Problem Description

The problem is about finding the maximum length of a substring in a given string s where all characters in the substring are the same. This length is referred to as the "power" of the string. A substring is a contiguous sequence of characters within a string. The uniqueness here means that within this substring, there should be no varying characters. It is a sequence of the same character repeated.

For example, in the string "aaabccc", the power would be 3, since the longest substring where the same character is repeated is "ccc".

The problem asks for a function that processes the input string s and outputs the integer power of that string.

Intuition

The intuition behind the solution relies on iterating through the string and keeping track of the current sequence of identical characters. To achieve that, we analyze each pair of adjacent characters in the string.

We need two variables: one to keep track of the current substring's length of consecutive identical characters (t) and another to keep a record of the maximum length found so far (ans).

1. Initialize ans and t to 1, because the minimum power for any non-empty string is 1 (any individual character counts as a substring of power 1).

2. Iterate through adjacent pairs of characters in the string s. In Python, this can be conveniently done by using the pairwise utility from the itertools module. However, since this utility is not mentioned in the problem statement and it is not available before Python 3.10, we can manually compare elements at indices i and i+1 while iterating with a normal loop from 0 to len(s) - 1.

3. For each pair (a, b) of adjacent characters, check if they are the same:

   • If they are the same, increment the temporary substring length t by 1.
   • Update the ans with the maximum of the current ans and the new t.

4. If the characters a and b are different, reset t to 1 because we have encountered a different character and thus need to start a new substring count.

5. Continue this process until the end of the string is reached.

6. Return the recorded maximum length ans as the power of the string.

This approach ensures that we effectively track the length of each sequence of repeating characters while always retaining the maximum sequence length found.

Solution Approach

The solution provided is straightforward and relies on a simple iteration. It does not require any complex data structures or algorithms. The core pattern used here is a linear scan across the input string, leveraging a sliding window approach to keep track of the current substring of identical characters.

Here's how the implementation unfolds:

• We initiate the answer (ans) and a temporary count (t) both set to 1. The minimal power for any string is 1, as any standalone character is a valid substring. These variables will keep track of the maximum power discovered so far and the current sequence length, respectively.

• The for loop in the code iterates over each pair of adjacent characters in the string s.

  for a, b in pairwise(s):

  This is accomplished by utilizing the pairwise function, which iterates the string such that in each iteration, a and b hold a pair of adjacent characters. The pairwise function, introduced in Python 3.10, effectively generates a sequence of tuples containing (s[i], s[i+1]) for i ranging from 0 to len(s) - 2. If pairwise is not available, it would be necessary to create these pairs manually using index-based iteration.

• The core logic takes place inside this loop, checking whether each consecutive pair of elements are the same:

  • If a == b, it means we are still looking at a substring of identical characters, so we increment our temporary count t and update the maximum power ans if necessary:

    t += 1
    ans = max(ans, t)

  • When a != b, we encounter a different character that breaks the current sequence. Therefore, we reset t to 1 to start counting a new sequence:

    else:
        t = 1

• Once the loop has finished, we've scanned the whole string and determined the maximum length of a substring with only one unique character, providing us with the power of the string s.

• Finally, the function returns the value of ans, which is the maximum power that we were looking for:

  return ans

This approach is effective because it only requires a single pass through the string, making it an ( O(n) ) solution, where ( n ) is the length of the input string. The space complexity is ( O(1) ) as we use only a few variables regardless of the input size.

Example Walkthrough

Let's illustrate the solution approach with a small example. Consider the string s = "aabbb".

• We start by initializing ans and t to 1. The string s has a minimum substring power of 1 by default because even a single character is considered a substring.

• We enter the loop and compare each pair of adjacent characters:

  • We compare s[0] (which is 'a') with s[1] (also 'a'). Since they are the same, we increment t to 2. We also update ans to 2 because it's greater than the initial value of 1.

  • Next, we compare s[1] with s[2], but s[2] is 'b', so they are different. We reset t to 1 as we are now starting to count a new sequence of characters.

  • Moving on, we compare s[2] (which is 'b') with s[3] (also 'b'). They match, so t is incremented to 2.

  • We compare s[3] with s[4], and again they are the same ('b'), so t goes up to 3. We compare ans with the new t, and since 3 is greater than the current ans value of 2, we update ans to 3.

• After the loop is done, we've gone through the entire string and the maximum t value we encountered was 3. Since there are no more characters to check, ans is already the maximum power of the string, which is 3.

In this example, the substring with the highest power is "bbb", which has a power of 3, and that's what our function correctly returns.

By following this step-by-step process, we ensure that, as we traverse the string, we keep the count of consecutive identical characters with t and always remember the maximum such count in ans. Once the traversal is complete, ans contains our final result, which is the power of string s.

Solution Implementation

Time and Space Complexity

The given Python code is designed to find the maximum power of a string, which is defined as the maximum length of a non-empty substring that contains only one unique character.

Here is an analysis of its time and space complexities:

Time Complexity:

The time complexity of the function is dictated by the single for loop over the adjacent elements produced by the pairwise function. The pairwise function creates an iterator that will produce n-1 pairs, where n is the length of the string s.

The loop runs exactly n-1 times if n is the length of the string s. Each iteration performs a constant time operation; either incrementing t, updating ans with the max function, or resetting t to 1. Therefore, the time complexity is O(n), where n is the length of the string.

Space Complexity:

The space complexity of the function is O(1). The reason is that the amount of extra memory used does not depend on the size of the input string. It only uses a fixed number of variables (ans and t), and pairwise (assuming it is similar to itertools.pairwise) generates pairs using an iterator, which doesn't consume additional memory proportional to the input size.

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