Explanation of Word Break Problem in Easy Fashion:

The Word Break Problem is a classic algorithmic challenge that involves determining if a given non-empty string can be segmented into a space-separated sequence of words from a dictionary. In simpler terms, we want to find out if we can form the input string by using words from a given set of valid words.

Step-by-Step Approach:

  1. We are given a non-empty string and a list of valid words in the dictionary.
  2. We need to check if the input string can be broken down into a sequence of words such that each word is a valid word from the dictionary.
  3. To solve this problem, we use a technique called Dynamic Programming.
  4. We create a DP array, where each element dp[i] represents whether the substring from index 0 to i in the input string can be segmented into valid words or not.
  5. The DP array is initialized with False values.
  6. We iterate through the input string, considering all possible substrings from index 0 to i.
  7. At each index i, we check if the substring from 0 to i is a valid word or if it can be formed by combining valid words from previous substrings.
  8. If either of these conditions is true, we update dp[i] to True, indicating that the substring from 0 to i can be segmented into valid words.
  9. After completing the iteration, the value of dp[n-1], where n is the length of the input string, will represent whether the entire string can be segmented or not.

Example:
Suppose we have the following input:

  • String: “leetcode”
  • Dictionary: [“leet”, “code”]

Explanation:
We can break down the input string “leetcode” into the valid words “leet” and “code.” Thus, the output will be True.

Python Solution:

def word_break(s, word_dict):
    n = len(s)
    dp = [False] * n

    for i in range(n):
        if s[:i + 1] in word_dict:
            dp[i] = True
        else:
            for j in range(i):
                if dp[j] and s[j + 1:i + 1] in word_dict:
                    dp[i] = True
                    break

    return dp[-1]

if __name__ == "__main__":
    input_string = "leetcode"
    dictionary = ["leet", "code"]
    print(word_break(input_string, dictionary))

Explanation of Python Solution:
The Python solution implements the Word Break Problem using Dynamic Programming. The word_break function takes the input string s and a list of valid words word_dict as inputs and returns True if the string can be segmented into valid words, and False otherwise.

The provided example demonstrates the input string “leetcode” and a dictionary containing the valid words “leet” and “code.” Since we can break down the input string into “leet” and “code,” the function will return True.

By using the Dynamic Programming technique, we can efficiently solve the Word Break Problem and determine if a given string can be segmented into valid words from the dictionary.

Explanation of Word Break Problem in Easy Fashion:

The Word Break Problem is a classic algorithmic challenge that involves determining if a given non-empty string can be segmented into a space-separated sequence of words from a dictionary. In simpler terms, we want to find out if we can form the input string by using words from a given set of valid words.

Step-by-Step Approach:

  1. We are given a non-empty string and a list of valid words in the dictionary.
  2. We need to check if the input string can be broken down into a sequence of words such that each word is a valid word from the dictionary.
  3. To solve this problem, we use a technique called Dynamic Programming.
  4. We create a DP array, where each element dp[i] represents whether the substring from index 0 to i in the input string can be segmented into valid words or not.
  5. The DP array is initialized with False values.
  6. We iterate through the input string, considering all possible substrings from index 0 to i.
  7. At each index i, we check if the substring from 0 to i is a valid word or if it can be formed by combining valid words from previous substrings.
  8. If either of these conditions is true, we update dp[i] to True, indicating that the substring from 0 to i can be segmented into valid words.
  9. After completing the iteration, the value of dp[n-1], where n is the length of the input string, will represent whether the entire string can be segmented or not.

Example:
Suppose we have the following input:

  • String: “leetcode”
  • Dictionary: [“leet”, “code”]

Explanation:
We can break down the input string “leetcode” into the valid words “leet” and “code.” Thus, the output will be True.

Python Solution:

def word_break(s, word_dict):
    n = len(s)
    dp = [False] * n

    for i in range(n):
        if s[:i + 1] in word_dict:
            dp[i] = True
        else:
            for j in range(i):
                if dp[j] and s[j + 1:i + 1] in word_dict:
                    dp[i] = True
                    break

    return dp[-1]

if __name__ == "__main__":
    input_string = "leetcode"
    dictionary = ["leet", "code"]
    print(word_break(input_string, dictionary))

Explanation of Python Solution:
The Python solution implements the Word Break Problem using Dynamic Programming. The word_break function takes the input string s and a list of valid words word_dict as inputs and returns True if the string can be segmented into valid words, and False otherwise.

The provided example demonstrates the input string “leetcode” and a dictionary containing the valid words “leet” and “code.” Since we can break down the input string into “leet” and “code,” the function will return True.

By using the Dynamic Programming technique, we can efficiently solve the Word Break Problem and determine if a given string can be segmented into valid words from the dictionary.