Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 5.4, Problem 2E
Program Plan Intro
To find the expected number of ball tosses so that each ball is equally likely to end up in any bin.
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Q5-The efficiency of a 200 KVA, single phase transformer is 98% when operating at full load 0.8
lagging p.f. the iron losses in the transformer is 2000 watt. Calculate the i) Full load copper losses ii)
half load copper losses and efficiency at half load. Ans: 1265.306 watt, 97.186%
2. Consider the following pseudocode for partition:
function partition (A,L,R)
pivotkey = A [R]
t = L
for i
L to R-1 inclusive:
if A[i] A[i]
t = t + 1
end if
end for
A [t] A[R]
return t
end function
Suppose we call partition (A,0,5) on A=[10,1,9,2,8,5]. Show the state of the list at the
indicated instances.
Initial A
After i=0 ends
After 1 ends
After i 2 ends
After i = 3 ends
After i = 4 ends
After final swap
10 19 285
[12 pts]
.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…
Chapter 5 Solutions
Introduction to Algorithms
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