Dynamic Programming Questions Medium
The time complexity of the Dynamic Programming approach for solving the Longest Bitonic Subsequence problem is O(n^2), where n is the length of the input sequence.
In the Dynamic Programming approach, we use a table to store the lengths of the longest increasing subsequences ending at each index and the lengths of the longest decreasing subsequences starting from each index.
To calculate the length of the longest increasing subsequence ending at index i, we iterate through all previous indices j (0 <= j < i) and check if the element at index i is greater than the element at index j. If it is, we update the length of the longest increasing subsequence ending at index i as the maximum of its current length and the length of the longest increasing subsequence ending at index j plus one.
Similarly, to calculate the length of the longest decreasing subsequence starting from index i, we iterate through all subsequent indices j (i < j < n) and check if the element at index i is greater than the element at index j. If it is, we update the length of the longest decreasing subsequence starting from index i as the maximum of its current length and the length of the longest decreasing subsequence starting from index j plus one.
By using this approach, we fill the table for all indices in the input sequence, resulting in a time complexity of O(n^2).