Answer: (iii) Density based

DENCLUE (DEnsity-based CLUstEring) models the overall density of a dataset as a superposition of kernel density functions ('influence functions') contributed by every data point, and then climbs the gradient of this density surface to reach density attractors. Points sharing an attractor form a cluster, so clusters are simply high-density regions separated by low-density regions — the defining property of density-based clustering.

It is not partitioning (it does not split data into k given groups), not hierarchical (it builds no dendrogram), and not grid-based (it does not quantise the space into grid cells). Hence (iii).