Construct the Longest New String

class Solution:
    def longestString(self, x: int, y: int, z: int) -> int:
        return min(x + y + z, x + x + 1 + z, y + y + 1 + z) * 2

The problem “Construct the Longest New String” involves some key aspects like string manipulation, frequency counting, and the construction of new strings based on some conditions. Here are 10 problems to prepare for it:

  1. 383. Ransom Note: This problem is about constructing a string from given characters, which is a key part of the “Construct the Longest New String” problem.

  2. 387. First Unique Character in a String: This problem will help you in understanding the frequency counting of characters in a string.

  3. 392. Is Subsequence: This problem also involves creating a new string from the given string, though with different constraints.

  4. 344. Reverse String: This problem involves basic string manipulation, which is often useful.

  5. 459. Repeated Substring Pattern: This problem involves string manipulation and checking patterns in strings.

  6. 937. Reorder Data in Log Files: This problem involves reordering a string based on certain conditions, which can help in understanding how to construct strings.

  7. 205. Isomorphic Strings: This problem is about finding patterns in strings, which might be helpful.

  8. 242. Valid Anagram: This problem involves frequency counting and comparison of two strings.

  9. 49. Group Anagrams: This problem involves string manipulation and categorizing based on certain conditions.

  10. 349. Intersection of Two Arrays: This problem involves finding common elements from two arrays, similar to finding common characters from two strings.

These cover string manipulation, frequency counting, and constructing new strings based on certain conditions, which will be useful when dealing with problems like the target problem.

class Solution:
    def longestString(self, x: int, y: int, z: int) -> int:
        ans = z * 2

        if x == 0 and y == 0: return ans
        elif x == 0 or y == 0: return ans + 2
        elif x == y: return ans + (x * 4)
        else: return ans + (min(x, y) * 4) + 2

Problem Classification

This problem falls under the category of String Manipulation and Dynamic Programming.

What Components:

  1. Three integers x, y, and z, representing the number of “AA”, “BB”, and “AB” strings, respectively.
  2. The task of concatenating these strings in a way that the resultant string does not contain “AAA” or “BBB” as a substring.
  3. The goal of maximizing the length of the newly formed string.

This problem is asking to manipulate strings based on certain conditions (not containing “AAA” or “BBB” as a substring) and to maximize the length of the resultant string.

This problem can be classified as an Optimization problem, a subcategory of Dynamic Programming problems. It involves finding the best (in this case, longest) possible outcome from all possible outcomes that could be obtained by different concatenations of the given strings. This requires devising a strategy to make the optimal decision at each step (which string to concatenate next), taking into account the impact of each decision on future steps.

Moreover, given the focus on string operations and substring conditions, this problem also falls under the String Manipulation category. String manipulation tasks involve working with and altering strings, which is a significant aspect of this problem.

Since the problem involves iterative concatenation operations which may require recursion or looping through the available strings, this problem can also be seen as a problem of Iteration or Recursion.

The problem is a combination of Dynamic Programming (for the optimization part), String Manipulation (for the concatenation operation and substring condition), and Iteration or Recursion (for performing the concatenation operations).

Clarification Questions

What are the clarification questions we can ask about this problem?

Identifying Problem Isomorphism

“Construct the Longest New String” can be approximately mapped to “Longest Palindromic Subsequence”.

“Construct the Longest New String” involves constructing a new string from an existing one with certain restrictions. “Longest Palindromic Subsequence” involves finding the longest subsequence from a given string that is also a palindrome.

These two problems share the similarity of deriving a new string from a given string, but they differ in terms of the constraints applied. “Construct the Longest New String” has specific character-based constraints, while “Longest Palindromic Subsequence” has palindromic constraints.

“Longest Palindromic Subsequence” is more straightforward as it does not involve specific character-based constraints, making it simpler than “Construct the Longest New String”.

Language Agnostic Coding Drills

  1. Dissection of the code:

    The code contains several different programming concepts:

    a. Function Definitions: The concept of defining functions that accept parameters and return a value.

    b. Arithmetic Operations: The concept of performing basic mathematical operations like multiplication and addition.

    c. Control Flow - Conditional Statements: The use of if, elif and else statements to direct the flow of the program based on conditions.

    d. Relational Operators: The use of equality (==) and inequality (!=) operators to compare values.

    e. Logical Operators: The use of logical operators (and, or) to combine conditions.

    f. Built-in Python functions: The use of the min() function to find the smallest value among the given numbers.

  2. Order of difficulty:

    a. Function Definitions (Easy): Defining functions is a fundamental concept in programming and is usually one of the first concepts learned by beginners.

    b. Arithmetic Operations (Easy): Basic arithmetic operations like addition and multiplication are simple to implement and understand.

    c. Relational Operators (Easy): Comparing values is a straightforward concept and frequently used in many programs.

    d. Control Flow - Conditional Statements (Medium): Conditional statements involve a bit of logical thinking and understanding how the program’s flow is controlled.

    e. Logical Operators (Medium): Using logical operators requires an understanding of boolean logic. It can be tricky for beginners to understand how to correctly use these to combine conditions.

    f. Built-in Python functions (Medium): Using built-in functions requires knowledge of what functions are available and how to use them.

  3. Problem-solving approach:

    The problem is solved by first setting the length of the string ‘ans’ to 2 times ‘z’ (the length of all ‘AB’ strings). Then, depending on the number of ‘AA’ and ‘BB’ strings (represented by ‘x’ and ‘y’), the length of ‘ans’ is further increased. Each ‘AA’ or ‘BB’ string contributes 2 to the length of ‘ans’, but since ‘AAA’ and ‘BBB’ are not allowed, the number of ‘AA’ or ‘BB’ strings that can be added is limited to the smaller of ‘x’ and ‘y’, and an additional ‘AA’ or ‘BB’ string can only be added if ‘x’ is not equal to ‘y’.

    To implement this strategy, the code starts by defining a function that accepts ‘x’, ‘y’, and ‘z’ as parameters. Inside this function, it performs arithmetic operations to calculate the initial length of ‘ans’. Then it uses conditional statements to check various conditions about ‘x’ and ‘y’ and uses more arithmetic operations to further increase the length of ‘ans’ as necessary. The min() function is used to find the smaller of ‘x’ and ‘y’ when calculating the additional length that can be added from ‘AA’ and ‘BB’ strings. Finally, the length of ‘ans’ is returned as the result.

Targeted Drills in Python

a. Function Definitions: Define a function that calculates the square of a number.

def square(n):
    return n * n

b. Arithmetic Operations: Write a program that calculates the area of a rectangle given its length and width.

length = 5
width = 4
area = length * width

c. Relational Operators: Write a program that checks if a number is equal to 10.

num = 10
if num == 10:
    print("The number is equal to 10.")

d. Control Flow - Conditional Statements: Write a program that checks if a number is positive, negative, or zero.

num = -5
if num > 0:
elif num < 0:

e. Logical Operators: Write a program that checks if a number is between 1 and 10.

num = 5
if num >= 1 and num <= 10:
    print("The number is between 1 and 10.")

f. Built-in Python functions: Use the min() function to find the minimum of three numbers.

num1 = 5
num2 = 10
num3 = 15
minimum = min(num1, num2, num3)
  1. Specific drills:

    a. String Concatenation: Concatenate two strings and print the result.

    str1 = "Hello"
    str2 = "World"
    result = str1 + str2

    b. String Length: Find the length of a string.

    str = "Hello World"
    length = len(str)
  2. Merging Drills:

    a. Begin by defining a function that takes in three parameters x, y, and z. These are integers that represent the count of each type of string available.

    b. Perform an arithmetic operation to calculate the initial string length considering the length of ‘AB’ strings.

    c. Use conditional statements to check if there are no ‘AA’ and ‘BB’ strings. If so, return the initial string length as the result.

    d. Add another condition to check if there are only ‘AA’ or ‘BB’ strings. If so, add 2 to the string length and return the result.

    e. Use the min() function in conjunction with a conditional statement to check if there are an equal number of ‘AA’ and ‘BB’ strings. If so, add the result of 4 times the number of ‘AA’ or ‘BB’ strings to the string length and return the result.

    f. Finally, add a condition to handle the case where the number of ‘AA’ and ‘BB’ strings is unequal. In this case, add the result of 4 times the smaller number of ‘AA’ or ‘BB’ strings, plus 2, to the string length and return the result. This final return value is the maximum possible length of the new string.