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Change Minimum Characters to Satisfy One of Three Conditions

Medium

Google

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Topics:

Strings

You are given two strings a and b that consist of lowercase letters. In one operation, you can change any character in a or b to any lowercase letter.

Your goal is to satisfy one of the following three conditions:

Every letter in a is strictly less than every letter in b in the alphabet.
Every letter in b is strictly less than every letter in a in the alphabet.
Both a and b consist of only one distinct letter.

Return the minimum number of operations needed to achieve your goal.

For example:

a = "aba", b = "caa"

Output: 2

Explanation:

Change b to "ccc" in 2 operations, then every letter in a is less than every letter in b.
Change a to "bbb" and b to "aaa" in 3 operations, then every letter in b is less than every letter in a.
Change a to "aaa" and b to "aaa" in 2 operations, then a and b consist of one distinct letter.

The best way was done in 2 operations (either condition 1 or condition 3).

a = "dabadd", b = "cda"

Output: 3

Explanation:

The best way is to make condition 1 true by changing b to "eee".

Change Minimum Characters to Satisfy One of Three Conditions

Medium

Google

2 views

Topics:

Strings

You are given two strings a and b that consist of lowercase letters. In one operation, you can change any character in a or b to any lowercase letter.

Your goal is to satisfy one of the following three conditions:

Every letter in a is strictly less than every letter in b in the alphabet.
Every letter in b is strictly less than every letter in a in the alphabet.
Both a and b consist of only one distinct letter.

Return the minimum number of operations needed to achieve your goal.

For example:

a = "aba", b = "caa"

Output: 2

Explanation:

Change b to "ccc" in 2 operations, then every letter in a is less than every letter in b.
Change a to "bbb" and b to "aaa" in 3 operations, then every letter in b is less than every letter in a.
Change a to "aaa" and b to "aaa" in 2 operations, then a and b consist of one distinct letter.

The best way was done in 2 operations (either condition 1 or condition 3).

a = "dabadd", b = "cda"

Output: 3

Explanation:

The best way is to make condition 1 true by changing b to "eee".

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:

Can you please clarify the possible characters in strings a and b? Are they limited to lowercase English letters, or can they include uppercase letters, numbers, or other special characters?
What are the constraints on the lengths of strings a and b? Can either string be empty or null?
If none of the three conditions can be satisfied, what should the function return?
Could you provide a more precise definition of 'changing' a character? Does it mean replacing it with any other character from the allowed character set, or can I also delete/add characters?
In the case where multiple minimum changes are possible to satisfy one of the conditions, is any one of those valid results acceptable?

Brute Force Solution

Approach

The brute force approach is about trying out every possible combination to see which one works best. For this problem, we'll explore all ways to make the strings 'a' and 'b' satisfy the conditions, and count the changes each way requires. Finally we pick the way that requires the least changes.

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

First, let's consider the condition where every character in 'a' must be less than or equal to every character in 'b'. We'll try every possible character, say 'x'.
For each 'x', we'll change all characters in 'a' that are greater than 'x' to 'x'. We'll also change all characters in 'b' that are less than 'x' to 'x'.
Count how many changes were needed in 'a' and 'b' for this particular 'x'.
Repeat this process for all possible characters 'x'.
Next, let's consider the condition where every character in 'b' must be less than or equal to every character in 'a'. We do almost the same as above, just swapping the roles of 'a' and 'b'. Try every possible character 'x'.
For each 'x', we'll change all characters in 'b' that are greater than 'x' to 'x'. We'll also change all characters in 'a' that are less than 'x' to 'x'.
Count how many changes were needed in 'a' and 'b' for this particular 'x'.
Repeat this process for all possible characters 'x'.
Finally, let's consider the case where all characters in 'a' are the same. Try setting all characters in 'a' to 'x', and count the changes needed.
Do this for all possible characters 'x'.
Also consider the case where all characters in 'b' are the same. Try setting all characters in 'b' to 'x', and count the changes needed.
Do this for all possible characters 'x'.
Compare all the change counts from all the above scenarios.
The smallest number of changes we found is our answer.

Code Implementation

def min_characters(a_string, b_string):    minimum_changes = float('inf')
    # Iterate through all possible split characters
    for split_character_code in range(ord('a'), ord('z') + 1):
        split_character = chr(split_character_code)
        changes_a = 0
        changes_b = 0
        # Calculate changes to satisfy a <= b condition
        for character in a_string:
            if character > split_character:
                changes_a += 1
        for character in b_string:
            if character < split_character:
                changes_b += 1
        minimum_changes = min(minimum_changes, changes_a + changes_b)
        changes_a = 0
        changes_b = 0
        # Calculate changes to satisfy b <= a condition
        for character in a_string:
            if character < split_character:
                changes_a += 1
        for character in b_string:
            if character > split_character:
                changes_b += 1
        minimum_changes = min(minimum_changes, changes_a + changes_b)

    #Check when all characters in a are same
    for target_character_code in range(ord('a'), ord('z') + 1):
        target_character = chr(target_character_code)
        changes = 0
        for character in a_string:
            if character != target_character:
                changes += 1
        minimum_changes = min(minimum_changes, changes)

    #Check when all characters in b are same
    for target_character_code in range(ord('a'), ord('z') + 1):
        target_character = chr(target_character_code)
        changes = 0
        for character in b_string:
            if character != target_character:
                changes += 1
        minimum_changes = min(minimum_changes, changes)
    # Return the minimum changes
    return minimum_changes

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through all possible characters (26 in the English alphabet) to find the minimum changes required to satisfy the conditions. For each character, it iterates through strings 'a' and 'b' to count the changes needed (up to 2 * n where n is the length of the longer string). Since the outer loop iterates a fixed number of times (26) and the inner loops are proportional to the length of the strings 'a' and 'b' respectively, the overall time complexity is dominated by the linear scan. Therefore the runtime scales linearly with the length of the strings, giving a time complexity of O(n).

Space Complexity

O(1) – The algorithm's space complexity is O(1) because it uses a fixed amount of extra memory regardless of the input string lengths. It iterates through characters (a-z) which is a constant number of iterations (26), and for each character, it only stores a constant number of integer variables to track the number of changes needed for each condition. There are no auxiliary data structures, such as lists or hash maps, whose size scales with the input strings a and b.

Optimal Solution

Approach

The goal is to make two strings satisfy one of three conditions by changing the fewest letters possible. We will check each condition independently and then pick the one that required the fewest changes overall.

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

First, we will examine making all letters in the first string smaller than all the letters in the second string. For each possible dividing point in the alphabet, we count how many letters in the first string are bigger than or equal to that letter, and how many letters in the second string are smaller than that letter. The total of these two counts represents the number of changes needed to achieve this condition. We track the minimum count of changes.
Next, we will examine making all letters in the second string smaller than all the letters in the first string. We do the same process as above, but with the roles of the strings reversed. Again, we track the minimum count of changes.
Finally, we need to examine making both strings consist of the same letter. For each letter of the alphabet, we will count the number of changes needed in both strings to make all letters that letter. We track the minimum count of changes.
We compare the minimum number of changes from all three conditions and the smallest one is the answer.

Code Implementation

def min_characters(string_a, string_b):
    string_a_length = len(string_a)
    string_b_length = len(string_b)

    # Helper function to calculate changes for condition 1 or 2.
    def calculate_changes(first_string, second_string):
        minimum_changes = float('inf')
        for letter_code in range(1, 27):
            changes = 0
            for char in first_string:
                if ord(char) - ord('a') >= letter_code:
                    changes += 1
            for char in second_string:
                if ord(char) - ord('a') < letter_code:
                    changes += 1
            minimum_changes = min(minimum_changes, changes)
        return minimum_changes

    minimum_changes_overall = calculate_changes(string_a, string_b)
    minimum_changes_overall = min(minimum_changes_overall, calculate_changes(string_b, string_a))

    # Check if making all characters the same is optimal.
    minimum_same_char_changes = float('inf')

    # We must iterate over each character in the alphabet
    for letter_code in range(26):
        changes = 0
        for char in string_a:
            if ord(char) - ord('a') != letter_code:
                changes += 1
        for char in string_b:
            if ord(char) - ord('a') != letter_code:
                changes += 1
        minimum_same_char_changes = min(minimum_same_char_changes, changes)

    # Take the minimum of all three conditions.
    minimum_changes_overall = min(minimum_changes_overall, minimum_same_char_changes)
    return minimum_changes_overall

Big(O) Analysis

Time Complexity

O(n + m) – The algorithm iterates through the alphabet a fixed number of times (26, which is constant). For each letter in the alphabet, it iterates through the first string (length n) to count characters greater than or equal to the letter, and then iterates through the second string (length m) to count characters smaller than the letter. It also iterates through both strings (length n and m) to calculate the number of changes needed to make all letters the same. Therefore, the time complexity is dominated by the string traversals, which is O(26 * (n + m)). Since 26 is a constant, we simplify to O(n + m).

Space Complexity

O(1) – The algorithm primarily uses integer variables to track counts and minimum changes. The number of integer variables remains constant regardless of the length of the input strings. No auxiliary data structures like arrays or hash maps that scale with the input size are created, thus the space complexity is constant.

Edge Cases

Case	How to Handle
Empty strings as input	Return 0 because no changes are needed as the condition is trivially satisfied.
Strings with length 1	Return 0 because any of the conditions can be satisfied without changes.
Strings with all identical characters	Return 0 because the condition that all characters are equal is already met.
Strings where one string is significantly longer than the other	The algorithm should still process the strings correctly by considering all possible split points and applying the minimum change condition.
Strings with characters far apart in the alphabet (e.g., 'a' and 'z')	The character iteration in the loops should handle the entire range of characters and efficiently compute differences
Strings with repeated sequences of the same character	The core logic calculating necessary changes will correctly account for such patterns by iterating through the alphabet and comparing character counts.
Strings with the same characters but in different orders, needing many changes.	The algorithm correctly calculates changes needed in each condition, ensuring correct counts regardless of char order.
Large string inputs potentially causing memory issues	The solution should avoid storing intermediate results proportional to the input size, and use character counts to reduce memory usage.

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:

Can you please clarify the possible characters in strings a and b? Are they limited to lowercase English letters, or can they include uppercase letters, numbers, or other special characters?
What are the constraints on the lengths of strings a and b? Can either string be empty or null?
If none of the three conditions can be satisfied, what should the function return?
Could you provide a more precise definition of 'changing' a character? Does it mean replacing it with any other character from the allowed character set, or can I also delete/add characters?
In the case where multiple minimum changes are possible to satisfy one of the conditions, is any one of those valid results acceptable?

Brute Force Solution

Approach

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

First, let's consider the condition where every character in 'a' must be less than or equal to every character in 'b'. We'll try every possible character, say 'x'.
For each 'x', we'll change all characters in 'a' that are greater than 'x' to 'x'. We'll also change all characters in 'b' that are less than 'x' to 'x'.
Count how many changes were needed in 'a' and 'b' for this particular 'x'.
Repeat this process for all possible characters 'x'.
Next, let's consider the condition where every character in 'b' must be less than or equal to every character in 'a'. We do almost the same as above, just swapping the roles of 'a' and 'b'. Try every possible character 'x'.
For each 'x', we'll change all characters in 'b' that are greater than 'x' to 'x'. We'll also change all characters in 'a' that are less than 'x' to 'x'.
Count how many changes were needed in 'a' and 'b' for this particular 'x'.
Repeat this process for all possible characters 'x'.
Finally, let's consider the case where all characters in 'a' are the same. Try setting all characters in 'a' to 'x', and count the changes needed.
Do this for all possible characters 'x'.
Also consider the case where all characters in 'b' are the same. Try setting all characters in 'b' to 'x', and count the changes needed.
Do this for all possible characters 'x'.
Compare all the change counts from all the above scenarios.
The smallest number of changes we found is our answer.

Code Implementation

def min_characters(a_string, b_string):    minimum_changes = float('inf')
    # Iterate through all possible split characters
    for split_character_code in range(ord('a'), ord('z') + 1):
        split_character = chr(split_character_code)
        changes_a = 0
        changes_b = 0
        # Calculate changes to satisfy a <= b condition
        for character in a_string:
            if character > split_character:
                changes_a += 1
        for character in b_string:
            if character < split_character:
                changes_b += 1
        minimum_changes = min(minimum_changes, changes_a + changes_b)
        changes_a = 0
        changes_b = 0
        # Calculate changes to satisfy b <= a condition
        for character in a_string:
            if character < split_character:
                changes_a += 1
        for character in b_string:
            if character > split_character:
                changes_b += 1
        minimum_changes = min(minimum_changes, changes_a + changes_b)

    #Check when all characters in a are same
    for target_character_code in range(ord('a'), ord('z') + 1):
        target_character = chr(target_character_code)
        changes = 0
        for character in a_string:
            if character != target_character:
                changes += 1
        minimum_changes = min(minimum_changes, changes)

    #Check when all characters in b are same
    for target_character_code in range(ord('a'), ord('z') + 1):
        target_character = chr(target_character_code)
        changes = 0
        for character in b_string:
            if character != target_character:
                changes += 1
        minimum_changes = min(minimum_changes, changes)
    # Return the minimum changes
    return minimum_changes

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

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

First, we will examine making all letters in the first string smaller than all the letters in the second string. For each possible dividing point in the alphabet, we count how many letters in the first string are bigger than or equal to that letter, and how many letters in the second string are smaller than that letter. The total of these two counts represents the number of changes needed to achieve this condition. We track the minimum count of changes.
Next, we will examine making all letters in the second string smaller than all the letters in the first string. We do the same process as above, but with the roles of the strings reversed. Again, we track the minimum count of changes.
Finally, we need to examine making both strings consist of the same letter. For each letter of the alphabet, we will count the number of changes needed in both strings to make all letters that letter. We track the minimum count of changes.
We compare the minimum number of changes from all three conditions and the smallest one is the answer.

Code Implementation

def min_characters(string_a, string_b):
    string_a_length = len(string_a)
    string_b_length = len(string_b)

    # Helper function to calculate changes for condition 1 or 2.
    def calculate_changes(first_string, second_string):
        minimum_changes = float('inf')
        for letter_code in range(1, 27):
            changes = 0
            for char in first_string:
                if ord(char) - ord('a') >= letter_code:
                    changes += 1
            for char in second_string:
                if ord(char) - ord('a') < letter_code:
                    changes += 1
            minimum_changes = min(minimum_changes, changes)
        return minimum_changes

    minimum_changes_overall = calculate_changes(string_a, string_b)
    minimum_changes_overall = min(minimum_changes_overall, calculate_changes(string_b, string_a))

    # Check if making all characters the same is optimal.
    minimum_same_char_changes = float('inf')

    # We must iterate over each character in the alphabet
    for letter_code in range(26):
        changes = 0
        for char in string_a:
            if ord(char) - ord('a') != letter_code:
                changes += 1
        for char in string_b:
            if ord(char) - ord('a') != letter_code:
                changes += 1
        minimum_same_char_changes = min(minimum_same_char_changes, changes)

    # Take the minimum of all three conditions.
    minimum_changes_overall = min(minimum_changes_overall, minimum_same_char_changes)
    return minimum_changes_overall

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Empty strings as input	Return 0 because no changes are needed as the condition is trivially satisfied.
Strings with length 1	Return 0 because any of the conditions can be satisfied without changes.
Strings with all identical characters	Return 0 because the condition that all characters are equal is already met.
Strings where one string is significantly longer than the other	The algorithm should still process the strings correctly by considering all possible split points and applying the minimum change condition.
Strings with characters far apart in the alphabet (e.g., 'a' and 'z')	The character iteration in the loops should handle the entire range of characters and efficiently compute differences
Strings with repeated sequences of the same character	The core logic calculating necessary changes will correctly account for such patterns by iterating through the alphabet and comparing character counts.
Strings with the same characters but in different orders, needing many changes.	The algorithm correctly calculates changes needed in each condition, ensuring correct counts regardless of char order.
Large string inputs potentially causing memory issues	The solution should avoid storing intermediate results proportional to the input size, and use character counts to reduce memory usage.