Dynamic Programming Questions
The Longest Palindromic Substring problem is a problem in which we need to find the longest substring that is a palindrome within a given string. A palindrome is a string that reads the same forwards and backwards.
Dynamic Programming can be used to solve this problem efficiently. The basic idea is to use a 2D table to store the results of subproblems. The table will have a boolean value at each cell, indicating whether the substring from row index i to column index j is a palindrome or not.
To solve this problem using Dynamic Programming, we can follow these steps:
1. Initialize a 2D table of size n x n, where n is the length of the input string. Set all cells to false initially.
2. For each character in the string, mark the corresponding cell in the table as true. This means that single characters are palindromes.
3. Iterate over the string from length 2 to n (length of the string). For each length, iterate over all possible starting indices of substrings.
4. For each starting index i and length l, calculate the ending index j = i + l - 1. If the characters at indices i and j are equal and the substring from i+1 to j-1 is a palindrome (according to the table), mark the cell at (i, j) as true.
5. Keep track of the longest palindrome found so far and update it whenever a longer palindrome is found.
6. Finally, return the longest palindrome substring.
By using this Dynamic Programming approach, we can solve the Longest Palindromic Substring problem in O(n^2) time complexity, where n is the length of the input string.