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Design a dynamic programming algorithm for the Longest Increasing Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest increasing subsequence among these integers. The algorithm must take O(n2) time. You must also write and explain the recurrence. Example 1: Input: [5, 3, 6, 8, 4, 6, 2, 7, 9, 5] Output: 5 ([3, 4, 6, 7, 9]) Example 2: Input: [12, 42, 66, 73, 234, 7, 543, 16] Output: 6 ([42, 66, 73, 234, 543])

Design a dynamic programming algorithm for the Longest Increasing Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest increasing subsequence among these integers. The algorithm must take O(n2) time. You must also write and explain the recurrence. Example 1: Input: [5, 3, 6, 8, 4, 6, 2, 7, 9, 5] Output: 5 ([3, 4, 6, 7, 9]) Example 2: Input: [12, 42, 66, 73, 234, 7, 543, 16] Output: 6 ([42, 66, 73, 234, 543])

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C++ for Engineers and Scientists

C++ for Engineers and Scientists

4th Edition

ISBN: 9781133187844

Author: Bronson, Gary J.

Publisher: Course Technology Ptr

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Transcribed Image Text:Design a dynamic programming algorithm for the Longest Increasing Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest increasing subsequence among these integers. The algorithm must take O(n2) time. You must also write and explain the recurrence. Example 1: Input: [5, 3, 6, 8, 4, 6, 2, 7, 9, 5] Output: 5 ([3, 4, 6, 7, 9]) Example 2: Input: [12, 42, 66, 73, 234, 7, 543, 16] Output: 6 ([42, 66, 73, 234, 543])

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