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101年 - 101 國立中山大學_碩士班招生考試_資工系(甲組):作業系統與資料結構#105907
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題組內容
10. Consider the adjacency matrix of an undirected graph as follows:
(a)Please show the order in which the edges are added to the minimum spanning tree using the Kruskal's algorithm.
相關申論題
(b) Assuming that vertex A is the root, please show the order in which the edges are added to the minimum spanning tree using the Prim's algorithm. (Notice: In your answer, you can use weights to represent edges.)
#451755
1. Assume that a sequence of numbers is deined by x0 = 0, x1 = 1, and> 1. Find the generating function for the sequence, and then find an explicit expression for .
#451756
2. Solve the following recurrence equation for T(n), n > 0. if n =1 T(n)=(2(In/2])+logn, ifn>1. 10,
#451757
3. Assume that, for any two people : and y, a is a friend of y if and only if y is a friend of x. Show that, in any group of two or more people, there are always two people with exactly the same number of friends inside the group.
#451758
4. Let G be a simple graph. A path of G is a sequence of distinct vertices v0,v1, Uh such that and are adjacent for each i = 1,2,..., k. The length of the path v0, v1 , ..., is k. The degree of a vertex is the number of edges incident to that vertex. Show that if the minimum degree of G is greater than or equal to k, then G has a path whose length is at least k.
#451759
5. A lattice path from (x0, y0) to in the ay plane is defined as a sequence of points (x0, y0), (x1,y1), , such that each and each, ± 1,i =1,2, n - 1. How many lattices paths are there from (0,1) to (10,3)? How many of them do not touch or cross the t axis?
#451760
6. Fibonacci numbers are delined as f0 = 0, f1= 1 and for n > 1. Show that is even, for every positive integer k.
#451761
(a) Prove that if n is even then any n/2 + 1 subset of S contains two numbers whose sum is n + 1.
#451762
(b) In general, determine the value k such that any k subset of S contains two numbers whose sum is n + 1.
#451763
1. Please find the solution of y for the first order differential equation.
#451764
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