Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
Question
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Chapter 7, Problem 5P

(a)

Program Plan Intro

To give an exact formula for pi of n and i , for i=1,2,.....,n1 .

(b)

Program Plan Intro

To explain the increase of likelihood value so choosing the pivot as x=A'[(n+1)/2]

(c)

Program Plan Intro

To explain the increase in likelihood of getting a good split compared with the ordinary implementation.

(d)

Program Plan Intro

To argue that the median-of-3 method affects only the constant factor if the running time of quick sort is Ω(nlgn) .

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.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…
.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…
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