Question: Given a sequence, find a longest increasing subsequence. A longest increasing subsequence is that the subsequences elements are in sorted order, lowest to highest, and

Given a sequence, find a longest increasing subsequence. A longest increasing subsequence is that the subsequences elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. A subsequence is not necessarily contiguous, or unique. For example, consider below sequence: 0, 8, 4, 12, 2, 10, 6,14, 1, 9, 5, 13, 3, 11, 7, 15, a longest subsequence is 0, 2, 6, 9, 11, 15 or 0, 4, 6, 9, 13, 15. Please discuss the principle of optimality by using dynamic programming, and design a recurrence equations. Use Java.

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