The assignment is in the File labeled Coding_Problem, the tests to confirm work are provided as well as examples of correct solutions and a the idea behind the program. Please provide clear comments...

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Title: Description of Solution & Runtime Analysis
Contents
Description of Solution    3
Pseudocode for LLCS     3
Analysis of Runtime complexity of Algo    3
Description of Solution
    As we know, A sequence a0, a1, a2…, an of positive real numbers is logarithmically concave if 2*ln(ai) >= ln(ai-1) + ln(ai + 1) for all 0 < i < n. So, the first solution that we can think of is generating all the subsequences of the array and then checking for each subsequence, whether it follows the condition that is necessary for LLCS. For Optimization, we can think of using recursion and considering every index as the last index and then recursively finding out the index that can work as the middle and next index to satisfy the condition. So, we run a loop and check for every index after current index that fit in the condition and then call recursively for current index as last and next index as current. Furthur optimization includes, using...