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Longest Diverse String Problem: Step-by-Step Explanation

This README explains the approach for solving the Longest Diverse String Problem in multiple languages: C++, Java, JavaScript, Python, and Go. The goal of this problem is to construct the longest string possible using the characters 'a', 'b', and 'c', where no three consecutive characters are the same, and the counts of these characters do not exceed the given limits.

We will break down the approach in each language step-by-step, describing the logic behind each part of the code.

C++ Code

Step-by-Step Explanation

  1. Use of Priority Queue:

    • A max-heap (priority queue) is used to always select the character with the highest count remaining (a, b, or c).

  2. Inserting Characters into the Priority Queue:

    • Characters with non-zero counts (a, b, and c) are inserted into the priority queue along with their respective counts.

  3. Main Loop - Constructing the String:

    • The loop runs until there are no valid characters left. Each iteration selects the character with the most remaining occurrences.

  4. Check for Three Consecutive Characters:

    • If the most frequent character has already appeared consecutively twice, the next most frequent character is selected instead to avoid three consecutive characters.

  5. Adding to the Result:

    • The selected character is added to the result string, its count is decremented, and it is reinserted into the queue if there are still remaining occurrences.

  6. Terminate When No More Valid Choices:

    • The process ends when no valid character can be selected without breaking the consecutive rule.

Java Code

Step-by-Step Explanation

  1. Priority Queue for Maximum Selection:

    • A priority queue is used to store the characters (a, b, c) with their counts in descending order.

  2. Insert Characters with Counts:

    • If any of the character counts (a, b, c) are non-zero, they are inserted into the priority queue.

  3. While Loop for String Construction:

    • The loop iterates while there are characters left to use. It always picks the character with the highest remaining count.

  4. Handling Consecutive Repetitions:

    • If the last two characters in the result string are the same as the currently selected character, the next most frequent character is chosen to avoid consecutive repetitions.

  5. Add Characters to the Result:

    • The selected character is appended to the result string, and its count is decremented. If the count is still positive, it is re-added to the priority queue.

  6. Completion:

    • The loop ends when no more valid characters can be selected, and the result string is returned.

JavaScript Code

Step-by-Step Explanation

  1. Simulated Priority Queue:

    • JavaScript lacks a built-in priority queue, so an array is used and sorted after every modification to mimic the behavior of a max-heap.

  2. Insert Characters into the Array:

    • Characters (a, b, c) are pushed into the array along with their counts. The array is then sorted by counts in descending order.

  3. Loop to Build the String:

    • The loop continues as long as there are characters available. Each iteration picks the character with the highest count.

  4. Check for Three Consecutive Characters:

    • If the last two characters in the result are the same as the current character, the next most frequent character is chosen to prevent three consecutive characters.

  5. Update and Re-Sort:

    • The selected character is added to the result, and its count is decremented. The array is then re-sorted to ensure the next selection picks the most frequent character.

  6. Terminate When No Valid Moves Left:

    • The loop ends when no further valid characters can be added, and the result string is returned.

Python Code

Step-by-Step Explanation

  1. Priority Queue (Heap):

    • Python’s heapq module is used to create a max-heap where the character with the highest count can be efficiently selected.

  2. Push Characters into the Heap:

    • Characters with non-zero counts (a, b, c) are pushed into the heap. The heap stores counts in a negative form to simulate a max-heap (since heapq is a min-heap by default).

  3. Main Loop for Building the String:

    • The loop runs as long as there are characters in the heap. The character with the largest remaining count is selected in each iteration.

  4. Avoid Consecutive Characters:

    • If the last two characters in the result string are the same as the currently selected character, the next most frequent character is used instead.

  5. Append Character to Result:

    • The chosen character is appended to the result, its count is decremented, and it is pushed back into the heap if its count remains positive.

  6. Stop When No Valid Characters:

    • The loop ends when there are no characters left to use, and the result string is returned.

Go Code

Step-by-Step Explanation

  1. Custom Priority Queue with Heap Interface:

    • Go does not have a built-in priority queue, so a custom heap is implemented using the container/heap package to always select the character with the highest remaining count.

  2. Push Characters into the Heap:

    • The counts of 'a', 'b', and 'c' are added to the heap if they are greater than zero.

  3. Main Loop to Construct the String:

    • The loop runs while the heap contains characters. In each iteration, the character with the most occurrences is selected.

  4. Handling Consecutive Characters:

    • If the last two characters in the result are the same as the selected character, the second most frequent character is used to avoid breaking the consecutive rule.

  5. Append Character and Update Count:

    • The selected character is added to the result, and its count is decremented. If the count remains greater than zero, it is pushed back into the heap.

  6. End When No More Valid Characters:

    • The loop terminates when no valid character can be selected, and the result string is returned.

Conclusion

In all five languages, the logic follows a greedy approach with the use of a priority queue to always select the character with the highest count, ensuring no three consecutive characters are the same. While the syntax and data structures may vary across languages, the underlying algorithm remains the same.