Dynamic Programming Questions
The Longest Repeated Substring problem is a problem in computer science that involves finding the longest substring that appears more than once in a given string.
Dynamic Programming can be used to solve this problem efficiently. The approach involves creating a 2D table where each cell represents the length of the longest common suffix of two substrings. By comparing each pair of suffixes, we can fill the table and identify the longest repeated substring.
The steps to solve this problem using Dynamic Programming are as follows:
1. Create a 2D table of size (n+1) x (n+1), where n is the length of the given string.
2. Initialize all the cells in the first row and first column with 0.
3. Iterate through each cell (i, j) in the table, starting from the second row and second column.
4. If the characters at indices (i-1) and (j-1) in the string are the same, set the value of the current cell as the value of the cell at (i-1, j-1) plus 1.
5. If the characters are not the same, set the value of the current cell as 0.
6. Keep track of the maximum value encountered during the iteration and its corresponding indices.
7. The longest repeated substring can be obtained by extracting the substring from the given string using the indices obtained in step 6.
By following this approach, we can solve the Longest Repeated Substring problem using Dynamic Programming with a time complexity of O(n^2), where n is the length of the given string.