1405. Longest Happy String - Detailed Explanation

Problem Statement

You are given three integers a, b, and c representing the maximum number of occurrences of the characters 'a', 'b', and 'c' respectively. Your task is to return the longest happy string that can be formed using these characters.

A string is considered happy if it does not contain any of these three substrings: "aaa", "bbb", or "ccc" (i.e. no three identical consecutive characters).

Note:

• You do not have to use all the characters.
• If no happy string can be constructed, return an empty string.

Examples

Example 1

• Input: a = 1, b = 1, c = 7
• Output: "ccaccbcc"
• Explanation:
  One possible valid string is "ccaccbcc". It uses at most 1 'a', 1 'b', and 7 'c' (here 7 'c' are available, but not all may be used). The string does not contain "ccc" consecutively (there are never three 'c' in a row), nor does it have three consecutive 'a' or 'b'.

Example 2

• Input: a = 2, b = 2, c = 1
• Output: "aabbc" (or any valid arrangement, e.g., "ababc")
• Explanation:
  The output string uses at most the given counts and is happy because it does not contain three identical consecutive characters.

Hints

1. Greedy Approach:

   • Use a max-heap (priority queue) to always choose the character with the highest remaining count.
   • Before appending the chosen character, check if adding it would cause three consecutive identical letters.
   • If it would, try using the next highest count character instead.
   • If no alternative is available, the process stops.

2. Alternative Approaches:

   • An iterative greedy solution (without an explicit heap) can also work by manually comparing counts.
   • A recursive/backtracking method exists, but it is less efficient given the problem’s constraints.

Approach 1: Greedy with Max-Heap (Optimal)

Idea

1. Max-Heap Setup:

   • Create a max-heap of pairs (count, char) for 'a', 'b', and 'c' (use negative counts in Python since its heap is a min-heap).

2. Building the Result:

   • Repeatedly extract the character with the highest count.
   • If the last two characters in the result are equal to this candidate, then try the next candidate.
   • Append the chosen character and decrement its count.
   • Push back any character that still has a positive count.

3. Termination:

   • Stop if no character can be appended without breaking the happy condition.

Complexity Analysis

• Time Complexity: O(n log 3) ≈ O(n), where n is the length of the result string (since the heap size is constant—at most 3).
• Space Complexity: O(n) for the result string and O(1) extra space for the heap (only three elements).

Python Implementation