I was reading some of the notes (made easy and ACE) and noticed that some teacher have taught that time complexity for Binary Knapsack O(2^(n/2)). which can not be reduced further. but What I have seen here that in worst case by using memoization we can reduce the time complexity upto O(n.W) where n is number of Object and W is capacity of knapsack.
What I am thinking that, Is it really Binary knapsack is NPC, Like Travelling Salesman problem because TSP tales O(n^2*2^n) times to calculate the tour by using dynamic method, which is efficient than o(n^n) of TSP brutforce techniques? Put some light, Am I missing something. Should I stop seeing those notes which people have posted over the internet.