Problem Description

In this problem, we are dealing with the concept of a "fancy string". A string is considered fancy if no three consecutive characters are identical. The goal is to transform any given string s into a fancy string by removing the minimum number of characters necessary.

For example, if the input string is s = "aaabaaaa", a possible fancy string could be s = "aabaa" after deleting the right characters. The task is to return the modified string that fulfills the condition of being a fancy string.

Intuition

To approach this problem, we need to scan through the input string and check for any occurrence of three identical consecutive characters. Whenever we find such a sequence, we don't include the third character in our result.

A straightforward way to do this is to iterate over each character in the input string while maintaining a separate list to build the fancy string. For each character, we compare it with the last two characters in the list. If all three are the same, we skip adding the current character to the list; otherwise, we add it.

This process ensures that at no point will there be three identical consecutive characters in our resultant list. In the end, we join the characters in the list to form the final fancy string and return it. This solution has the advantage of examining each character only once, giving us a time-efficient approach to making the string fancy.

Solution Approach

The solution to the problem makes use of a simple iteration pattern over the characters of the string, coupled with a condition check to enforce the "fancy" constraint.

To implement this, we use a Python list, ans, which is a dynamic array in this context. We iterate through each character c in the input string s, and check if this character is about to form a triplet with the two previously added characters (if any).

Here's a step-by-step breakdown of the solution:

1. Initialization: An empty list ans is created which will store the characters that will eventually make up the fancy string.

2. Iteration: We iterate over each character c in the given string s.

3. Condition Check: Before adding the character c to the list ans, we perform a check:

   • If the length of ans is greater than 1 (which means there are at least two characters already in ans),
   • And the last character (ans[-1]) and the second to last character (ans[-2]) in ans are both equal to c,
   • Then this character c would create a sequence of three identical consecutive characters. In this case, we simply skip adding c to ans.

4. Character Addition: If the check fails (meaning adding c won't lead to three consecutive identical characters), we add c to the list ans.

5. Result Formation: Once we've finished iterating over the string, we use ''.join(ans) to concatenate all the elements in the list ans into a string, which is the fancy string that we return as the result.

By using a for loop and a conditional statement, we are able to enforce the consecutive character constraint efficiently. The usage of an array (list in Python) to build our result allows for easy appending and checking of the last two characters. This approach has a linear runtime complexity because each character in the input string is processed exactly once.

Example Walkthrough

Let's consider a smaller example to illustrate the solution approach using the input string s = "xxxyyyz". Following the solution approach step by step, we will transform s into a fancy string.

1. Initialization: We create an empty list ans which will collect the characters for the fancy string.

2. Iteration:

   • We begin by iterating over each character in s. The first character is 'x'.

3. Condition Check:

   • Since ans is empty, we do not need to check for triplets. There are no previous characters to compare with.

4. Character Addition:

   • We add 'x' to ans, resulting in ans = ['x'].

5. Next Iteration:

   • The next character is 'x'. We check ans and find there is only one 'x', so we can safely add another.
   • ans = ['x', 'x'].

6. Next Iteration:

   • We encounter 'x' again. We check the last two characters of ans and find that adding another 'x' would create three in a row, which is not allowed for a fancy string.
   • We skip adding this 'x' and move on to the next character.

7. Next Iteration:

   • The next character is 'y'. There's no issue in adding 'y' to ans as it wouldn't create three identical consecutive characters.
   • ans = ['x', 'x', 'y'].

8. Continued Iteration:

   • We continue this process for the remaining characters 'y', 'y', and 'z'. For both occurrences of 'y' after the first, we skip adding them since they would create a triplet with the previous two 'y's. Finally, 'z' can be added without any problems.
   • ans = ['x', 'x', 'y', 'z'].

9. Result Formation:

   • At the end of the iteration, we join the characters in ans to form the final string.
   • The fancy string is 'xxyz'.

In this example, by following the solution approach, we removed two characters 'y' and one character 'x' to transform "xxxyyyz" into a fancy string "xxyz". This process minimizes the number of deletions needed and ensures that no three consecutive characters in the result are identical.

Solution Implementation

Time and Space Complexity

Time Complexity

The given code loops over each character in the input string s only once. The condition inside the loop checks the last two characters in the ans list to determine if the current character c should be added to ans.

Since each character in s is processed once and each operation within the loop, including comparison and list appending, is O(1), the overall time complexity of the algorithm is O(n), where n is the length of the input string s.

Space Complexity

The space complexity of the code is mostly determined by the space used to store the ans list. In the worst case, when no characters are the same, ans will contain all the characters of s. Therefore, the space complexity is O(n) as well, where n is the length of the input string s.

Learn more about how to find time and space complexity quickly using problem constraints.