EFFICIENT ALGORITHM DESIGN FOR SPECIAL CASES OF SUBSET SUM
ASYMPTOTIC COMPARISON OF FUNCTIONS
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Alogrithim expert here, I have made quite a few algo's starting from google search engine duplicate and then optimizing the billing system of electric company, and I am sure that I can help you with this.
This is well known CS problem. But edge-cases cover is little difficult for this algorithm. I have already developed algorithm which can cover all edge-cases.