensive, but leveraging data structures can offer a more optimized solution. The core idea is to work backward, checking if we can iteratively remove characters from the ends of the string until we are left with an empty string or the character 'a'.

Why Choose a Deque?

A deque (double-ended queue) is a generalized queue that allows insertion and deletion of elements from both the front and the rear

. This bi-directional capability makes it an ideal choice for solving the 'Alphabetical Strings' problem. We need to simulate adding (and, in reverse, removing) characters from both ends of the string, a perfect fit for the deque’s functionality.

Think of a deque as a dynamic array that can grow or shrink at both ends. Standard operations include:

• push_front(x): Inserts element x at the front of the deque.
• push_back(x): Inserts element x at the rear of the deque.
• pop_front(): Removes the element at the front of the deque.
• pop_back(): Removes the element at the rear of the deque.
• front(): Accesses the element at the front of the deque.
• back(): Accesses the element at the rear of the deque.
• empty(): Checks if the deque is empty.
• size(): Returns the number of elements in the deque.

With these operations, we can easily simulate the construction and deconstruction of alphabetical strings, which is essential for solving this problem efficiently.

Algorithm Implementation with Deque

To solve the 'Alphabetical Strings' problem using a deque, we will follow these steps:

1. Initialization:

   • Read the input string s.
   • Create a deque of characters dq.
   • Push all characters of s into the deque dq.
   • Find the maximum character in the string s. This will be our starting point for validation.

     Because, we will be going from that character to the beginning.

2. Validation:

   • Iterate from the maximum character down to 'a'.
   • At each iteration, check if the front or back of the deque matches the current character.
   • If the front matches, pop the front. If the back matches, pop the back.
   • If neither matches, the string is not alphabetical; return false.

3. Termination:

   • If the deque is empty after iterating through all characters down to 'a', the string is alphabetical; return true.
   • If the deque is not empty or any character fails to match during iteration, the string is not alphabetical; return false.

By following this approach, we can efficiently determine whether a given string is alphabetical according to the problem's definition. A step-by-step guide is given below in How to Use module.

Consider the string “fecàbd”. We first identify ‘f’ as the maximum character. We then attempt to match ‘f’ at either end of the deque. If matched, we pop the corresponding end and proceed to ‘e’, and so on. If, at any point, we cannot find the expected character at either end, or if the deque isn't empty when reaching 'a', we conclude it's not an alphabetical string.

Step 1: Read the Input String and Initialize the Deque

Start by reading the input string from the user. Then, create a deque data structure and push all the characters of the string into the deque.

#include <iostream>
#include <string>
#include <deque>

using namespace std;

bool solve() {
    string s;
    cin >> s;

    deque<char> dq;
    for (char c : s) {
        dq.push_back(c);
    }

    // Next steps will be added here
    return true; // Placeholder
}

This code snippet initializes the deque with the characters from the input string, setting the stage for the core validation process. Here, it just needs some steps to be added, that are mentioned below.

Step 2: Find the Maximum Character

Identify the maximum character in the string. This character serves as the starting point for our reverse-engineering process. We need to validate the string from that maximum character down to ‘a’.

    char maxChar = 'a';
    for (char c : s) {
        maxChar = max(maxChar, c);
    }

This code iterates through the string to find the character with the highest ASCII value, which will be our starting point for the deconstruction process.

Step 3: Iterate and Validate

Iterate from the maximum character down to ‘a’. In each iteration, check if the current character matches either the front or the back of the deque. If a match is found, pop the corresponding end. If no match is found, the string is not alphabetical.

    for (char ch = maxChar; ch >= 'a'; --ch) {
        if (dq.empty()) return false; // Deque is empty before reaching 'a'

        if (dq.front() == ch) {
            dq.pop_front();
        } else if (dq.back() == ch) {
            dq.pop_back();
        } else {
            return false; // Character not found at either end
        }
    }

In this code snippet, we loop from the maximum character down to 'a'. If the deque's front matches the current character, we pop it; similarly, for the back. If neither end matches, we return false, indicating that the string is not alphabetical.

Step 4: Check for Empty Deque

After iterating through all characters down to ‘a’, check if the deque is empty. If it is, the string is alphabetical. If not, it is not.

    return dq.empty(); // If deque is empty, the string is alphabetical
}

This final check ensures that we have successfully reduced the string back to its origin. If the deque is empty, it confirms that the original string was indeed alphabetical.

Step 5: Complete Code

Now, let’s assemble the complete code, to have a better and more complete understanding:

#include <iostream>
#include <string>
#include <deque>

using namespace std;

bool solve() {
    string s;
    cin >> s;

    deque<char> dq;
    for (char c : s) {
        dq.push_back(c);
    }

    char maxChar = 'a';
    for (char c : s) {
        maxChar = max(maxChar, c);
    }

    for (char ch = maxChar; ch >= 'a'; --ch) {
        if (dq.empty()) return false; // Deque is empty before reaching 'a'

        if (dq.front() == ch) {
            dq.pop_front();
        } else if (dq.back() == ch) {
            dq.pop_back();
        } else {
            return false; // Character not found at either end
        }
    }

    return dq.empty(); // If deque is empty, the string is alphabetical
}

int main() {
    int t;
    cin >> t;

    while (t--) {
        if (solve()) {
            cout << "YES" << endl;
        } else {
            cout << "NO" << endl;
        }
    }

    return 0;
}

Pricing for codeforces

Codeforces is a platform that offers a range of services and features to its users. Here's a breakdown of the pricing structure for these services:

As of December 2025, Codeforces remains a predominantly free platform for competitive programming and learning.

Key features to take into consideration for codeforces

Codeforces has been known to be a great platform for programming. This section presents the key features of codeforces:

• Regular Contests: Codeforces hosts regular competitive programming contests. These contests are typically held several times a month and offer a variety of problems with varying difficulty levels. Participating in these contests allows you to test your skills, improve your problem-solving abilities, and compete against other programmers from around the world.

• Problem Archive: The platform maintains an extensive archive of past contest problems. This archive is a valuable resource for practicing and improving your skills. Problems are categorized by difficulty, topic, and contest, making it easy to find problems that suit your needs.

  

• Educational Resources: Codeforces provides a wealth of educational resources to help you learn new concepts and improve your programming skills. These resources include tutorials, articles, and problem sets covering a wide range of topics, such as data structures, algorithms, and mathematical techniques.

• Community Features: The platform fosters a vibrant community of programmers. Users can connect with each other, share their knowledge, and collaborate on projects through forums, blogs, and user profiles. This community support can be invaluable for learning and growth.

• Rating System: Codeforces uses a rating system to track the performance of its users. Your rating is updated after each contest based on your performance. This rating system provides a measure of your skill level and allows you to compare yourself to other programmers.

• Practice and Training: The platform offers various tools and features to help you practice and train for contests. These include virtual contests, where you can simulate the experience of participating in a real contest, and the Codeforces Gym, where you can practice on past contest problems.

Different use cases for codeforces

Codeforces, as a competitive programming platform, serves numerous use cases for programmers of all levels. Whether you're a student honing your skills or a professional looking to stay sharp, Codeforces offers valuable opportunities.

• Skill Development: Codeforces is an excellent platform for developing and improving your programming skills. The regular contests and extensive problem archive provide ample opportunities to practice and learn new concepts.

  By participating in contests and solving problems, you can enhance your problem-solving abilities, algorithmic thinking, and coding proficiency.

• Competitive Programming Training: If you're interested in competitive programming, Codeforces is a must-use platform. The contests are designed to mimic real-world programming competitions, providing valuable experience and training. The rating system allows you to track your progress and compete against other programmers of similar skill levels.
• Interview Preparation: Many companies use programming problems in their technical interviews. Codeforces can be a valuable resource for preparing for these interviews. The problem archive contains a wide variety of problems that are similar to those found in technical interviews. By practicing these problems, you can improve your chances of success in your job search.
• Staying Sharp: Even if you're not actively participating in contests, Codeforces can be a great way to stay sharp and keep your programming skills up-to-date. The problem archive provides a constant source of new challenges, and the educational resources can help you learn about new technologies and techniques.
• Community Engagement: Codeforces provides a platform for connecting with other programmers, sharing your knowledge, and collaborating on projects. The forums and blogs can be great resources for learning new things and getting help with your coding problems. By engaging with the community, you can expand your network and build valuable relationships.