Jobs

Interviews

Discussions

Find the Lexicographically Largest String From the Box I

Medium

Google

1 view

Topics:

Strings

You are given a string word, and an integer numFriends. Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round:

word is split into numFriends non-empty strings, such that no previous round has had the exact same split.
All the split words are put into a box.

Find the lexicographically largest string from the box after all the rounds are finished.

For example:

Input: word = "dbca", numFriends = 2
Output: "dbc"

All possible splits are:

"d" and "bca".
"db" and "ca".
"dbc" and "a".

Another example:

Input: word = "gggg", numFriends = 4
Output: "g"

The only possible split is: "g", "g", "g", "g".

Find the Lexicographically Largest String From the Box I

Medium

Google

1 view

Topics:

Strings

You are given a string word, and an integer numFriends. Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round:

word is split into numFriends non-empty strings, such that no previous round has had the exact same split.
All the split words are put into a box.

Find the lexicographically largest string from the box after all the rounds are finished.

For example:

Input: word = "dbca", numFriends = 2
Output: "dbc"

All possible splits are:

"d" and "bca".
"db" and "ca".
"dbc" and "a".

Another example:

Input: word = "gggg", numFriends = 4
Output: "g"

The only possible split is: "g", "g", "g", "g".

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 are the possible characters within the strings in the box? Are they limited to lowercase English letters, or can they include uppercase, numbers, or other special characters?
Can the box be empty (no strings)? What should I return in that case?
If there are multiple lexicographically largest strings, should I return all of them, the first one encountered, or is there another tie-breaking condition?
What is the maximum number of strings that can be in the box, and what is the maximum length of each string?
Is the input guaranteed to be valid, or should I handle potential null or invalid string inputs in the box?

Brute Force Solution

Approach

The brute force approach for this problem involves trying out every possible combination of characters we can pick from the input box. We will then compare these combinations to see which one is the 'biggest' alphabetically, according to the rules of lexicographical ordering.

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

Consider every possible way to build a string by picking characters from the box.
For example, pick one character, then another, then another, until the string is as long as possible (or we run out of characters).
Create all possible strings that could be formed by selecting a different combination of characters each time.
Compare these strings alphabetically.
The string that comes last in alphabetical order (the 'biggest' one) is the answer.

Code Implementation

def find_lexicographically_largest_string_brute_force(input_string):
    all_possible_strings = []

    def generate_strings(current_string, remaining_characters):
        all_possible_strings.append(current_string)

        # If no characters remain, then we can't make additional combinations.
        if not remaining_characters:
            return

        for index in range(len(remaining_characters)):
            # Build all combinations by choosing a starting character
            generate_strings(
                current_string + remaining_characters[index],
                remaining_characters[index+1:]
            )

    generate_strings("", input_string)

    # Find the lexicographically largest string in the list
    lexicographically_largest_string = ""
    for possible_string in all_possible_strings:
        # Compare and update if larger than current largest string
        if possible_string > lexicographically_largest_string:
            lexicographically_largest_string = possible_string

    return lexicographically_largest_string

Big(O) Analysis

Time Complexity

O(n!) – The brute force approach generates every possible string that can be formed by picking characters from the box. If the input box has 'n' characters, in the worst-case, we explore all possible permutations of these 'n' characters. Generating all permutations of 'n' items takes O(n!) time because there are n! possible orderings. Comparing these strings lexicographically will add a further overhead; however, the dominant factor is the generation of the permutations, so the overall time complexity remains O(n!).

Space Complexity

O(N!) – The brute force approach constructs every possible string from the input. In the worst case, where all characters are unique, this results in generating a factorial number of strings. Each of these strings requires storage, leading to a memory usage proportional to the sum of lengths of all possible strings, which is bounded by O(N!). Therefore, the auxiliary space used to store these strings is O(N!).

Optimal Solution

Approach

The main idea is to build the lexicographically largest string one character at a time by always choosing the largest available character. We repeatedly select the largest character that can be legally added to the current string without violating the constraints of the box.

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

First, count how many of each character you have available to use.
Start building your string. At each position, ask yourself: What's the largest character I can use right now?
To figure that out, hypothetically add that character and check if you'll still have enough characters remaining to fill the rest of the string according to the rules of the box.
If you don't have enough remaining characters to finish the string after adding the character, try the next largest character.
Keep going down the list of characters (from largest to smallest) until you find one that lets you complete the string.
Add that character to the string, reduce the count of available characters, and move to the next position in the string.
Repeat this process until the string is complete.

Code Implementation

def find_lexicographically_largest_string(character_counts):
    string_length = sum(character_counts.values())
    result = ""

    character_counts_copy = character_counts.copy()

    for _ in range(string_length):
        for char_code in range(ord('z'), ord('a') - 1, -1):
            current_character = chr(char_code)

            # Check if the character is available.
            if character_counts_copy.get(current_character, 0) > 0:

                character_counts_copy[current_character] -= 1

                remaining_length = string_length - len(result) - 1
                remaining_counts = sum(character_counts_copy.values())

                # Check if we can still complete the string.
                if remaining_counts >= remaining_length:
                    result += current_character
                    break
                else:
                    # If we can't complete the string, backtrack.
                    character_counts_copy[current_character] += 1

    return result

Big(O) Analysis

Time Complexity

O(n*m) – We iterate n times to build the final string. In each iteration, we search for the largest suitable character from 'm' distinct characters (where 'm' is the size of the alphabet, e.g., 26 for lowercase English letters). The search involves decrementing from the largest character to the smallest, checking at each step if adding that character is feasible. Therefore, for each position in the final string, we may need to examine all 'm' characters. Hence, the total time complexity becomes O(n*m).

Space Complexity

O(1) – The algorithm uses a character count array (or similar data structure) to store the frequency of each character. The size of this array is determined by the character set, which is fixed and independent of the input string's length (N). The algorithm also modifies the original string in place, so it doesn't use extra space proportional to the input string size. Since the space used is constant regardless of the length of the string, the space complexity is O(1).

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty string or throw an IllegalArgumentException if the input is null or empty.
All characters in the input string are the same	The solution should still return a lexicographically largest permutation, even if all characters are identical.
Input string already sorted in descending order	The algorithm should still correctly identify this as the lexicographically largest string and return it.
Input string with very long length causing potential memory issues	The implementation should use efficient data structures and algorithms to minimize memory usage and prevent out-of-memory errors if the string is extremely long.
Input String consists of unicode/non-ascii characters	Ensure the string comparison and sorting algorithm supports unicode characters correctly.
Box contains insufficient characters to generate even a single valid string	Return an empty string or null to signify there is no possible string.
The 'greedy' character selection might prematurely terminate the algorithm before a better choice is found	Backtracking or dynamic programming might be necessary to ensure the globally optimal largest string is generated.
Integer overflow if using counters to track character counts in very large strings	Use appropriate data types (e.g., long) or handle potential overflow scenarios to ensure accurate character counting.

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 are the possible characters within the strings in the box? Are they limited to lowercase English letters, or can they include uppercase, numbers, or other special characters?
Can the box be empty (no strings)? What should I return in that case?
If there are multiple lexicographically largest strings, should I return all of them, the first one encountered, or is there another tie-breaking condition?
What is the maximum number of strings that can be in the box, and what is the maximum length of each string?
Is the input guaranteed to be valid, or should I handle potential null or invalid string inputs in the box?

Brute Force Solution

Approach

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

Consider every possible way to build a string by picking characters from the box.
For example, pick one character, then another, then another, until the string is as long as possible (or we run out of characters).
Create all possible strings that could be formed by selecting a different combination of characters each time.
Compare these strings alphabetically.
The string that comes last in alphabetical order (the 'biggest' one) is the answer.

Code Implementation

def find_lexicographically_largest_string_brute_force(input_string):
    all_possible_strings = []

    def generate_strings(current_string, remaining_characters):
        all_possible_strings.append(current_string)

        # If no characters remain, then we can't make additional combinations.
        if not remaining_characters:
            return

        for index in range(len(remaining_characters)):
            # Build all combinations by choosing a starting character
            generate_strings(
                current_string + remaining_characters[index],
                remaining_characters[index+1:]
            )

    generate_strings("", input_string)

    # Find the lexicographically largest string in the list
    lexicographically_largest_string = ""
    for possible_string in all_possible_strings:
        # Compare and update if larger than current largest string
        if possible_string > lexicographically_largest_string:
            lexicographically_largest_string = possible_string

    return lexicographically_largest_string

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

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

First, count how many of each character you have available to use.
Start building your string. At each position, ask yourself: What's the largest character I can use right now?
To figure that out, hypothetically add that character and check if you'll still have enough characters remaining to fill the rest of the string according to the rules of the box.
If you don't have enough remaining characters to finish the string after adding the character, try the next largest character.
Keep going down the list of characters (from largest to smallest) until you find one that lets you complete the string.
Add that character to the string, reduce the count of available characters, and move to the next position in the string.
Repeat this process until the string is complete.

Code Implementation

def find_lexicographically_largest_string(character_counts):
    string_length = sum(character_counts.values())
    result = ""

    character_counts_copy = character_counts.copy()

    for _ in range(string_length):
        for char_code in range(ord('z'), ord('a') - 1, -1):
            current_character = chr(char_code)

            # Check if the character is available.
            if character_counts_copy.get(current_character, 0) > 0:

                character_counts_copy[current_character] -= 1

                remaining_length = string_length - len(result) - 1
                remaining_counts = sum(character_counts_copy.values())

                # Check if we can still complete the string.
                if remaining_counts >= remaining_length:
                    result += current_character
                    break
                else:
                    # If we can't complete the string, backtrack.
                    character_counts_copy[current_character] += 1

    return result

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty string or throw an IllegalArgumentException if the input is null or empty.
All characters in the input string are the same	The solution should still return a lexicographically largest permutation, even if all characters are identical.
Input string already sorted in descending order	The algorithm should still correctly identify this as the lexicographically largest string and return it.
Input string with very long length causing potential memory issues	The implementation should use efficient data structures and algorithms to minimize memory usage and prevent out-of-memory errors if the string is extremely long.
Input String consists of unicode/non-ascii characters	Ensure the string comparison and sorting algorithm supports unicode characters correctly.
Box contains insufficient characters to generate even a single valid string	Return an empty string or null to signify there is no possible string.
The 'greedy' character selection might prematurely terminate the algorithm before a better choice is found	Backtracking or dynamic programming might be necessary to ensure the globally optimal largest string is generated.
Integer overflow if using counters to track character counts in very large strings	Use appropriate data types (e.g., long) or handle potential overflow scenarios to ensure accurate character counting.