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

### Solution

## 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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