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Minimum Number of Frogs Croaking

#2 Most AskedMedium

Minimum Number of Frogs Croaking #2 Most Asked

Medium

Zoox

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Topics:

ArraysStringsStacks

You are given the string croakOfFrogs, which represents a combination of the string "croak" from different frogs, that is, multiple frogs can croak at the same time, so multiple "croak" are mixed.

Return the minimum number of different frogs to finish all the croaks in the given string.

A valid "croak" means a frog is printing five letters 'c', 'r', 'o', 'a', and 'k' sequentially. The frogs have to print all five letters to finish a croak. If the given string is not a combination of a valid "croak" return -1.

Example 1:

Input: croakOfFrogs = "croakcroak"
Output: 1 
Explanation: One frog yelling "croak" twice.

Example 2:

Input: croakOfFrogs = "crcoakroak"
Output: 2 
Explanation: The minimum number of frogs is two. 
The first frog could yell "crcoakroak".
The second frog could yell later "crcoakroak".

Example 3:

Input: croakOfFrogs = "croakcrook"
Output: -1
Explanation: The given string is an invalid combination of "croak" from different frogs.

Constraints:

1 <= croakOfFrogs.length <= 10⁵
croakOfFrogs is either 'c', 'r', 'o', 'a', or 'k'.

Try coding it in LeetCode

Minimum Number of Frogs Croaking

#2 Most AskedMedium

Minimum Number of Frogs Croaking #2 Most Asked

Medium

Zoox

64 views

Topics:

ArraysStringsStacks

Return the minimum number of different frogs to finish all the croaks in the given string.

Example 1:

Input: croakOfFrogs = "croakcroak"
Output: 1 
Explanation: One frog yelling "croak" twice.

Example 2:

Input: croakOfFrogs = "crcoakroak"
Output: 2 
Explanation: The minimum number of frogs is two. 
The first frog could yell "crcoakroak".
The second frog could yell later "crcoakroak".

Example 3:

Input: croakOfFrogs = "croakcrook"
Output: -1
Explanation: The given string is an invalid combination of "croak" from different frogs.

Constraints:

1 <= croakOfFrogs.length <= 10⁵
croakOfFrogs is either 'c', 'r', 'o', 'a', or 'k'.

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:

Is the input string `croakOfFrogs` guaranteed to only contain characters from the set {'c', 'r', 'o', 'a', 'k'}?
What is the maximum possible length of the input string `croakOfFrogs`?
If the croaks are not possible, is returning -1 the only acceptable way to indicate failure, or are there other specific error conditions?
Can a single frog start a new croak before finishing its previous one?
Does the order of croaks within the string imply a strict temporal sequence, meaning a 'c' must be heard before its corresponding 'r', and so on, across all frogs simultaneously?

Brute Force Solution

Approach

The brute force approach involves checking every single possible way to assign the sounds the frogs make. It's like trying every combination to see which one works.

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

Imagine you have a sequence of frog sounds. For the first sound, consider all the different frogs that could have made it.
For the second sound, again, consider every possible frog that could have made it, regardless of what you assumed for the first sound.
Continue this for every sound in the sequence, trying every single frog for each sound independently.
After you've made a choice for every sound, check if your choices are valid. A choice is valid if no frog is asked to make overlapping sounds (meaning, if a frog is croaking, it can't be simultaneously starting a new 'croak' sound of the same type if it's already mid-'croak').
If a set of choices is valid, see how many frogs you ended up using.
Do this for all possible combinations of frog assignments for all sounds.
Finally, pick the set of choices that used the smallest number of frogs while still being valid.

Code Implementation

import itertools

def minimum_number_of_frogs_croaking(croak_string):
    sound_sequence = ['c', 'r', 'o', 'a', 'k']
    minimum_frogs_needed = float('inf')

    # We need to consider assigning each sound to each possible frog.
    # This generates all possible assignments of sounds to frogs.
    for frog_assignments in itertools.product(range(1, len(croak_string) + 1), repeat=len(croak_string)):
        current_frog_states = {frog_id: [] for frog_id in set(frog_assignments)}
        is_assignment_valid = True
        
        # We must verify that no frog is assigned overlapping sounds.
        # This check ensures the temporal consistency of each frog's croak sequence.
        for sound_index, sound_char in enumerate(croak_string):
            assigned_frog_id = frog_assignments[sound_index]
            expected_sound_index = sound_sequence.index(sound_char)

            # If a frog is already in the middle of a croak, it must be the next sound in sequence.
            if current_frog_states[assigned_frog_id]:
                last_sound_made = current_frog_states[assigned_frog_id][-1]
                if sound_sequence.index(last_sound_made) != expected_sound_index - 1:
                    is_assignment_valid = False
                    break
            elif expected_sound_index != 0:
                # If a frog is starting, it must be the 'c' sound.
                is_assignment_valid = False
                break
            
            current_frog_states[assigned_frog_id].append(sound_char)

        if is_assignment_valid:
            # If the assignment is valid, we check the number of frogs used.
            # This is crucial for finding the minimum requirement.
            number_of_frogs_used = len(set(frog_assignments))
            minimum_frogs_needed = min(minimum_frogs_needed, number_of_frogs_used)

    return minimum_frogs_needed if minimum_frogs_needed != float('inf') else -1

Big(O) Analysis

Time Complexity

O(S! * 2^S) – Let S be the number of sounds in the sequence. The brute force approach explores every possible assignment of each sound to a potential frog. For each of the S sounds, we are essentially trying to assign it to one of S frogs (or a new frog), which leads to exploring permutations of frog assignments. Furthermore, for each sound, we can think of it as assigning a 'state' to a frog (start, middle, end of croak), which can be visualized as a power set of possibilities for each sound. The total number of combinations to check becomes S factorial (for permutations of frogs) multiplied by 2 to the power of S (for possible states or assignments), resulting in an overall time complexity that grows extremely rapidly and is approximately O(S! * 2^S).

Space Complexity

O(1) – The brute force approach described involves iterating through all possible combinations of assigning sounds to frogs. Each assignment decision is made independently for each sound, and validity checks are performed. No auxiliary data structures are explicitly created or maintained to store intermediate results across different combinations. The memory usage is dominated by a few variables to track current assignments and the minimum frogs used, which remains constant regardless of the input sequence length.

Optimal Solution

Approach

We can keep track of the active croaks for each sound ('c', 'r', 'o', 'a', 'k') as they happen. The maximum number of 'c's that are currently active without being completed by an 'r' will tell us the minimum number of frogs needed.

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

Imagine a counter for each distinct croak sound: 'c', 'r', 'o', 'a', 'k'.
When you encounter a 'c', increment the 'c' counter. This represents a frog starting to croak.
When you encounter an 'r', check if there's an active 'c' (meaning the 'c' counter is greater than zero). If so, decrement the 'c' counter and increment the 'r' counter. If not, it's an invalid sequence, and we can't form a complete croak.
Follow the same logic for 'o' after 'r', 'a' after 'o', and 'k' after 'a'. Each step requires the previous sound to be active.
At each step, after updating the counters for the current sound, keep track of the highest number of active 'c's you've seen so far that haven't been completed by an 'r'.
If at any point you need to use a sound (like 'r') but its preceding sound ('c') doesn't have an active count (is zero), then the sequence is impossible.
The final answer is the largest count of active 'c's you observed throughout the entire sequence of sounds.

Code Implementation

def minimum_number_of_frogs_croaking(croak_sequence):
    count_c = 0
    count_r = 0
    count_o = 0
    count_a = 0
    count_k = 0
    active_croaks = 0
    max_frogs_needed = 0

    for sound_character in croak_sequence:
        if sound_character == 'c':
            count_c += 1
            active_croaks = max(active_croaks, count_c)
        elif sound_character == 'r':
            # Ensure there's an active 'c' before processing an 'r'.
            if count_c == 0:
                return -1
            count_c -= 1
            count_r += 1
        elif sound_character == 'o':
            # Ensure there's an active 'r' before processing an 'o'.
            if count_r == 0:
                return -1
            count_r -= 1
            count_o += 1
        elif sound_character == 'a':
            # Ensure there's an active 'o' before processing an 'a'.
            if count_o == 0:
                return -1
            count_o -= 1
            count_a += 1
        elif sound_character == 'k':
            # Ensure there's an active 'a' before processing a 'k'.
            if count_a == 0:
                return -1
            count_a -= 1
            count_k += 1
            # When a 'k' is found, a full croak is completed.
            if count_k == count_r and count_k == count_o and count_k == count_a:
                active_frogs_completing_croak = count_k
                # Decrease the count of currently active frogs by one for each completed croak.
                count_c -= active_frogs_completing_croak
                count_r -= active_frogs_completing_croak
                count_o -= active_frogs_completing_croak
                count_a -= active_frogs_completing_croak
                count_k -= active_frogs_completing_croak
        else:
            # Any character other than 'c', 'r', 'o', 'a', 'k' invalidates the sequence.
            return -1

    # If any sounds are left incomplete, the sequence is invalid.
    if count_c > 0 or count_r > 0 or count_o > 0 or count_a > 0 or count_k > 0:
        return -1

    return active_croaks

Big(O) Analysis

Time Complexity

O(n) – The solution iterates through the input string once. For each character in the string, a constant number of operations are performed: checking a counter, incrementing or decrementing it, and potentially updating a maximum value. Since the input string has a length of n, and each character is processed in constant time, the total number of operations is directly proportional to n. Therefore, the time complexity is O(n).

Space Complexity

O(1) – The solution uses a fixed number of counters (one for each of 'c', 'r', 'o', 'a', 'k') and a variable to track the maximum active croaks. Regardless of the input string's length (N), the amount of auxiliary memory required remains constant. Therefore, the space complexity is O(1).

Edge Cases

Case	How to Handle
Empty or null input string	An empty or null input string represents no croaks, thus requiring 0 frogs, which is a valid base case.
Input string is not a permutation of 'croak'	The algorithm must detect invalid character sequences or incomplete croaks and return -1.
Input string contains characters other than 'c', 'r', 'o', 'a', 'k'	Any character outside the 'croak' sequence invalidates the entire croaking pattern, resulting in a -1 return.
Croaks are not in the correct 'c', 'r', 'o', 'a', 'k' order	The solution must maintain counts for each letter in the sequence and ensure that a letter only progresses if its preceding letter has been accounted for.
A 'k' appears without a preceding 'c', 'r', 'o', 'a'	This indicates an incomplete croak, and the algorithm should identify this invalid state and return -1.
A 'c' appears after a completed 'croak' sequence from another frog	This is a valid scenario where a new frog starts its croak, and the algorithm should correctly increment the frog count if necessary.
The string is a perfect sequence of one croak, e.g., 'croak'	A single complete croak requires exactly one frog, and the solution should accurately reflect this.
The string ends with an incomplete croak, e.g., 'croa'	An incomplete croak at the end of the string means the sequence cannot be formed, and the function should return -1.

Empty or null input string

How to Handle:

An empty or null input string represents no croaks, thus requiring 0 frogs, which is a valid base case.

Input string is not a permutation of 'croak'

How to Handle:

The algorithm must detect invalid character sequences or incomplete croaks and return -1.

Input string contains characters other than 'c', 'r', 'o', 'a', 'k'

How to Handle:

Any character outside the 'croak' sequence invalidates the entire croaking pattern, resulting in a -1 return.

Croaks are not in the correct 'c', 'r', 'o', 'a', 'k' order

How to Handle:

The solution must maintain counts for each letter in the sequence and ensure that a letter only progresses if its preceding letter has been accounted for.

A 'k' appears without a preceding 'c', 'r', 'o', 'a'

How to Handle:

This indicates an incomplete croak, and the algorithm should identify this invalid state and return -1.

A 'c' appears after a completed 'croak' sequence from another frog

How to Handle:

This is a valid scenario where a new frog starts its croak, and the algorithm should correctly increment the frog count if necessary.

The string is a perfect sequence of one croak, e.g., 'croak'

How to Handle:

A single complete croak requires exactly one frog, and the solution should accurately reflect this.

The string ends with an incomplete croak, e.g., 'croa'

How to Handle:

An incomplete croak at the end of the string means the sequence cannot be formed, and the function should return -1.

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:

Is the input string `croakOfFrogs` guaranteed to only contain characters from the set {'c', 'r', 'o', 'a', 'k'}?
What is the maximum possible length of the input string `croakOfFrogs`?
If the croaks are not possible, is returning -1 the only acceptable way to indicate failure, or are there other specific error conditions?
Can a single frog start a new croak before finishing its previous one?
Does the order of croaks within the string imply a strict temporal sequence, meaning a 'c' must be heard before its corresponding 'r', and so on, across all frogs simultaneously?

Brute Force Solution

Approach

The brute force approach involves checking every single possible way to assign the sounds the frogs make. It's like trying every combination to see which one works.

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

Imagine you have a sequence of frog sounds. For the first sound, consider all the different frogs that could have made it.
For the second sound, again, consider every possible frog that could have made it, regardless of what you assumed for the first sound.
Continue this for every sound in the sequence, trying every single frog for each sound independently.
After you've made a choice for every sound, check if your choices are valid. A choice is valid if no frog is asked to make overlapping sounds (meaning, if a frog is croaking, it can't be simultaneously starting a new 'croak' sound of the same type if it's already mid-'croak').
If a set of choices is valid, see how many frogs you ended up using.
Do this for all possible combinations of frog assignments for all sounds.
Finally, pick the set of choices that used the smallest number of frogs while still being valid.

Code Implementation

import itertools

def minimum_number_of_frogs_croaking(croak_string):
    sound_sequence = ['c', 'r', 'o', 'a', 'k']
    minimum_frogs_needed = float('inf')

    # We need to consider assigning each sound to each possible frog.
    # This generates all possible assignments of sounds to frogs.
    for frog_assignments in itertools.product(range(1, len(croak_string) + 1), repeat=len(croak_string)):
        current_frog_states = {frog_id: [] for frog_id in set(frog_assignments)}
        is_assignment_valid = True
        
        # We must verify that no frog is assigned overlapping sounds.
        # This check ensures the temporal consistency of each frog's croak sequence.
        for sound_index, sound_char in enumerate(croak_string):
            assigned_frog_id = frog_assignments[sound_index]
            expected_sound_index = sound_sequence.index(sound_char)

            # If a frog is already in the middle of a croak, it must be the next sound in sequence.
            if current_frog_states[assigned_frog_id]:
                last_sound_made = current_frog_states[assigned_frog_id][-1]
                if sound_sequence.index(last_sound_made) != expected_sound_index - 1:
                    is_assignment_valid = False
                    break
            elif expected_sound_index != 0:
                # If a frog is starting, it must be the 'c' sound.
                is_assignment_valid = False
                break
            
            current_frog_states[assigned_frog_id].append(sound_char)

        if is_assignment_valid:
            # If the assignment is valid, we check the number of frogs used.
            # This is crucial for finding the minimum requirement.
            number_of_frogs_used = len(set(frog_assignments))
            minimum_frogs_needed = min(minimum_frogs_needed, number_of_frogs_used)

    return minimum_frogs_needed if minimum_frogs_needed != float('inf') else -1

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

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

Imagine a counter for each distinct croak sound: 'c', 'r', 'o', 'a', 'k'.
When you encounter a 'c', increment the 'c' counter. This represents a frog starting to croak.
When you encounter an 'r', check if there's an active 'c' (meaning the 'c' counter is greater than zero). If so, decrement the 'c' counter and increment the 'r' counter. If not, it's an invalid sequence, and we can't form a complete croak.
Follow the same logic for 'o' after 'r', 'a' after 'o', and 'k' after 'a'. Each step requires the previous sound to be active.
At each step, after updating the counters for the current sound, keep track of the highest number of active 'c's you've seen so far that haven't been completed by an 'r'.
If at any point you need to use a sound (like 'r') but its preceding sound ('c') doesn't have an active count (is zero), then the sequence is impossible.
The final answer is the largest count of active 'c's you observed throughout the entire sequence of sounds.

Code Implementation

def minimum_number_of_frogs_croaking(croak_sequence):
    count_c = 0
    count_r = 0
    count_o = 0
    count_a = 0
    count_k = 0
    active_croaks = 0
    max_frogs_needed = 0

    for sound_character in croak_sequence:
        if sound_character == 'c':
            count_c += 1
            active_croaks = max(active_croaks, count_c)
        elif sound_character == 'r':
            # Ensure there's an active 'c' before processing an 'r'.
            if count_c == 0:
                return -1
            count_c -= 1
            count_r += 1
        elif sound_character == 'o':
            # Ensure there's an active 'r' before processing an 'o'.
            if count_r == 0:
                return -1
            count_r -= 1
            count_o += 1
        elif sound_character == 'a':
            # Ensure there's an active 'o' before processing an 'a'.
            if count_o == 0:
                return -1
            count_o -= 1
            count_a += 1
        elif sound_character == 'k':
            # Ensure there's an active 'a' before processing a 'k'.
            if count_a == 0:
                return -1
            count_a -= 1
            count_k += 1
            # When a 'k' is found, a full croak is completed.
            if count_k == count_r and count_k == count_o and count_k == count_a:
                active_frogs_completing_croak = count_k
                # Decrease the count of currently active frogs by one for each completed croak.
                count_c -= active_frogs_completing_croak
                count_r -= active_frogs_completing_croak
                count_o -= active_frogs_completing_croak
                count_a -= active_frogs_completing_croak
                count_k -= active_frogs_completing_croak
        else:
            # Any character other than 'c', 'r', 'o', 'a', 'k' invalidates the sequence.
            return -1

    # If any sounds are left incomplete, the sequence is invalid.
    if count_c > 0 or count_r > 0 or count_o > 0 or count_a > 0 or count_k > 0:
        return -1

    return active_croaks

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Empty or null input string	An empty or null input string represents no croaks, thus requiring 0 frogs, which is a valid base case.
Input string is not a permutation of 'croak'	The algorithm must detect invalid character sequences or incomplete croaks and return -1.
Input string contains characters other than 'c', 'r', 'o', 'a', 'k'	Any character outside the 'croak' sequence invalidates the entire croaking pattern, resulting in a -1 return.
Croaks are not in the correct 'c', 'r', 'o', 'a', 'k' order	The solution must maintain counts for each letter in the sequence and ensure that a letter only progresses if its preceding letter has been accounted for.
A 'k' appears without a preceding 'c', 'r', 'o', 'a'	This indicates an incomplete croak, and the algorithm should identify this invalid state and return -1.
A 'c' appears after a completed 'croak' sequence from another frog	This is a valid scenario where a new frog starts its croak, and the algorithm should correctly increment the frog count if necessary.
The string is a perfect sequence of one croak, e.g., 'croak'	A single complete croak requires exactly one frog, and the solution should accurately reflect this.
The string ends with an incomplete croak, e.g., 'croa'	An incomplete croak at the end of the string means the sequence cannot be formed, and the function should return -1.

Empty or null input string

How to Handle:

An empty or null input string represents no croaks, thus requiring 0 frogs, which is a valid base case.

Input string is not a permutation of 'croak'

How to Handle:

The algorithm must detect invalid character sequences or incomplete croaks and return -1.

Input string contains characters other than 'c', 'r', 'o', 'a', 'k'

How to Handle:

Any character outside the 'croak' sequence invalidates the entire croaking pattern, resulting in a -1 return.

Croaks are not in the correct 'c', 'r', 'o', 'a', 'k' order

How to Handle:

The solution must maintain counts for each letter in the sequence and ensure that a letter only progresses if its preceding letter has been accounted for.

A 'k' appears without a preceding 'c', 'r', 'o', 'a'

How to Handle:

This indicates an incomplete croak, and the algorithm should identify this invalid state and return -1.

A 'c' appears after a completed 'croak' sequence from another frog

How to Handle:

This is a valid scenario where a new frog starts its croak, and the algorithm should correctly increment the frog count if necessary.

The string is a perfect sequence of one croak, e.g., 'croak'

How to Handle:

A single complete croak requires exactly one frog, and the solution should accurately reflect this.

The string ends with an incomplete croak, e.g., 'croa'

How to Handle:

An incomplete croak at the end of the string means the sequence cannot be formed, and the function should return -1.

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