Dynamic Programming Questions Medium
To solve the Longest Valid Parentheses problem using Dynamic Programming, we can follow the below approach:
1. Create a dynamic programming array dp of size n, where n is the length of the given string.
2. Initialize all elements of dp to 0.
3. Iterate through the given string from left to right.
4. For each character at index i, check if it is a closing parenthesis ')'. If it is, then check the character at index i-1.
5. If the character at index i-1 is an opening parenthesis '(', then we have found a valid pair of parentheses. In this case, update dp[i] as dp[i-2] + 2.
6. If the character at index i-1 is a closing parenthesis ')', then we need to check if there is a valid pair of parentheses ending at index i-1. To do this, we check if the character at index i-dp[i-1]-1 is an opening parenthesis '('. If it is, then we have found a valid pair of parentheses. In this case, update dp[i] as dp[i-1] + 2 + dp[i-dp[i-1]-2].
7. After iterating through the entire string, the maximum value in the dp array will represent the length of the longest valid parentheses substring.
8. Return the maximum value from the dp array as the result.
By using this dynamic programming approach, we can efficiently solve the Longest Valid Parentheses problem in linear time complexity, i.e., O(n), where n is the length of the given string.