Jobs

Interviews

Discussions

Encode String with Shortest Length

Hard

Asked by:

11 views

Topics:

StringsDynamic Programming

Given a string s, encode the string such that its length is minimized.

To encode, pick any non-empty substring of s and replace it with the substring's encoding, which is the substring surrounded by square brackets with the number of times the substring is repeated. For example, the substring "abcabcabc" could be encoded as "3[abc]", which has length of 7 (instead of 9).

Return the shortest encoding of s.

Example 1:

Input: s = "aaa"
Output: "aaa"
Explanation: There is no way to encode it such that it is shorter than the original string, so we return "aaa".

Example 2:

Input: s = "aaaaa"
Output: "5[a]"
Explanation: "5[a]" is shorter than "aaaaa" by 1 character.

Example 3:

Input: s = "abab"
Output: "2[ab]"
Explanation: "2[ab]" is shorter than "abab" by 1 character.

Example 4:

Input: s = "abcabcdede"
Output: "2[abc]dede"
Explanation: "abcabc" can be encoded as "2[abc]", which leaves the substring "dede" to be encoded as "dede".

Constraints:

1 <= s.length <= 150
s consists of only lowercase English letters.

Try coding it in LeetCode

Encode String with Shortest Length

Hard

Asked by:

11 views

Topics:

StringsDynamic Programming

Given a string s, encode the string such that its length is minimized.

Return the shortest encoding of s.

Example 1:

Input: s = "aaa"
Output: "aaa"
Explanation: There is no way to encode it such that it is shorter than the original string, so we return "aaa".

Example 2:

Input: s = "aaaaa"
Output: "5[a]"
Explanation: "5[a]" is shorter than "aaaaa" by 1 character.

Example 3:

Input: s = "abab"
Output: "2[ab]"
Explanation: "2[ab]" is shorter than "abab" by 1 character.

Example 4:

Input: s = "abcabcdede"
Output: "2[abc]dede"
Explanation: "abcabc" can be encoded as "2[abc]", which leaves the substring "dede" to be encoded as "dede".

Constraints:

1 <= s.length <= 150
s consists of 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 characters might the input string contain (e.g., only lowercase letters, alphanumeric, special characters)?
What is the maximum length of the input string?
If the input string is empty, what should the encoded (return) string be?
If there are multiple shortest encoded strings, is any one acceptable?
Could you provide some examples of how the encoding/compression should work beyond the problem description (e.g., how substrings are identified and repeated)?

Brute Force Solution

Approach

The brute force method tackles string encoding by exhaustively exploring all possible ways to break down the original string. It checks every conceivable substring and repetition pattern. Eventually, it finds the shortest possible encoding among all the explored options.

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

First, consider the entire string as is. This is our initial, uncompressed version.
Next, check if any part of the string repeats. See if a shorter piece can be repeated multiple times to form the whole or a large part of it.
Break the string into two parts at every possible location. For each pair of parts, check if either part can be further compressed by finding repeating patterns.
Continue breaking down the string into smaller and smaller parts, always checking for repetitions at each stage.
Keep track of every possible way to represent the string using repetitions and smaller substrings.
After exploring all possible combinations of substrings and repetitions, compare the lengths of all the encoded versions you've found.
Finally, select the shortest encoding among all the possibilities. This is the brute force solution.

Code Implementation

def encode_string_with_shortest_length_brute_force(input_string):
    string_length = len(input_string)

    def find_shortest_encoding(current_string):
        if not current_string:
            return ""
        
        # Consider the original string as a possible encoding
        shortest_encoding = current_string
        string_length_inner = len(current_string)
        
        # Check for repeating patterns
        for pattern_length in range(1, string_length_inner // 2 + 1):
            pattern = current_string[:pattern_length]
            repetitions = string_length_inner // pattern_length
            
            if pattern * repetitions == current_string:
                encoded_string = str(repetitions) + "[" + pattern + "]"
                if len(encoded_string) < len(shortest_encoding):
                    shortest_encoding = encoded_string
        
        # Break the string into two parts at every possible location
        for split_index in range(1, string_length_inner):
            # Recursively encode the two substrings
            left_substring = current_string[:split_index]
            right_substring = current_string[split_index:]

            encoded_left = find_shortest_encoding(left_substring)
            encoded_right = find_shortest_encoding(right_substring)
            combined_encoding = encoded_left + encoded_right
            
            if len(combined_encoding) < len(shortest_encoding):
                shortest_encoding = combined_encoding
        
        return shortest_encoding

    # Begin the brute force approach by finding
    # the shortest encoding for the entire string
    return find_shortest_encoding(input_string)

Big(O) Analysis

Time Complexity

O(n^3) – The brute force approach explores all possible substrings. There are O(n^2) substrings. For each substring, we check for repetitions, which takes O(n) time in the worst case to identify the repeating pattern and its length. Thus, we iterate through all possible substrings and check repetitions resulting in a time complexity of O(n^2 * n), which simplifies to O(n^3).

Space Complexity

O(N^2) – The brute force approach explores all possible substrings and their combinations. This often involves memoization or dynamic programming to store the shortest encodings of all substrings encountered. Since there are O(N^2) possible substrings of a string with length N, the space complexity is dominated by the storage required for these substring encodings. Therefore, the algorithm uses O(N^2) auxiliary space to store intermediate results and shortest encodings of the substrings.

Optimal Solution

Approach

The challenge is to find the shortest possible encoded version of a given string. The core idea is to leverage repeated patterns within the string and represent them using counts and the pattern itself.

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

First, check if encoding the string is actually shorter than just leaving it as it is. If the original string is already short, there's no point in encoding.
Try breaking the string down into smaller repeating pieces. See if the string can be made by repeating one of its parts.
If a repeating part is found, represent the string by the number of times the part repeats, followed by the part itself inside square brackets.
If the string cannot be represented by repeating a single part, consider breaking it into smaller parts and recursively applying this encoding strategy to those parts.
Compare all the different possible encodings that were created and choose the shortest one.

Code Implementation

def encode_string_with_shortest_length(input_string):
    string_length = len(input_string)

    if string_length <= 4:
        return input_string

    dp_table = [input_string] * (string_length + 1)

    for length in range(1, string_length + 1):
        for start_index in range(string_length - length + 1):
            substring = input_string[start_index:start_index + length]

            # Check if encoding is shorter than the original substring.
            if len(substring) < len(dp_table[start_index]):
                dp_table[start_index] = substring

            # Find repeating patterns within the substring
            for pattern_length in range(1, length):
                pattern = substring[:pattern_length]
                if length % pattern_length == 0 and pattern * (length // pattern_length) == substring:
                    encoded_string = str(length // pattern_length) + "[" + dp_table[start_index][:pattern_length] + "]"

                    # Choose the shorter representation: encoded or existing
                    if len(encoded_string) < len(dp_table[start_index]):
                        dp_table[start_index] = encoded_string

    return dp_table[0]

Big(O) Analysis

Time Complexity

O(n^3) – The algorithm explores all possible substrings within the input string of length n. Checking for repeating substrings in step 2 involves iterations that could take O(n^2) time. The recursive application of the encoding strategy in step 4 on smaller parts adds another factor of n in the worst-case scenario, when the string cannot be compressed. Consequently, the overall time complexity is approximately O(n * n^2), which simplifies to O(n^3).

Space Complexity

O(N^2) – The algorithm utilizes dynamic programming, where a 2D array (dp) of size N x N is used to store the shortest encoded strings for all substrings of the input string. This dp table stores intermediate encoded results. Recursive calls, while present in the process of finding the shortest encodings of substrings, are implicitly managed by the dp table, which stores and reuses computed results. Thus, the dominant factor in space complexity is the dp table of size N x N, where N is the length of the input string.

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty string since there's nothing to encode.
Input string of length 1	Return the input string itself as it cannot be further encoded.
Input string consists of repeating characters (e.g., 'aaaa')	The algorithm should be able to identify and encode repeating patterns effectively, like encoding 'aaaa' to '4[a]'.
Input string already in encoded format (e.g., '2[abc]')	The algorithm should handle potentially nested encoded strings without issues by properly parsing encoded segments.
Maximum string length approaching memory limits	Consider the memory implications of string manipulation and intermediate results to avoid out-of-memory errors, potentially optimizing for in-place operations if feasible.
Overlapping patterns that might lead to suboptimal encoding	The dynamic programming approach will handle optimal solutions to overlapping cases.
Input string with very long repeating substrings	Ensure the repeating number doesn't overflow integer limits, and that the string building from repetitions remains efficient.
Input containing special characters	Special characters should be treated as literal characters when applying the compression, rather than causing errors.

Null or empty input string

How to Handle:

Return an empty string since there's nothing to encode.

Input string of length 1

How to Handle:

Return the input string itself as it cannot be further encoded.

Input string consists of repeating characters (e.g., 'aaaa')

How to Handle:

The algorithm should be able to identify and encode repeating patterns effectively, like encoding 'aaaa' to '4[a]'.

Input string already in encoded format (e.g., '2[abc]')

How to Handle:

The algorithm should handle potentially nested encoded strings without issues by properly parsing encoded segments.

Maximum string length approaching memory limits

How to Handle:

Consider the memory implications of string manipulation and intermediate results to avoid out-of-memory errors, potentially optimizing for in-place operations if feasible.

Overlapping patterns that might lead to suboptimal encoding

How to Handle:

The dynamic programming approach will handle optimal solutions to overlapping cases.

Input string with very long repeating substrings

How to Handle:

Ensure the repeating number doesn't overflow integer limits, and that the string building from repetitions remains efficient.

Input containing special characters

How to Handle:

Special characters should be treated as literal characters when applying the compression, rather than causing errors.

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 characters might the input string contain (e.g., only lowercase letters, alphanumeric, special characters)?
What is the maximum length of the input string?
If the input string is empty, what should the encoded (return) string be?
If there are multiple shortest encoded strings, is any one acceptable?
Could you provide some examples of how the encoding/compression should work beyond the problem description (e.g., how substrings are identified and repeated)?

Brute Force Solution

Approach

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

First, consider the entire string as is. This is our initial, uncompressed version.
Next, check if any part of the string repeats. See if a shorter piece can be repeated multiple times to form the whole or a large part of it.
Break the string into two parts at every possible location. For each pair of parts, check if either part can be further compressed by finding repeating patterns.
Continue breaking down the string into smaller and smaller parts, always checking for repetitions at each stage.
Keep track of every possible way to represent the string using repetitions and smaller substrings.
After exploring all possible combinations of substrings and repetitions, compare the lengths of all the encoded versions you've found.
Finally, select the shortest encoding among all the possibilities. This is the brute force solution.

Code Implementation

def encode_string_with_shortest_length_brute_force(input_string):
    string_length = len(input_string)

    def find_shortest_encoding(current_string):
        if not current_string:
            return ""
        
        # Consider the original string as a possible encoding
        shortest_encoding = current_string
        string_length_inner = len(current_string)
        
        # Check for repeating patterns
        for pattern_length in range(1, string_length_inner // 2 + 1):
            pattern = current_string[:pattern_length]
            repetitions = string_length_inner // pattern_length
            
            if pattern * repetitions == current_string:
                encoded_string = str(repetitions) + "[" + pattern + "]"
                if len(encoded_string) < len(shortest_encoding):
                    shortest_encoding = encoded_string
        
        # Break the string into two parts at every possible location
        for split_index in range(1, string_length_inner):
            # Recursively encode the two substrings
            left_substring = current_string[:split_index]
            right_substring = current_string[split_index:]

            encoded_left = find_shortest_encoding(left_substring)
            encoded_right = find_shortest_encoding(right_substring)
            combined_encoding = encoded_left + encoded_right
            
            if len(combined_encoding) < len(shortest_encoding):
                shortest_encoding = combined_encoding
        
        return shortest_encoding

    # Begin the brute force approach by finding
    # the shortest encoding for the entire string
    return find_shortest_encoding(input_string)

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

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

First, check if encoding the string is actually shorter than just leaving it as it is. If the original string is already short, there's no point in encoding.
Try breaking the string down into smaller repeating pieces. See if the string can be made by repeating one of its parts.
If a repeating part is found, represent the string by the number of times the part repeats, followed by the part itself inside square brackets.
If the string cannot be represented by repeating a single part, consider breaking it into smaller parts and recursively applying this encoding strategy to those parts.
Compare all the different possible encodings that were created and choose the shortest one.

Code Implementation

def encode_string_with_shortest_length(input_string):
    string_length = len(input_string)

    if string_length <= 4:
        return input_string

    dp_table = [input_string] * (string_length + 1)

    for length in range(1, string_length + 1):
        for start_index in range(string_length - length + 1):
            substring = input_string[start_index:start_index + length]

            # Check if encoding is shorter than the original substring.
            if len(substring) < len(dp_table[start_index]):
                dp_table[start_index] = substring

            # Find repeating patterns within the substring
            for pattern_length in range(1, length):
                pattern = substring[:pattern_length]
                if length % pattern_length == 0 and pattern * (length // pattern_length) == substring:
                    encoded_string = str(length // pattern_length) + "[" + dp_table[start_index][:pattern_length] + "]"

                    # Choose the shorter representation: encoded or existing
                    if len(encoded_string) < len(dp_table[start_index]):
                        dp_table[start_index] = encoded_string

    return dp_table[0]

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty string since there's nothing to encode.
Input string of length 1	Return the input string itself as it cannot be further encoded.
Input string consists of repeating characters (e.g., 'aaaa')	The algorithm should be able to identify and encode repeating patterns effectively, like encoding 'aaaa' to '4[a]'.
Input string already in encoded format (e.g., '2[abc]')	The algorithm should handle potentially nested encoded strings without issues by properly parsing encoded segments.
Maximum string length approaching memory limits	Consider the memory implications of string manipulation and intermediate results to avoid out-of-memory errors, potentially optimizing for in-place operations if feasible.
Overlapping patterns that might lead to suboptimal encoding	The dynamic programming approach will handle optimal solutions to overlapping cases.
Input string with very long repeating substrings	Ensure the repeating number doesn't overflow integer limits, and that the string building from repetitions remains efficient.
Input containing special characters	Special characters should be treated as literal characters when applying the compression, rather than causing errors.

Null or empty input string

How to Handle:

Return an empty string since there's nothing to encode.

Input string of length 1

How to Handle:

Return the input string itself as it cannot be further encoded.

Input string consists of repeating characters (e.g., 'aaaa')

How to Handle:

The algorithm should be able to identify and encode repeating patterns effectively, like encoding 'aaaa' to '4[a]'.

Input string already in encoded format (e.g., '2[abc]')

How to Handle:

The algorithm should handle potentially nested encoded strings without issues by properly parsing encoded segments.

Maximum string length approaching memory limits

How to Handle:

Consider the memory implications of string manipulation and intermediate results to avoid out-of-memory errors, potentially optimizing for in-place operations if feasible.

Overlapping patterns that might lead to suboptimal encoding

How to Handle:

The dynamic programming approach will handle optimal solutions to overlapping cases.

Input string with very long repeating substrings

How to Handle:

Ensure the repeating number doesn't overflow integer limits, and that the string building from repetitions remains efficient.

Input containing special characters

How to Handle:

Special characters should be treated as literal characters when applying the compression, rather than causing errors.