The running time is O(NW) for an unbounded knapsack problem with N items and knapsack of size W. W is not polynomial in the length of the input though, which is what makes it pseudo-polynomial.
Consider W = 1,000,000,000,000. It only takes 40 bits to represent this number, so input size = 40, but the computational runtime uses the factor 1,000,000,000,000 which is O(240).
So the runtime is more accurately said to be O(N.2bits in W), which is exponential.
Also see:
- How to understand the knapsack problem is NP-complete?
- The NP-Completeness of Knapsack
- Complexity of dynamic programming algorithm for the 0-1 knapsack problem
- Pseudo-polynomial time