How can Dynamic Programming be used to solve the Word Break problem?

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How can Dynamic Programming be used to solve the Word Break problem?

Dynamic Programming can be used to solve the Word Break problem by breaking it down into smaller subproblems and solving them iteratively.

The Word Break problem involves determining whether a given string can be segmented into a space-separated sequence of dictionary words. To solve this problem using Dynamic Programming, we can follow these steps:

1. Define a boolean array dp of size n+1, where n is the length of the input string. dp[i] will represent whether the substring from index 0 to i-1 can be segmented into words.

2. Initialize dp[0] as true, indicating that an empty string can always be segmented.

3. Iterate through the input string from index 1 to n. For each index i, iterate through all previous indices j from 0 to i-1.

4. Check if dp[j] is true, indicating that the substring from index 0 to j-1 can be segmented into words. If it is true, then check if the substring from index j to i-1 is present in the dictionary. If it is, set dp[i] as true.

5. After iterating through all previous indices j, dp[i] will be true if there exists a valid segmentation of the substring from index 0 to i-1.

6. Finally, return dp[n], which represents whether the entire input string can be segmented into words.

By using this Dynamic Programming approach, we can efficiently solve the Word Break problem in O(n^2) time complexity, where n is the length of the input string.