Question $1$:

Prove that running time $T(n)=n^3+20n+1$ is $O(n^3)$

Prove that running time $T(n)=n^3+20n+1$inO$(n^4)$

Prove that running time $T(n)=2n+10$ is $O(n)$

Prove that $2n^3-7n+1=(n^3)$

Question $2$:

Use the DP to find the alignment between the two sequences $s1=$ ATTGC and s$2=$AGTTC using the following score: match $=2,$ mismatch $=-1$ and the gap $=-2.$

Question $3$

Use Prime's and Kruskal algorithms to construct the MST for the given graph $.$

Question $3$

Use Prime's and Kruskal algorithms to construct the MST for the given graph $.$

Question $4$

Based on Dijkstra Algorithms find the shortest path from A to all the nodes of the following graph.