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1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n²)

1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n²)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n2)
Transcribed Image Text:1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n2)
You have N magical bags of candies in front of you. The ith bag has A; candies in it. It takes you one minute to finish a bag of candies, no matter how many candies are in it. Every time you finish a bag with X candies in it, the bag is magically replenished with X/2 (rounded down to the nearest integer) more candies. Write an algorithm that determines the maximum number of candies you can eat in K minutes. Also determine the time complexity of your algorithm in the worst case situation. The input is a sequence of integers. The first integer N is the number of bags. The next integer K is the number of minutes you have. The next N integers is the number of candies in the bags. The output of your program is a single integer which represents the maximum number of candies you can eat. If the input is 5 3 217 4 2. the output would be 14.
Transcribed Image Text:You have N magical bags of candies in front of you. The ith bag has A; candies in it. It takes you one minute to finish a bag of candies, no matter how many candies are in it. Every time you finish a bag with X candies in it, the bag is magically replenished with X/2 (rounded down to the nearest integer) more candies. Write an algorithm that determines the maximum number of candies you can eat in K minutes. Also determine the time complexity of your algorithm in the worst case situation. The input is a sequence of integers. The first integer N is the number of bags. The next integer K is the number of minutes you have. The next N integers is the number of candies in the bags. The output of your program is a single integer which represents the maximum number of candies you can eat. If the input is 5 3 217 4 2. the output would be 14.
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