讲解：algorithm、R、RSQL|Matlab

(Exercise 10) This week you will revise the Ford-Fulkerson algorithm and at thesame time think about implementing it on a computer. It is not a simple algorithmto write so I don’t expect you to complete it. Various useful bits of code and elementsof performing the algorithm are broken up for this week’s exercise. You can choosewhich parts to tackle in whatever order you like. Although some parts are advisedbefore others.This week it would be great to see you use a variety of the functions you’ve beenusing so far this term. Here’s a reminder of some of the clever things I’ve seen usedthis term which are useful for the exercises this week:• For a random vector v 4 look like?• What does the as.integer function do?• Type ?union for a the help file relating to a number of popular set functions.• In R you can perform a for loop not only over a range like 1:10 but also overa set, via syntax like this:W X for ( i in W) {for ( j in X ) {print(1000 ∗ i + j )}}• For vectors, and even matrices you can use the all () function to find out ifevery element satisfies some property.• What does matrix(0, nrow=7, ncol=7) create?• The which function, when applied to matrices, doesn’t return something entirelyhelpful. There is a parameter called arr.ind you can set to TRUE whichreturns answers in terms of co-ordinates. e.g. try the followingM which(M > 8 )which(M > 8 , arr . ind = TRUE)• If you desire the 1st, 3rd and 7th rows from a matrix M, then if B then M[B, ] is what you want. Similarly, M[ , 2] is the second column of M.You can even combine these ideas with conditions. Have a look at theseoutputs:M M[ , 1 ] %% 3M[ , 1 ] %% 3 == 0M[M[ , 1 ] %% 3 == 0 , ]M[ , 2 ] == max(M[ , 2 ] )M[M[ , 2 ] == max(M[ , 2 ] ) , ]4-14Exercise 10 (Hunayn). The Ford-Fulkerson algorithmFor all tasks below:• You should set n=7, or keep n unknown if you are very adventurous.• You can then also assume all flows are from vertex 1 to vertex 7 (or n).• Code in later parts should not, however, exploit any specific known values ofother parameters/algorithm留学生作业代写、代做R程序语言作业、代写R课程设计作业 代做数据库SQL|调试Matlab程序variables, and so should work for general M, S, cij , andflows – not just the for M, S, etc. . . with which you are working.• The idea behind writing general code is that it will also work when someonecomes along with a different starting graph G = (V, E) without any changes tothe code.You should all attempt these three parts: Code up the problem from the start ofthe chapter (with the proposed flow) as follows:• Type out the capacity matrix M, where M[i, j ]=cij , (or 0 if no edge exists).e.g M[1, 2]=12, M[1, 3]=10, etc. . . . (Hint: Start with a matrix full of zeroes!)• Type out a flow matrix representing a particular flow. By hand type the entriesof the flow drawn during lectures onto the diagram in the notes.• Write some code to create an adjacency matrix, A: entry (i, j) is 1 if the edge(i, j) edge exists in the graph, 0 if not. You should use the variable M asa starting point. (Not by hand! There are short solutions to this, but longsolutions are more instructive.)You should select some of the below exercises:(A) Get R to create a list of all the edges in the network, using the capacity oradjacency matrix. (Not by hand! Hints in accompanying text.)(B) Write a function to check a flow is feasible (meets all the constraints). This codeshould take M, and a flow matrix as the starting point.(C) (i) Given n, and a given subset S of V , create the complement Sc.(ii) Create code to list all the edges between a given set S, and the complementof S. (You may assume you have a capacity matrix or adjacency matrix,and are given S)(D) For a given list of edges, and a given flow matrix, identify if there are any edgesalong which flow could be increased.You should all comment briefly how the parts you attempted might beuseful in a full version of the Ford-Fulkerson algorithm. Describe also theelements of the algorithm that haven’t been discussed.HW Exercise 4.8. Useful related non-computing exercise: By hand try performingthe Ford-Fulkerson algorithm starting from the feasible flow described at the startof the chapter. In comments give details of the set(s) S formed and the paths alongwhich flow is increased. What maximal flow do you get to? Can you identify theminimal cut?4-15转自：http://www.daixie0.com/contents/18/4509.html