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Distinct Echo Substrings

Hard

Asked by:

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Topics:

Strings

Return the number of distinct non-empty substrings of text that can be written as the concatenation of some string with itself (i.e. it can be written as a + a where a is some string).

Example 1:

Input: text = "abcabcabc"
Output: 3
Explanation: The 3 substrings are "abcabc", "bcabca" and "cabcab".

Example 2:

Input: text = "leetcodeleetcode"
Output: 2
Explanation: The 2 substrings are "ee" and "leetcodeleetcode".

Constraints:

1 <= text.length <= 2000
text has only lowercase English letters.

Try coding it in LeetCode

Distinct Echo Substrings

Hard

Asked by:

23 views

Topics:

Strings

Return the number of distinct non-empty substrings of text that can be written as the concatenation of some string with itself (i.e. it can be written as a + a where a is some string).

Example 1:

Input: text = "abcabcabc"
Output: 3
Explanation: The 3 substrings are "abcabc", "bcabca" and "cabcab".

Example 2:

Input: text = "leetcodeleetcode"
Output: 2
Explanation: The 2 substrings are "ee" and "leetcodeleetcode".

Constraints:

1 <= text.length <= 2000
text has only lowercase English letters.

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the maximum length of the input string, and are there any limitations on the characters it can contain (e.g., only lowercase letters)?
By 'distinct', do you mean unique substrings based on their content (e.g., 'ab' and 'ab' are considered the same), or based on their starting and ending positions?
Is an empty string considered a valid echo substring (i.e., is a single empty substring allowed in the distinct count)?
If the input string is empty or null, what should be the return value?
Can you provide an example of an echo substring for clarification? For instance, does 'abab' contain one or two distinct echo substrings ('ab')?

Brute Force Solution

Approach

The brute force approach to finding distinct echo substrings means we'll check every possible substring to see if it repeats itself immediately after. We will generate all possible substrings, and then check if they are 'echo substrings'.

Here's how the algorithm would work step-by-step:

Consider every possible starting point for a substring in the given text.
For each starting point, consider every possible length for a substring.
Extract the substring based on the starting point and length.
Check if a copy of this substring immediately follows it in the original text.
If a copy of the substring immediately follows it, we've found an echo substring.
Keep track of all the unique echo substrings that we find.
After checking all possible substrings and their lengths, report the number of unique echo substrings we found.

Code Implementation

def distinct_echo_substrings_brute_force(text):
    text_length = len(text)
    echo_substrings = set()

    for substring_start_index in range(text_length):
        for substring_length in range(1, text_length - substring_start_index + 1):
            substring = text[substring_start_index:substring_start_index + substring_length]

            # Check if there's enough space after the substring to contain a copy of it.
            if substring_start_index + 2 * substring_length <= text_length:

                #Compare this substring against the substring directly after it.
                if substring == text[substring_start_index + substring_length:substring_start_index + 2 * substring_length]:
                    echo_substrings.add(substring)

    # Return the count of unique echo substrings.
    return len(echo_substrings)

Big(O) Analysis

Time Complexity

O(n^3) – The algorithm iterates through all possible starting positions for substrings, which contributes a factor of n to the time complexity. For each starting position, it iterates through all possible substring lengths, contributing another factor of n. For each substring, it performs a string comparison to check if the substring is immediately followed by an identical substring, which takes O(n) time in the worst case. Therefore, the overall time complexity is O(n * n * n) which simplifies to O(n^3).

Space Complexity

O(N) – The dominant space usage comes from storing the unique echo substrings. In the worst-case scenario, where almost every substring is a unique echo substring, the set to store these substrings could grow linearly with the number of possible substrings. Since the number of substrings is proportional to N^2, the set could theoretically store O(N^2) substrings. However, the length of each substring is limited by N, where N is the length of the input string. Therefore, the auxiliary space complexity is O(N) because, in the worst case, we might store a large number of short echo substrings, and the memory used to store these substrings is proportional to the length of the input string.

Optimal Solution

Approach

The problem is about finding repeating substrings within a larger string. To avoid checking every single substring, we can focus on substrings that have the potential to be echoes by only considering even lengths and efficiently checking for repetitions.

Here's how the algorithm would work step-by-step:

Start by only looking at substrings that have an even number of characters, since an echo substring must repeat itself exactly.
For each even length, slide a window across the string. This window represents a potential echo substring.
Within each window, compare the first half of the characters with the second half of the characters. If they match, you've found an echo substring.
Keep track of the unique echo substrings you find. Avoid counting the same echo substring multiple times.
After checking all possible even lengths and window positions, report the number of unique echo substrings you identified.

Code Implementation

def distinct_echo_substrings(text):
    unique_echo_substrings = set()
    text_length = len(text)

    # Echo substrings must have an even length
    for substring_length in range(2, text_length + 1, 2):
        for i in range(text_length - substring_length + 1):
            substring = text[i:i + substring_length]
            half_length = substring_length // 2

            # Compare the first and second halves
            if substring[:half_length] == substring[half_length:]:

                # Ensure uniqueness of echo substrings
                unique_echo_substrings.add(substring)

    return len(unique_echo_substrings)

Big(O) Analysis

Time Complexity

O(n²) – The algorithm iterates through all possible even lengths of substrings, up to n. For each even length (from 2 to n), it slides a window of that length across the string. Within each window, it compares the first half of the substring with the second half, which takes O(length/2) = O(length) time. Since the outer loop iterates up to n/2 (for even lengths), and the inner loop slides the window (n - length + 1) times, and the comparison within the window takes length/2 time, the total time complexity is proportional to the sum of (n - length + 1) * (length/2) for length from 2 to n. This sum is dominated by n², leading to a time complexity of O(n²).

Space Complexity

O(N) – The algorithm stores unique echo substrings to avoid recounting. In the worst case, where many distinct echo substrings exist, the set used to store them could grow to a size proportional to the length of the input string N. Therefore, the space complexity is O(N), where N is the length of the input string. No other significant data structures are used that scale with the input size.

Edge Cases

Case	How to Handle
Null or empty string input	Return 0 if the input string is null or empty, as there can be no substrings.
String of length 1	Return 0 as a string of length 1 cannot contain an echo substring.
String with all identical characters (e.g., 'aaaa')	The solution should correctly identify all echo substrings in this case, such as 'a', 'aa', and 'aaa'.
String containing only non-alphanumeric characters or special symbols.	The solution should handle these characters correctly, comparing them based on their ASCII values.
Maximum string length as defined by problem constraints or system memory	Ensure the algorithm has acceptable time complexity (ideally O(n^2) or better) to avoid timeout errors.
Overlapping Echo Substrings (e.g., 'ababab')	The solution must correctly identify and count distinct echo substrings, avoiding double-counting overlapping occurrences of same subtring.
String with a very long repeating sequence (e.g., 'aaaaaaaaab')	Ensure the substring comparison and length calculations do not lead to integer overflows or performance bottlenecks.
String with no echo substrings	The solution should return 0, demonstrating it correctly handles cases with no valid output.

Null or empty string input

How to Handle:

Return 0 if the input string is null or empty, as there can be no substrings.

String of length 1

How to Handle:

Return 0 as a string of length 1 cannot contain an echo substring.

String with all identical characters (e.g., 'aaaa')

How to Handle:

The solution should correctly identify all echo substrings in this case, such as 'a', 'aa', and 'aaa'.

String containing only non-alphanumeric characters or special symbols.

How to Handle:

The solution should handle these characters correctly, comparing them based on their ASCII values.

Maximum string length as defined by problem constraints or system memory

How to Handle:

Ensure the algorithm has acceptable time complexity (ideally O(n^2) or better) to avoid timeout errors.

Overlapping Echo Substrings (e.g., 'ababab')

How to Handle:

The solution must correctly identify and count *distinct* echo substrings, avoiding double-counting overlapping occurrences of same subtring.

String with a very long repeating sequence (e.g., 'aaaaaaaaab')

How to Handle:

Ensure the substring comparison and length calculations do not lead to integer overflows or performance bottlenecks.

String with no echo substrings

How to Handle:

The solution should return 0, demonstrating it correctly handles cases with no valid output.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the maximum length of the input string, and are there any limitations on the characters it can contain (e.g., only lowercase letters)?
By 'distinct', do you mean unique substrings based on their content (e.g., 'ab' and 'ab' are considered the same), or based on their starting and ending positions?
Is an empty string considered a valid echo substring (i.e., is a single empty substring allowed in the distinct count)?
If the input string is empty or null, what should be the return value?
Can you provide an example of an echo substring for clarification? For instance, does 'abab' contain one or two distinct echo substrings ('ab')?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Consider every possible starting point for a substring in the given text.
For each starting point, consider every possible length for a substring.
Extract the substring based on the starting point and length.
Check if a copy of this substring immediately follows it in the original text.
If a copy of the substring immediately follows it, we've found an echo substring.
Keep track of all the unique echo substrings that we find.
After checking all possible substrings and their lengths, report the number of unique echo substrings we found.

Code Implementation

def distinct_echo_substrings_brute_force(text):
    text_length = len(text)
    echo_substrings = set()

    for substring_start_index in range(text_length):
        for substring_length in range(1, text_length - substring_start_index + 1):
            substring = text[substring_start_index:substring_start_index + substring_length]

            # Check if there's enough space after the substring to contain a copy of it.
            if substring_start_index + 2 * substring_length <= text_length:

                #Compare this substring against the substring directly after it.
                if substring == text[substring_start_index + substring_length:substring_start_index + 2 * substring_length]:
                    echo_substrings.add(substring)

    # Return the count of unique echo substrings.
    return len(echo_substrings)

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Start by only looking at substrings that have an even number of characters, since an echo substring must repeat itself exactly.
For each even length, slide a window across the string. This window represents a potential echo substring.
Within each window, compare the first half of the characters with the second half of the characters. If they match, you've found an echo substring.
Keep track of the unique echo substrings you find. Avoid counting the same echo substring multiple times.
After checking all possible even lengths and window positions, report the number of unique echo substrings you identified.

Code Implementation

def distinct_echo_substrings(text):
    unique_echo_substrings = set()
    text_length = len(text)

    # Echo substrings must have an even length
    for substring_length in range(2, text_length + 1, 2):
        for i in range(text_length - substring_length + 1):
            substring = text[i:i + substring_length]
            half_length = substring_length // 2

            # Compare the first and second halves
            if substring[:half_length] == substring[half_length:]:

                # Ensure uniqueness of echo substrings
                unique_echo_substrings.add(substring)

    return len(unique_echo_substrings)

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty string input	Return 0 if the input string is null or empty, as there can be no substrings.
String of length 1	Return 0 as a string of length 1 cannot contain an echo substring.
String with all identical characters (e.g., 'aaaa')	The solution should correctly identify all echo substrings in this case, such as 'a', 'aa', and 'aaa'.
String containing only non-alphanumeric characters or special symbols.	The solution should handle these characters correctly, comparing them based on their ASCII values.
Maximum string length as defined by problem constraints or system memory	Ensure the algorithm has acceptable time complexity (ideally O(n^2) or better) to avoid timeout errors.
Overlapping Echo Substrings (e.g., 'ababab')	The solution must correctly identify and count distinct echo substrings, avoiding double-counting overlapping occurrences of same subtring.
String with a very long repeating sequence (e.g., 'aaaaaaaaab')	Ensure the substring comparison and length calculations do not lead to integer overflows or performance bottlenecks.
String with no echo substrings	The solution should return 0, demonstrating it correctly handles cases with no valid output.

Null or empty string input

How to Handle:

Return 0 if the input string is null or empty, as there can be no substrings.

String of length 1

How to Handle:

Return 0 as a string of length 1 cannot contain an echo substring.

String with all identical characters (e.g., 'aaaa')

How to Handle:

The solution should correctly identify all echo substrings in this case, such as 'a', 'aa', and 'aaa'.

String containing only non-alphanumeric characters or special symbols.

How to Handle:

The solution should handle these characters correctly, comparing them based on their ASCII values.

Maximum string length as defined by problem constraints or system memory

How to Handle:

Ensure the algorithm has acceptable time complexity (ideally O(n^2) or better) to avoid timeout errors.

Overlapping Echo Substrings (e.g., 'ababab')

How to Handle:

The solution must correctly identify and count *distinct* echo substrings, avoiding double-counting overlapping occurrences of same subtring.

String with a very long repeating sequence (e.g., 'aaaaaaaaab')

How to Handle:

Ensure the substring comparison and length calculations do not lead to integer overflows or performance bottlenecks.

String with no echo substrings

How to Handle:

The solution should return 0, demonstrating it correctly handles cases with no valid output.