Question: General Algorithm and Algorithm Analysis Assignment Exercise 1 Big O-Notation Right or wrong 2n2 +3n4 E on Exercise 2 Integer Multiplication 1. Describe the recursive

General Algorithm and Algorithm Analysis Assignment

General Algorithm and Algorithm Analysis Assignment Exercise 1 Big O-Notation Right or wrong 2n2 +3n4 E on Exercise 2 Integer Multiplication 1. Describe the

Exercise 1 Big O-Notation Right or wrong 2n2 +3n4 E on Exercise 2 Integer Multiplication 1. Describe the recursive school multiplication algorithm for multiplying two n-digit numbers. Develop the recursive formula for the number of primitive operations 2. Describe the Karatsuba multiplication algorithm for multiplying two n-digit num- bers. Develop the recursive formula for the number of primitive operations. Why is nptotically faster than the school multiplication? the Karatsuba multiplication Exercise 3 Heaps and Heapsort What are the basic properties of a heap? Describe the operations insert and delete for heaps. Give an algorithm that makes an array heap-ordered in linear time. Analyze the runtime of your algorithim Describe the Heapsort algorithm. Analyze its runtime Exercise 4 Binary Search Trees What are the basic properties of binary search trees? Describe the operations find, insert, and remove for binary search trees. . What is the height of a perfectly balanced binary search tree? What is the worst case height of a binary search tree? Exercise 1 Big O-Notation Right or wrong 2n2 +3n4 E on Exercise 2 Integer Multiplication 1. Describe the recursive school multiplication algorithm for multiplying two n-digit numbers. Develop the recursive formula for the number of primitive operations 2. Describe the Karatsuba multiplication algorithm for multiplying two n-digit num- bers. Develop the recursive formula for the number of primitive operations. Why is nptotically faster than the school multiplication? the Karatsuba multiplication Exercise 3 Heaps and Heapsort What are the basic properties of a heap? Describe the operations insert and delete for heaps. Give an algorithm that makes an array heap-ordered in linear time. Analyze the runtime of your algorithim Describe the Heapsort algorithm. Analyze its runtime Exercise 4 Binary Search Trees What are the basic properties of binary search trees? Describe the operations find, insert, and remove for binary search trees. . What is the height of a perfectly balanced binary search tree? What is the worst case height of a binary search tree

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