1) Optimal Substructure: The optimal cost for freq[i.j] can be recursively calculated using following formula. We need to calculate optCost(0, n-1) to find the result.
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The idea of above formula is simple, we one by one try all nodes as root (r varies from i to j in second term). When we make rth node as root, we recursively calculate optimal cost from i to r-1 and r+1 to j. We add sum of frequencies from i to j (see first term in the above formula), this is added because every search will go through root and one comparison will be done for every search. 2) Overlapping Subproblems Following is recursive implementation that simply follows the recursive structure mentioned above.
Optimal does not mean highest. It means best or most efficient level of some thing that can vary in strength or intensity over a range of values. If you have zero blood pressure, it should be clear that you are a corpse.
If you have the highest blood pressure ever recorded, it should be clear that you are probably close to becoming a corpse. Optimal blood pressure is the very best blood pressure you can have given your present activity level, for maintaining proper blood flow with minimal stress on the circulation and the body in general. Think of it this way: more is not always better.