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1. Find 

2. Longest Palindrome Subsequence: Optimal substructure is inner nested strings. The algorithm branches down and examines substrings, and percolates up by examining each of the letters that nest this substring. You start with each letter, and then every time you’ve examined that substring. 

3. Closest unvisited leftmost/rightmost. Number of subproblems is n-1. 

4. Our subproblems are how to optimally arrange words 1,….j, where j= 1,….n. (n is number of words in input). Number of subproblems is N/M. M is number of spaces, N is number of words. 

5. Subproblems: how to go from one character to another. 5 subproblems for every character. So 5m. 

6. Subproblems: the max number of conviviality points, that would come from inviting the node and not inviting its children vs not inviting it and inviting its sub people. 

7. Subproblem: smaller concatenation of sounds that build up to the actual sound looking for. 

8. Subproblem: minimum total cost of the three pixels of the