Word Break II

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from typing import List

class Solution:
    def wordBreak(self, s: str, wordDict: List[str]) -> List[str]:
        wordSet = set(wordDict)
        memo = {}

        def dfs(index):
            # If we've already solved this subproblem, return the result
            if index in memo:
                return memo[index]

            # If the index is at the end of the string, we found a valid break
            if index == len(s):
                return [""]

            sentences = []
            for end in range(index + 1, len(s) + 1):
                word = s[index:end]
                # If the word is in the dictionary, continue to search
                if word in wordSet:
                    rest_of_sentences = dfs(end)
                    for sentence in rest_of_sentences:
                        if sentence:
                            sentences.append(word + " " + sentence)
                        else:
                            sentences.append(word)

            # Memoize the result
            memo[index] = sentences
            return sentences

        # Start the recursion from the beginning of the string
        return dfs(0)

Identifying Problem Isomorphism

“Word Break II” requires you to determine all the possible ways a given string can be segmented into a sequence of one or more words in a dictionary of known words.

An easier problem with a similar concept is “Word Break”. In this problem, you must identify whether the string can be broken into valid words from a given dictionary. It’s a subset of the problem, where instead of identifying all possibilities, you’re only checking if it’s possible.

A more complex problem is “Concatenated Words”. In this problem, you are given a list of words and you need to return all the concatenated words in the list. This is a more complicated version of “Word Break II”, as here we’re not just breaking the string into dictionary words but forming words which are a concatenation of at least two words in the list.

The reasoning is that all three problems involve dividing or segmenting a string, but they increase in complexity:

  1. “Word Break” checks if it’s possible to break the string into valid words from a dictionary.
  2. “Word Break II” builds on this concept by requiring all possible segmentations to be found.
  3. “Concatenated Words” adds another layer of complexity by requiring to find all words that are concatenation of other words in the list.

So, in order of increasing complexity, the problems are:

  1. “Word Break”
  2. “Word Break II”
  3. “Concatenated Words”

This mapping is approximate as the problems aren’t isomorphic, but they share core principles of string segmentation and manipulation.

10 Prerequisite LeetCode Problems

“Word Break II” involves recursion, backtracking, and dynamic programming. Here are 10 problems for a better understanding:

  1. “Word Break” (LeetCode Problem #139): This problem is a simpler version of “Word Break II” and it introduces the basic concept of breaking a string based on a dictionary of words.

  2. “Word Pattern” (LeetCode Problem #290): This problem will provide a foundation for understanding mapping patterns with strings.

  3. “Subsets” (LeetCode Problem #78): This problem introduces the concept of generating all possible subsets of a given set, which is a basic form of backtracking.

  4. “Subsets II” (LeetCode Problem #90): This problem is a follow-up to the “Subsets” problem, where you have to deal with duplicates.

  5. “Permutations” (LeetCode Problem #46): This problem involves generating all permutations of a given set, a classic backtracking problem.

  6. “Permutations II” (LeetCode Problem #47): This problem builds on the “Permutations” problem by introducing the concept of duplicate permutations.

  7. “Palindrome Partitioning” (LeetCode Problem #131): This problem requires backtracking and dynamic programming to find all possible ways of partitioning a string into palindromic substrings.

  8. “Combination Sum” (LeetCode Problem #39): This problem introduces the concept of finding all possible combinations that add up to a specific target, using recursion and backtracking.

  9. “Letter Combinations of a Phone Number” (LeetCode Problem #17): This problem practices recursive string generation based on input digit mappings.

  10. “Decode Ways” (LeetCode Problem #91): This problem practices dynamic programming and recursion to decode a number into a string based on specific rules.

These cover dynamic programming, backtracking, and understanding how to deal with string manipulations and mappings.

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def fun(s,dc,memo):
    if(s in memo):
        return memo[s]
    ans=[]
    if(dc[s]==1):
        ans=[s]
    for i in range(1,len(s)):
        if(dc[s[:i]]==1):
            a=fun(s[i:],dc,memo)
            for x in a:
                ans.append(s[:i]+" "+x)
    memo[s]=ans
    return ans

class Solution:
    def wordBreak(self, s: str, wordDict: List[str]) -> List[str]:
        dc=defaultdict(lambda:0)
        for a in wordDict:
            dc[a]=1
        return(fun(s,dc,{}))

Problem Classification

This problem is about breaking a text into words from a dictionary in all possible ways. It’s about finding parts in a text that match a certain condition, so it’s a Text Matching Problem.

Language Agnostic Coding Drills

  1. Understanding Dictionaries or Hashmaps

    Dictionaries (in Python), also known as Hashmaps, are data structures that store key-value pairs. They allow for quick access to values using their keys.

    Drill:

    • Create a dictionary (or hashmap) with string keys mapping to integer values. Write code to add key-value pairs, retrieve a value given a key, and check if a key exists in the dictionary.

  2. Strings and String Manipulation

    Strings are a sequence of characters and offer various methods for manipulation.

    Drill:

    • Write a program that can reverse a string, concatenate two strings, convert a string to an array of characters, and slice a string to get a substring.

  3. Recursion

    Recursion is a method of solving problems that involves breaking a problem down into smaller and smaller subproblems until you get to a small enough problem that it can be solved trivially.

    Drill:

    • Implement a recursive function to calculate the factorial of a number.

  4. Dynamic Programming and Memoization

    Dynamic programming is a strategy for optimization problems involving making a sequence of choices in a way that avoids recalculations of subproblems. Memoization is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and reusing them when the same inputs occur again.

    Drill:

    • Implement a function to calculate the nth Fibonacci number using dynamic programming with memoization.

  5. Slicing and Iterating over Strings/Arrays

    Slicing is the operation of extracting a portion of a string or array, while iteration involves going through each element of a string or array one by one.

    Drill:

    • Write a function that takes an array (or string) and an index as arguments and returns a new array (or string) that is a slice from the start to the given index. Write another function that iterates over an array (or string) and prints each element.

  6. List Comprehensions

    List comprehensions provide a concise way to create lists based on existing lists. In Python, they take the form of [expression for item in list].

    Drill:

    • Write a program that uses list comprehension to create a new list that contains squares of all numbers from an existing list.

These drills should cover all the key concepts used in the provided code, arranged in an order of increasing difficulty. By practicing these drills, you should become more comfortable with these concepts, enabling you to understand and implement similar code.

Targeted Drills in Python

  1. Understanding Dictionaries or Hashmaps

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    # Create a dictionary and perform operations
d = {} # Empty dictionary
d["apple"] = 1 # Add key-value pair
print(d["apple"]) # Retrieve value of "apple"
print("orange" in d) # Check if "orange" exists in dictionary

  2. Strings and String Manipulation

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    s = "hello"
print(s[::-1]) # Reverse string
print(s + " world") # Concatenate strings
print(list(s)) # Convert string to list of characters
print(s[1:4]) # Slice string

  3. Recursion

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    def factorial(n):
    if n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n-1)
print(factorial(5))

  4. Dynamic Programming and Memoization

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    def fib(n, memo = {}):
    if n in memo:
        return memo[n]
    if n <= 2:
        return 1
    memo[n] = fib(n-1, memo) + fib(n-2, memo)
    return memo[n]
print(fib(6))

  5. Slicing and Iterating over Strings/Arrays

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    def slice_to_index(array, index):
    return array[:index]
print(slice_to_index([1, 2, 3, 4, 5], 3)) # Output: [1, 2, 3]

def print_elements(array):
    for element in array:
        print(element)
print_elements([1, 2, 3, 4, 5])

  6. List Comprehensions

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    nums = [1, 2, 3, 4, 5]
squares = [num**2 for num in nums]
print(squares)  # Output: [1, 4, 9, 16, 25]

The above drills cover all basic operations related to the mentioned concepts. However, for problem-specific drills, we might need to create a few more depending on the specific problem at hand.