Dynamic Programming Questions Medium
The time complexity of the Dynamic Programming approach for solving the Word Break problem is O(n^2), where n is the length of the input string.
In the Word Break problem, we are given a string and a dictionary of words. The task is to determine if the string can be segmented into a space-separated sequence of dictionary words.
The Dynamic Programming approach for this problem involves breaking down the problem into smaller subproblems and solving them iteratively. We create a boolean array dp of size n+1, where dp[i] represents whether the substring from index 0 to i-1 can be segmented into dictionary words.
To fill the dp array, we iterate through each index i from 1 to n and check if the substring from index 0 to i-1 can be segmented. We do this by iterating through each index j from 0 to i-1 and checking if dp[j] is true (indicating that the substring from index 0 to j-1 can be segmented) and the substring from index j to i-1 is present in the dictionary. If both conditions are satisfied, we set dp[i] to true.
The time complexity of this approach is determined by the nested loops used to fill the dp array. The outer loop iterates through each index i from 1 to n, and the inner loop iterates through each index j from 0 to i-1. Therefore, the total number of iterations is approximately n^2, resulting in a time complexity of O(n^2).
In conclusion, the time complexity of the Dynamic Programming approach for solving the Word Break problem is O(n^2).