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## Question: Given a string, find the longest palindromic substring within the string.

### Approach 1: Brute Force

We could simply examine every substring and check if it is palindromic. This would have a time complexity of `O(n^3),` which is not a great start but technically a solution that works.

### Approach 2: Dynamic Programming

Let s be the input string, i and j are two indexes of the string.

We can define a 2-dimensional array, “table”, in which table[ i ][ j ]` `denotes whether the substring from index i to index j is a palindrome (boolean true or false).

Our table will take on the following starting and changing conditions.

• `table[i][i] == 1`;

• If `table[i][i + 1] == 1`, then `s.charAt(i) == s.charAt(i + 1)`

• If `table[i+1][j-1] == 1 && s.charAt(i) == s.charAt(j),` then `table[i][j] == 1`

We’re done!

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