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Increasing Decreasing String

You are given a string s. Reorder the string using the following algorithm:

  1. Remove the smallest character from s and append it to the result.
  2. Remove the smallest character from s that is greater than the last appended character, and append it to the result.
  3. Repeat step 2 until no more characters can be removed.
  4. Remove the largest character from s and append it to the result.
  5. Remove the largest character from s that is smaller than the last appended character, and append it to the result.
  6. Repeat step 5 until no more characters can be removed.
  7. Repeat steps 1 through 6 until all characters from s have been removed.

If the smallest or largest character appears more than once, you may choose any occurrence to append to the result.

Return the resulting string after reordering s using this algorithm.

 

Example 1:

Input: s = "aaaabbbbcccc"
Output: "abccbaabccba"
Explanation: After steps 1, 2 and 3 of the first iteration, result = "abc"
After steps 4, 5 and 6 of the first iteration, result = "abccba"
First iteration is done. Now s = "aabbcc" and we go back to step 1
After steps 1, 2 and 3 of the second iteration, result = "abccbaabc"
After steps 4, 5 and 6 of the second iteration, result = "abccbaabccba"

Example 2:

Input: s = "rat"
Output: "art"
Explanation: The word "rat" becomes "art" after re-ordering it with the mentioned algorithm.

 

Constraints:

  • 1 <= s.length <= 500
  • s consists of only lowercase English letters.

Solution Explanation: Increasing Decreasing String

This problem requires rearranging a given string based on a specific algorithm involving alternating increasing and decreasing order of characters. The optimal approach involves using a counting technique to track character frequencies and then simulating the algorithm.

Approach:

  1. Character Counting: First, count the occurrences of each character (a-z) in the input string s. A hash map (dictionary in Python, map in C++, etc.) or a simple array of size 26 is ideal for this.

  2. Iterative Sorting: The core logic lies in iteratively building the result string. We do this in two phases within a loop:

    • Increasing Phase: Iterate through characters from 'a' to 'z'. If a character has a count greater than 0, add it to the result string and decrement its count.
    • Decreasing Phase: Iterate through characters from 'z' to 'a'. Again, if a character has a count greater than 0, add it to the result string and decrement its count.

  3. Loop Termination: This loop continues until the length of the result string equals the length of the input string s, indicating that all characters have been processed.

Time Complexity Analysis:

  • Character counting takes O(n) time, where n is the length of the input string.
  • The iterative sorting loop runs at most 26 times (the alphabet size) in each iteration of the outer loop. In the worst case where each character appears only once, the outer loop runs approximately n/26 times.
  • Therefore, the overall time complexity is approximately O(n), dominated by the character counting and the main loop's iterations. This is a linear time solution.

Space Complexity Analysis:

  • The space used for character counting is O(1) because the alphabet size is constant (26).
  • The space used for the result string is O(n) in the worst case.
  • Thus, the overall space complexity is O(n).

Code Examples (Python, Java, C++, Go, TypeScript, JavaScript):

The code examples provided in the prompt are quite comprehensive and reflect the described algorithm effectively. Each example uses a slightly different approach for character counting and string manipulation based on the language's features but the underlying algorithm is the same. Key aspects are:

  • Efficient character counting using Counter (Python), arrays (Java, C++, Go), or manual counting (TypeScript, JavaScript).
  • Iterative building of the result string using append (Python), StringBuilder (Java), += (C++), append (Go), and array manipulation (TypeScript, JavaScript).
  • Clever use of reversed iteration (e.g., [::-1] in Python) for the decreasing phase.

The code is well-structured, easy to understand, and directly implements the algorithm described above. The use of ascii_lowercase in Python, and similar character iteration techniques in other languages, demonstrates good coding style.