Which dynamic programming problem involves finding the longest increasing subseq

Which dynamic programming problem involves finding the longest increasing subsequence?

Which dynamic programming problem involves finding the longest increasing subsequence?

Step 1: Understand what a subsequence is. A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
Step 2: Know what an increasing subsequence is. An increasing subsequence is a subsequence where each element is greater than the previous one.
Step 3: Identify the problem. The longest increasing subsequence (LIS) problem asks for the longest subsequence that is strictly increasing.
Step 4: Learn about dynamic programming. Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations.
Step 5: Apply dynamic programming to the LIS problem. You can create an array to store the length of the longest increasing subsequence ending at each index of the original array.
Step 6: Iterate through the original array and update the lengths based on previous values, ensuring that you only consider increasing sequences.
Step 7: Find the maximum value in the lengths array, which will give you the length of the longest increasing subsequence.

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