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define edge. define minimum spanning tree problem, , in strong component problem what complete refers to ? what is relationship between mutual reachable , equivalence relation, and component digraph, find mst by using prims algo rithm , make adjacency list by using digraph. execute first three iteration of matrix using floyd warshall algo , : running time and space of floyd warshall algo
today my papr
2. Where Arise Clique Cover? (pg176)
The clique cover problem arises in applications of clustering. We put an edge between two nodes
if they are similar enough to be clustered in the same group. We want to know whether it is
possible to cluster all the vertices into k groups.
Suppose you could prove that an NP-complete problem cannot be solved in polynomial time. What would be the consequence? Answer: Page 173 If we can solve a problem in polynomial time, we can certainly verify the solution in polynomial time. More formally, we do not need to see a certificate to solve the problem; we can solve it in polynomial time anyway. However, it is not known whether P = NP. It seems unreasonable to think that this should be so. Being able to verify that you have a correct solution does not help you in finding the actual solution. The belief is that P 6= NP but no one has a proof for this. Q No.
Define according to Kruskal's algorithm creat_set(u) find_set(U) union(u,v) Answer: Page 147 Create-set(u): Create a set containing a single item u. Find-set(u): Find the set that contains u Union(u,v): merge the set containing u and set containing v into a common set.
Q what is free tree of 2 marks Answer: (Page 142) A free tree is a tree with no vertex designated as the root vertex.
Q:5 How to get Knapsack optimal solution with dynamic programming algorithm table ? (5) Answer: (Page 96) The algorithm for computing V[i, j] does not keep record of which subset of items gives the optimal solution. To compute the actual subset, we can add an auxiliary boolean array keep [i, j] which is 1 if we decide to take the ith item and 0 otherwise. We will use all the values keep[i, j] to determine the optimal subset T of items to put in the knapsack as follows: • If keep[n,W] is 1, then n 2 T. We can now repeat this argument for keep [n − 1,W − wn]. • If kee[n,W] is 0, the n 62 T and we repeat the argument for keep[n − 1,W].
Q: Consider the following Can an adjacency matrix for a directed graph ever not be square in shape? Why or why not?
Answer: click here 4 detail No. since we want to describe the relationship between each node and each other node, we need precisely n^2 matrix entries.
pseoudo code for strong component Answer: Page 139 STRONGCOMPONENTS(G) 1 Run DFS(G) computing finish times f[u] 2 Compute GT 3 Sort vertices of GT in decreasing f[u] 4 Run DFS(GT) using this order 5 Each DFS tree is a strong component
huffman tree bnana tha 5 marks
Prim algorithm k tree ko btana tha lable kr k...
mcq mostly book sy ay huy thy,,,
in-degree and out degree 2 marks
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