Announcements Announcements • Homework 2 Due on Friday • Exam 1 Solutions Online • Exam grades soon Last Time • Shortest Paths in Weighted Graphs • Priority Queue – Insert – DeleteMin – DecreaseKey – Saw Binary Heap • Dijkstra’s Algorithm – Runtime O(|V|)(Inserts/DeleteMins)+O(|E|)DecreaseKeys – O(log|V|(|V|+|E|)) w/ binary heap Binary Heap Store elements in a […]
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1Appendix A Basic Proof Techniques Induction 2Appendix A Basic Proof Techniques Correctness proofs We prove the correctness of iterative algorithms with the help of induction. 3Appendix A Basic Proof Techniques Weak induction Lemma: The sum of all integers from 1 to n is equal to n(n+1)/2. 4Appendix A Basic Proof Techniques Weak induction Lemma: The
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CM30173: Cryptography\reserved@d =[@let@token art IV CM30173: Cryptography Part IV The ElGamal signature scheme Security of the ElGamal signature scheme Careless uses of ElGamal signature scheme A downside of ElGamal ElGamal variants A problem… Part VI Signature schemes CM30173: Cryptography Part IV The ElGamal signature scheme Security of the ElGamal signature scheme Careless uses of ElGamal
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Announcements Announcements • Homework 5 Due on Friday • Homework 4 Solutions online Last Time • Dynamic Programs – Find family of related subproblems – Find recurrence relation solving one subproblem in terms of simpler ones – Tabulate and solve all subproblems Notes about DP • General Proof of Correctness Outline: – Prove by induction
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CSE 101 Homework 3 Winter 2021 This homework is due on gradescope Friday February 5th at 11:59pm pacific time. Remember to justify your work even if the problem does not explicitly say so. Writing your solutions in LATEXis recommend though not required. Question 1 (Public Transit on a Budget, 40 points). Lars is trying to
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Oliver Braun CSE 101 (Summer Session 2021) Homework 4: Algorithmic Complexity and NP-complete Problems Instructions Homework questions will be similar to your future exam questions. The homework will not be graded, however, you are highly recommended to practice using these questions for better preparations of the exams. Key Concepts Algorithms, Optimization Problems, Minimization: Assignment, Maximization:
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Announcements Announcements Homework 2 due today Homework 3 online soon Last Time Divide and Conquer (Ch 2) Break problem into pieces Solve pieces recursively Recombine pieces to get answer Karatsuba Multiplication Naïve algorithm for multiplying n-bit numbers is O(n2) time. Can we do better? Karatsuba (AX+B)(CX+D) = ACX2+[AD+BC]X+BD = ACX2+[(A+B)(C+D)-AC-BD]X+BD Can multiply two n-bit numbers
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Announcements Announcements • Homework 0 due today • Homework 1 online, due next week • Jaibei Han’s office hours will be Monday, Thursday, and Friday from 4-5pm. – The syllabus has been updated. – Sorry for the inconvenience. Last Time • Graph Definition – Edges connect pairs of vertices • Explore/DFS – O(|V|+|E|) runtime –
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Announcements Announcements • Homework 3 Due on Friday • Please fill out feedback survey: https://forms.gle/Rs1Jz4XZpaQqag13A https://forms.gle/Rs1Jz4XZpaQqag13A Last Time • Divide & Conquer – Split into smaller subproblems – Solve Recursively – Recombine to get answer • Master Theorem Master Theorem Theorem: Let T(n) be given by the recurrence: Then we have that Today • MergeSort
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Question 1 (Knapsack, 30 points). Consider the knapsack problem where you are allowed to take items more than once, have a total capacity of 10 and have the following items available: Item Weight Value A 2 4 B 3 5 C 4 9 D 5 10 E 7 16 What is the best combination of