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[10 marks] Consider the following graph. Assume we are interested to perform topic specific PageR...
Consider the following directed graph for each of the problems: 1. Perform a breadth-first search on...
Consider the following directed graph for each of the
problems:
1. Perform a breadth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Show the breadth-first search
tree that is generated.
2. Perform a depth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Classify each edge as tree, back
or cross edge. Label each
vertex with its start and finish time.
3. Remove all the...
ignore red marks. Thanks 10. (16) You will compute the strongly connected components of this graph...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
We are interested in the movement of patients within a hospital. For purposes of our analysis,...
We are interested in the movement of patients within a hospital. For purposes of our analysis, we consider the hospital to have three different types of rooms: general care, special care, and intensive care. Based on past data, 60% of arriving patients are initially admitted into the general care category, 30% in the special care category, and 10% in intensive care. A “general care” patient has a 55% chance of being released healthy the following day, a 30% chance of...
- Question 3. [25 marks] Consider the execution of the following function (written in the C...
- Question 3. [25 marks] Consider the execution of the following function (written in the C language). void test() { int a=1; fork(); a=a+2; if (fork()==0) H a=2*3;4 printf("la: %d\nma); 3(a) Draw the process graph for the execution of “test”. [10 marks] 3(b) Give an example of infeasible output of “test”. Explain why it is infeasible output. [8 marks] 3(c) The output of “test” depends on the scheduling of processes on CPU. There can be many feasible output of “test”....
Consider the following equations: SUPPLY: Q=10+2P DEMAND: Q=60-3P c) Assume there is not enough control from...
Consider the following equations: SUPPLY: Q=10+2P DEMAND: Q=60-3P c) Assume there is not enough control from the authorities, so there is a black market. Compute the black market price. Show it on the graph.
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution...
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.)
Problem 11. 12 marks] Consider the following two-point...
Bonus Problem 2 (Optional, Harder, 45 marks) (a) (10 marks) We consider a bond that pays...
Bonus Problem 2 (Optional, Harder, 45 marks) (a) (10 marks) We consider a bond that pays n coupons at the end of each coupon period. The length of each coupon period is T. The bondholder receives a redemption value at nth coupon payment date. The redemption value, face value and coupon rate (over a coupon period) are C, F and r respectively (see P.13 of Lecture Note 4). For any k = 0,1,2.,,, n, we let Pk be the bond...
10 Marks Consider the following second-order system 56 u. (a) 2 Marks] What are the poles...
10 Marks Consider the following second-order system 56 u. (a) 2 Marks] What are the poles of the system? (b) 2 Marks] What is the meaning that the system be stable in terms of system response x(t)? Is the system stable or not? (c) [6 Marks] Design a rate-feedback PD controller u(t) — К,(r — г) - Кай so that the system response to a step input has a settling time around 2 sec and an overshoot of about 5%....
Consider the following graph: 10 11 12 Calculate the number of independent paths for the above...
Consider the following graph: 10 11 12 Calculate the number of independent paths for the above graph and show all the independent paths.
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. ...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
Consider the following directed graph for each of the
problems:
1. Perform a breadth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Show the breadth-first search
tree that is generated.
2. Perform a depth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Classify each edge as tree, back
or cross edge. Label each
vertex with its start and finish time.
3. Remove all the...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
We are interested in the movement of patients within a hospital. For purposes of our analysis, we consider the hospital to have three different types of rooms: general care, special care, and intensive care. Based on past data, 60% of arriving patients are initially admitted into the general care category, 30% in the special care category, and 10% in intensive care. A “general care” patient has a 55% chance of being released healthy the following day, a 30% chance of...
- Question 3. [25 marks] Consider the execution of the following function (written in the C language). void test() { int a=1; fork(); a=a+2; if (fork()==0) H a=2*3;4 printf("la: %d\nma); 3(a) Draw the process graph for the execution of “test”. [10 marks] 3(b) Give an example of infeasible output of “test”. Explain why it is infeasible output. [8 marks] 3(c) The output of “test” depends on the scheduling of processes on CPU. There can be many feasible output of “test”....
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.)
Problem 11. 12 marks] Consider the following two-point...
Bonus Problem 2 (Optional, Harder, 45 marks) (a) (10 marks) We consider a bond that pays n coupons at the end of each coupon period. The length of each coupon period is T. The bondholder receives a redemption value at nth coupon payment date. The redemption value, face value and coupon rate (over a coupon period) are C, F and r respectively (see P.13 of Lecture Note 4). For any k = 0,1,2.,,, n, we let Pk be the bond...
10 Marks Consider the following second-order system 56 u. (a) 2 Marks] What are the poles of the system? (b) 2 Marks] What is the meaning that the system be stable in terms of system response x(t)? Is the system stable or not? (c) [6 Marks] Design a rate-feedback PD controller u(t) — К,(r — г) - Кай so that the system response to a step input has a settling time around 2 sec and an overshoot of about 5%....
Consider the following graph: 10 11 12 Calculate the number of independent paths for the above graph and show all the independent paths.
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
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