Text Justification

This requires text justification. Given an array of words and a maximum width, the goal is to format the text so that each line has exactly maxWidth characters and is fully justified (both left and right), with rules for distributing spaces.

Here’s a high-level algorithm to achieve this:

  1. Initialize Variables: Start with an empty result list and a temporary line list to hold words for the current line.

  2. Iterate Through Words: Loop through the words and add them to the current line, keeping track of the current line length.

  3. Check Line Length: If adding the next word would exceed maxWidth, justify the current line, add it to the result, and start a new line.

  4. Justify Lines: Distribute extra spaces between words as evenly as possible. If spaces don’t divide evenly, assign more spaces to the left slots.

  5. Handle Last Line: The last line is left-justified, with no extra spaces between words.

  6. Return Result: Return the list of justified lines.

Here’s a sample code that implements the algorithm:

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class Solution:
    def fullJustify(self, words: List[str], maxWidth: int) -> List[str]:
        result, line, line_length = [], [], 0

        for word in words:
            if line_length + len(word) + len(line) > maxWidth:
                for i in range(maxWidth - line_length):
                    line[i % (len(line) - 1 or 1)] += ' '
                result.append(''.join(line))
                line, line_length = [], 0
            line.append(word)
            line_length += len(word)

        # Handle the last line
        result.append(' '.join(line).ljust(maxWidth, ' '))

        return result

This code implements the constraints mentioned in the problem statement. It ensures that the resulting text is formatted according to the given rules, providing the expected output for the given examples.

Identifying Problem Isomorphism

“Text Justification” can be approximately mapped to “Palindrome Partitioning II”.

In “Text Justification”, you’re given a list of words and a width, and the task is to arrange those words into lines where the width of each line does not exceed the given width and the extra spaces are distributed as evenly as possible. If the spaces cannot be evenly distributed, the left-most gaps should have more spaces than the right-most ones.

In “Palindrome Partitioning II”, you’re given a string and your goal is to partition the string such that every substring of the partition is a palindrome, minimizing the number of cuts.

The reasoning is that both problems require partitioning an input (a list of words or a string) into distinct segments (lines or palindromic substrings) under certain constraints (line width or minimizing the number of cuts). The partitioning in both problems requires careful consideration of the properties of the input (word length or whether a substring is a palindrome).

Both are complex as they require careful partitioning of the input. However, “Palindrome Partitioning II” may be considered more complex due to the requirement to minimize the number of cuts, which adds an additional optimization problem to solve.

10 Prerequisite LeetCode Problems

“Text Justification” involves string manipulation, handling edge cases, and formatting output to meet certain requirements. Here are 10 problems to build these foundational skills:

  1. “Reverse Words in a String” (LeetCode Problem #151): This problem introduces the basics of string manipulation and word reversal, which are useful for text justification.

  2. “Valid Palindrome” (LeetCode Problem #125): This problem provides practice for basic string manipulation and edge case handling.

  3. “Implement strStr()” (LeetCode Problem #28): This problem gives practice on string matching, which may come in handy for the “Text Justification” problem.

  4. “Add Binary” (LeetCode Problem #67): This problem helps you practice formatting output strings and handling edge cases.

  5. “ZigZag Conversion” (LeetCode Problem #6): This problem also deals with text formatting and may provide useful insights for text justification.

  6. “Longest Common Prefix” (LeetCode Problem #14): This problem provides practice on string comparison and manipulation.

  7. “Count and Say” (LeetCode Problem #38): This problem gives practice on creating strings based on certain conditions, which is a key concept for “Text Justification”.

  8. “Valid Parentheses” (LeetCode Problem #20): This problem introduces the concept of stack in the context of string manipulation.

  9. “Simplify Path” (LeetCode Problem #71): This problem requires understanding of string manipulation, stack usage, and handling edge cases.

  10. “Reorder Data in Log Files” (LeetCode Problem #937): This problem provides practice on sorting and formatting strings.

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def fullJustify(self, words, maxWidth):
    res, cur, num_of_letters = [], [], 0
    for w in words:
        if num_of_letters + len(w) + len(cur) > maxWidth:
            for i in range(maxWidth - num_of_letters):
                cur[i%(len(cur)-1 or 1)] += ' '
            res.append(''.join(cur))
            cur, num_of_letters = [], 0
        cur += [w]
        num_of_letters += len(w)
    return res + [' '.join(cur).ljust(maxWidth)]

Problem Classification

Text Justification - The problem requires arranging words in a text such that each line is fully justified. It deals with manipulating text formatting according to specific rules, hence the classification Text Formatting.

Text Justification - This problem involves arranging words in a text to align properly on each line. It’s about adjusting text according to rules, so it’s Text Adjusting.

Language Agnostic Coding Drills

Here is a breakdown of the key concepts you’ll need to understand to implement the solution to the text justification problem:

  1. String Manipulation: Learning how to work with strings is one of the basic requirements in almost all languages. Python has many built-in functions that help in manipulating a string. A string is a sequence of characters.

    Coding Drill: Write a function that accepts a string as input and returns the string with all its characters converted to uppercase.

  2. Looping: To iterate over a sequence like a list (or tuple, string), you can use the for loop. If you want to iterate over a sequence of numbers, you can use the built-in function range().

    Coding Drill: Write a function that accepts a list of numbers and returns the sum of all the numbers in the list.

  3. Conditional Statements: Control flow with if-elif-else is an important aspect of Python programming. It allows the program to evaluate if certain conditions are met and perform a predetermined function based on the outcome of the evaluation.

    Coding Drill: Write a function that accepts a number as input and prints whether the number is positive, negative, or zero.

  4. List Manipulation: Python provides various ways to manipulate lists, which are one of the most frequently used data structures. Common operations include adding, removing, or modifying elements, as well as combining or splitting lists.

    Coding Drill: Write a function that accepts a list of numbers and returns a new list with all the numbers multiplied by 2.

  5. Working with List of Strings: Python allows operations on list of strings using simple methods including join(), split(), etc.

    Coding Drill: Write a function that accepts a list of strings and returns a single string that’s the result of concatenating all the strings in the list.

  6. Justification of Strings: The ljust(), rjust() and center() function in python, ljust() method in python is used to justify the string to the left side if size of string is less than the provided integer and fill the remaining space of integer size with specified character.

    Coding Drill: Write a function that accepts a string and an integer ’n’ and returns a string that is left-justified with respect to ’n'.

After understanding these concepts, you can start thinking about the problem. The problem is essentially to adjust the words in such a way that each line contains exactly maxWidth characters and is both left and right-justified. This involves dealing with string manipulation (including justification of strings), list manipulation and conditional statements inside a loop. You start by iterating over the words, adding them to the current line until you can’t fit any more, at which point you add the current line to your result and start a new line. You also need to handle the extra spaces required to make the lines both left and right-justified.

Targeted Drills in Python

Coding Drill 1 - String Manipulation: Write a function that accepts a string as input and returns the string with all its characters converted to uppercase.

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def convert_to_uppercase(input_string):
    return input_string.upper()

print(convert_to_uppercase("hello"))  # Expected output: HELLO

Coding Drill 2 - Looping: Write a function that accepts a list of numbers and returns the sum of all the numbers in the list.

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def sum_of_numbers(numbers):
    return sum(numbers)

print(sum_of_numbers([1, 2, 3, 4, 5]))  # Expected output: 15

Coding Drill 3 - Conditional Statements: Write a function that accepts a number as input and prints whether the number is positive, negative, or zero.

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def check_number(n):
    if n > 0:
        return "Positive"
    elif n < 0:
        return "Negative"
    else:
        return "Zero"

print(check_number(10))  # Expected output: Positive

Coding Drill 4 - List Manipulation: Write a function that accepts a list of numbers and returns a new list with all the numbers multiplied by 2.

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def multiply_by_two(numbers):
    return [n * 2 for n in numbers]

print(multiply_by_two([1, 2, 3]))  # Expected output: [2, 4, 6]

Coding Drill 5 - Working with List of Strings: Write a function that accepts a list of strings and returns a single string that’s the result of concatenating all the strings in the list.

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def concatenate_strings(strings):
    return ''.join(strings)

print(concatenate_strings(["hello", "world"]))  # Expected output: helloworld

Coding Drill 6 - Justification of Strings: Write a function that accepts a string and an integer ’n’ and returns a string that is left-justified with respect to ’n'.

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def left_justify(string, n):
    return string.ljust(n)

print(left_justify("hello", 10))  # Expected output: "hello     "

These drills cover the essential skills needed to implement the final solution, including string and list manipulations, loops, and conditionals. Once you’re comfortable with these, you should be able to piece them together to solve the problem.