  In this paper, we obtain a number of new simple pseudo-polynomial time
algorithms on the well-known knapsack problem, focusing on the running time
dependency on the number of items $n$, the maximum item weight
$w_\mathrm{max}$, and the maximum item profit $p_\mathrm{max}$. Our results
include:
  - An $\widetilde{O}(n^{3/2}\cdot \min\{w_\mathrm{max},p_\mathrm{max}\})$-time
randomized algorithm for 0-1 knapsack, improving the previous
$\widetilde{O}(\min\{n w_\mathrm{max} p_\mathrm{max}^{2/3},n p_\mathrm{max}
w_\mathrm{max}^{2/3}\})$ [Bringmann and Cassis, ESA'23] for the small $n$ case.
  - An $\widetilde{O}(n+\min\{w_\mathrm{max},p_\mathrm{max}\}^{5/2})$-time
randomized algorithm for bounded knapsack, improving the previous
$O(n+\min\{w_\mathrm{max}^3,p_\mathrm{max}^3\})$ [Polak, Rohwedder and
Wegrzyck, ICALP'21].
