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1. Prove the correctness of Dijkstra's algorithm for graphs with positive weights.
2. Design a linear-time algorithm for solving the single-source shortest-paths problem for dags (directed acyclic graphs) represented by their adjacency lists.
3. Explain how the minimum-sum descent problem (Problem 8 in Exercises 8.1) can be solved by Dijkstra's algorithm.
What types of programming languages are vulnerable to buffer overflows?
Name and detail three ways in which artificial intelligence will change the way that people work.
Acme Container Corporation produces egg cartons that are sold to egg dis- tributors. Acme has estimated this production function for its egg carton division
Demonstrate your understanding and knowledge gained about session's material. Complete with a short discussion for each question. The second question will take several paragraphs to answer thoroughly.
Write a single Boolean expression that can be used to determine if a year is a leap year.
Explain why the graph of Figure 8.19 can be interpreted to mean that if you find many faults in your code at compile time, you should throw away your code and write it again.
Compute the shortest distance from New York to London
If p denotes the selling price (in dollars) of a commodity and x is the corresponding demand (in number sold per day), then the relationship between p and x is sometimes given by p = p0e(-ax), where p0 and a are positive constants. Express x as a ..
Interest on a loan is paid on a declining balance, and hence a loan with an interest rate of, say, 14 percent can cost significantly less than 14 percent of the balance. Write a program that takes a loan amount and interest rate as input and then ..
Cite a risk in computing for which it is impossible or infeasible to develop a classical probability of occurence. Why?
Define software project team management in your own words. What motivation techniques are available to motivate the project team? Explain in brief what you understand by knowledge management.
Starting with your answer to part (b), use gradient descent to find the optimum w and b. Note that if you start with a separating hyper plane, and you scale w properly, then the second term of Equation 12.4 will always be 0, which simplifies your ..
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