= ax+b is
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Use Big O notation to create winesses C and K, such that:
1) f(x) = ax+b is O(x2)
2) explain a condition where the code isn't O(x). also prove witness and graph
***consider the search
Step by step
Solved in 2 steps
- Develop a piece of code for following four cases and measure the processing time of different inputs starting from 1 to 50. Plot your processing time as a graph and explain the differences. A) g(n) (Recursively)B) g(n) (Iteratively)C) Fibonacci (Recursively) D) Fibonacci (Iteratively) PLEASE DO PARTS A B C AND D in C/C++!Generate a sequence U1, U2,..., U1000 of independent uniform random variables on a computer. Let Sn = ni=1 Ui for n = 1, 2,..., 1000. Plot each ofthe following versus n: d. (Sn − n/2)/ne. (Sn − n/2)/√nExplain the shapes of the resulting graphs using the concepts of this chapter. Can you do these as well i need it fast?Use recursion tree to guess a bound, then proof it using induction. Finally, use master theorem (if applicable) to directly get the bound. Try to make your bounds as tight as possible. T(n) = 2T(n/2) + n T(n) = 2T(n-2) + n
- Let G = (X ∪ Y, E) be a bipartite graph such that the vertices are partitioned into two groups Xand Y , and each edge has one end point in X and one end point in Y .A 2-1 generalized matching is a set of edges S ⊂ E satisfying the following two conditions:1. Every vertex in X belongs to at most two edges in S.2. Every vertex in Y belongs to at most one edge in S.Give an algorithm to find the size (number of edges) of maximum 2-1 generalized matchingUsing A* Search, show the process of identifying the correct path from the start node (A) to end node (M). Heuristic Values State Value A 0 B 3 C 6 D 5 E 1 F 3 G 2 H 4 I 3 J 2 K 1 L 2 M 1Let G be an undirected edge-weighted graph with V vertices and O(V2) edges. Describe an efficient algorithm to compute a minimum spanning tree that runs in O(V2) time. You are only allowed to use data structures such as arrays and priority queues. Do not use complex data structures such as Fibonacci heaps. Give an efficient algorithm (to the best of your knowledge) and a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm. You must write down your algorithm as pseudocode
- Under what circumstances might the A* algorithm fail even when using admissible heuristics? Give a clear example.Implement Queens algorithm: pre-cond: C = 1, c1, 2, c2, ... , r, cr places the jth queen in the jth row and the cjth column. The remaining rows have no queen.post-cond: Returned if possible is a placement optSol of the n queens consistent with this initial placement of the first r queens. A placement is legal if no two queens can capture each other. Whether this is possible is flagged with optCost equal to one or zero.Consider the “recursion tree” and “subproblem graph” for our two algorithms. The case n = 4 is illustrated below. For the case n = 4, the recursion tree has 16 vertices and 15 edges, while the subproblem graph has 5 vertices and 10 edges. For the case n = 10, determine the number of vertices and edges in the recursion tree, as well as the number of vertices and edges in the subproblem graph. Clearly justify your answers.
- Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python. dont copy ans from bartleby its wrongFor the 8-queens problem, define a heuristic function, design a Best First Search algorithm in which the search process is guided by f(n) = g(n) + h(n), where g(n) is the depth of node n and h(n) is the heuristic function you define, and give the pseudo code description.In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. in its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.", Wikipedia a) Apply your algorithm in the graph below. What is the accuracy ratio? b) Show that the performance ratio of your algorithm can go unbounded above or never at all.