Problem $2$: Hierarchical Clustering $(30$ points$)$

Run agglomerative hierarchical clustering on the following $1$D dataset: $\{3,4,7,14,16,17\}.$

$(10$ points$)$ If we use single$-$linkage as the cluster distance, perform the hierarchical clustering

step$-$by$-$step and show the resulting dendrogram.

$(10$ points$)$ What clusters will we get if we cut the dendrogram at a height of $5?$

$(10$ points$)$ Discuss the differences between single$-$linkage and complete$-$linkage methods. How

might the choice of linkage method impact the final clusters?

Please solve the problem step$-$by$-$step