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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.

See Approach 1

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

See Approach 2

We’re done!

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