Problem Description

The problem involves compressing a sequence of characters into a string where each group of consecutive, identical characters is represented by the character, followed by the number of occurrences if the occurrences are more than 1. For example, "aabccc" would compress to "a2bc3".

Here's how the algorithm works:

• We iterate over the provided array, chars.
• For each unique character, we find the number of times it repeats consecutively.
• We then overwrite the original chars array with the character followed by the number of occurrences if more than one.
• We have to return the length of the array after the modifications.
• The space complexity needs to be constant; therefore, we cannot use any additional arrays or strings for our computations.

The challenge is to edit the array in place since we aren't allowed to return a separate compressed string but instead must modify the chars array directly.

Intuition

To solve this problem, we maintain two pointers and a counter:

• The first pointer (i) marks the start of a sequence of identical characters.
• The second pointer (j) is used to find the end of this sequence by iterating through the array until a different character is found.
• As we identify the consecutive characters, we store the current character and its count (if necessary) into the array, keeping track of where we're writing with a k index.

The process operates as follows:

• Iterate over each character with the i pointer.
• Use the j pointer to count how many times the character at position i repeats consecutively.
• Write the character at the i index position into the k index of the chars list.
• Increase k by 1 to move to the next position in the list.
• If the number of repetitions is greater than 1, convert it into a string and iterate over each character of this string count.
• For each digit of the count, write it at the k index of the chars list and increment k.
• Move i to the position where j has ended up to process the next set of unique characters.
• Continue this process until you have finished iterating over the entire array.
• Lastly, return k as the new length of the compressed chars array.

The solution ensures the use of constant space by overwriting the original list with no additional list or string allocation.

Learn more about Two Pointers patterns.

Solution Approach

The solution to the problem of compressing consecutive characters into a shorter representation involves a straightforward approach with a focus on in-place array manipulation to keep the space complexity constant. The key idea is to use a "read-write" mechanism facilitated by pointer manipulation in the array.

Here is a step-by-step breakdown of the implementation details:

• Two Pointers Technique: We initialize two pointers: i and k. Pointer i is utilized to identify contiguous blocks of the same character, and k is used to write the compressed form of these blocks back into the chars list.
• Iteration Over the Characters: As we iterate over the chars with pointer i, we aim to identify groups of the same character and count their occurrences.
• Counting Group Occurrences: We initialize another pointer j that starts from i + 1 and increments until it finds a character different from chars[i]. The difference j - i then gives us the count of consecutive characters.
• Writing the Character: Regardless of the count, we always write the character in consideration to the chars list at chars[k] and increment k.
• Writing the Count: If the count is greater than one (meaning there are repetitions), we convert the count to a string (str(j - i)) and iterate over each character of this count string, writing the digits sequentially into the chars list at subsequent k positions, incrementing k after each write.
• Updating Pointers: After handling one set of consecutive characters, we set i to the current position of j, effectively jumping to the next new character or the end of the list.
• Returning the New Length: Once we reach the end of the list with pointer i, k points to the next unwritten position in chars and thus represents the length of the compressed character list. We then return k.

This approach does not require sorting or any additional data structures, but it efficiently leverages the given array itself to store the result. By overwriting the original array, we maintain a space complexity of O(1), aside from the space needed to hold the input itself. The complexity is achieved by utilizing the in-place rewriting of the array, a key requirement specified in the problem description.

In terms of time complexity, each character in chars is read and written at least once. In the worst case, each write operation for counts might take O(log n) time (if we represent the count in decimal form and n is the number of occurrences), but since count increments for each group of identical characters need to be written at most once, it doesn't affect the overall linear time complexity of O(n), where n is the total number of characters in chars.

The main takeaway from the solution is the effective use of pointers and the in-place writing technique to transform the array without the use of additional memory, which is a common constraint in more complex problems involving arrays.

Example Walkthrough

Let's use the string chars = ['a', 'a', 'b', 'b', 'c', 'c', 'c'] to walk through the solution approach:

1. Initialization: We start with pointers i, j, and k all set to 0. The chars array looks like this: ['a', 'a', 'b', 'b', 'c', 'c', 'c'].

2. Iteration and Counting: The i pointer is at the first a. We advance j to find the end of the a group, which is at index 2. Therefore, we have 2 a's in a row.

3. Compression Writing: We write 'a' into chars[k] and increment k; chars now looks like this: ['a', 'a', 'b', 'b', 'c', 'c', 'c'] with k pointing at index 1.

4. Writing the Count: The count is 2, so we write '2' into chars[k] and increment k again; chars looks like: ['a', '2', 'b', 'b', 'c', 'c', 'c'].

5. Updating Pointers: We move the i pointer where j stopped, which is index 2, the first b.

6. Repeat Steps 2-5 for character b: j will stop at index 4 and we write 'b' and then '2' into the array. The array now looks like: ['a', '2', 'b', '2', 'c', 'c', 'c'], and k is at index 4.

7. Repeat Steps 2-5 for character c: j moves to the end of the array since there are no more characters after c. We write 'c' and then '3' into the array. The final array is ['a', '2', 'b', '2', 'c', '3', 'c'], and k would be at index 6.

8. Final Step: Since we've reached the end of the chars array with pointer i, we can now return k as the length of the compressed list. However, due to the previous compressions, there is a leftover 'c', which we do not count. The final compressed length is 6, and the compressed array is ['a', '2', 'b', '2', 'c', '3'].

In summary, the chars array, which initially included 7 characters, has been compressed in place to a length of 6, representing the sequence "a2b2c3". The algorithm executed in constant space, as required by the problem definition.

Solution Implementation

Time and Space Complexity

Time Complexity

The given Python code follows a two-pointer approach to compress a list of characters in-place.

1. We have two pointers i and j; i is used to traverse the character list, while j is used to find the next character different from chars[i].
2. The while loop with i as its iterator runs for each unique character in the list, so it runs 'n' times in the worst-case scenario (n being the length of the list).
3. The inner while loop increments j until a different character is found. In the worst case, where all characters are the same, the loop runs 'n' times.

Hence, in the worst case, where the inner loop is considered for every character, the time complexity would be considered linear with respect to the length of the list, i.e., O(n).

Space Complexity

The algorithm adjusts the characters in the list in-place and uses a fixed number of variables (i, j, k, n, cnt). It does not utilize any additional data structure that grows with the input size. Therefore, the space complexity of the algorithm is O(1) regardless of the input size.

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