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This is a problem in coding theory. We have used methods of combinatorics to solve the problem.
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(2.1.4) PROBLEM. Prove that in A with A, a...
Consider the set of words of length n over the 3-letter alphabet {0，1，2} a) Prove that...
Consider the set of words of length n over the 3-letter alphabet {0，1，2} a) Prove that the number of such words with an even number of 0’s is (3^n+1)/2 and the number of such words with an odd number of 0’s is (3^n-1)/2. (Hint: Try a proof by induction.) b) Prove that C(n,0)*2^n+C(n,1)2^(n-2)+C(n,4)2^(n-4)+....+C(n,q)2^(n-q)=(3^n+1)/2.
Prove that the number of unordered sequences of length k with elements from a set X...
Prove that the number of unordered sequences of length k with elements from a set X of size n is n+k−1 k . Hint: For illustration, first consider the example n = 4, k = 6. Let the 4 elements of the set X be denoted a, b, c, d. Argue that any unordered sequence of size 6 consisting of elements a, b, c, d can be represented uniquely by a symbol similar to “··|·|··|·”, corresponding to the sequence aabccd....
Must be done in Java. PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS WELL....
Must be done in Java.
PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end, show the exact Output that's shown in
Problem 2.
CODE PROVIDED FOR PROBLEM 1:
import java.util.Scanner;
public class Problem1
{
public static void main( String [] args )
{
//N denoting the size of the
board
int n;
...
Must be done in Java. PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS WELL....
Must be done in Java.
PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end show the exact Output that's shown in the
Problem 2.
CODE PROVIDED FOR PROBLEM 1:
import java.util.Scanner;
public class Problem1
{
public static void main( String [] args )
{
//N denoting the size of the
board
int...
in this problem I have a problem understanding the exact steps, can they be solved and...
in this problem I have a problem understanding the
exact steps, can they be solved and simplified in a clearer and
smoother wayTo understand it .
Q/ How can I prove (in detailes) that the following examples match their definitions mentioned with each of them? 1. Definition 1.4[42]: (G-algebra) Let X be a nonempty set. Then, a family A of subsets of X is called a o-algebra if (1) XE 4. (2) if A € A, then A = X...
The attached document is a C++ source code, INTERFACE__Class{aSet}.cpp, which contains an interface for class aSet and an implementation section which is largely left empty, so that students could fill in the missing code, where it is written // C++ code
/* FILE NAME: Class{aSet}.cpp FUNCTION: A template class for a set in C++. It implements all the set operations, except set compliment: For any two sets, S1 and S2 and an element, e A. Operations which result in a new set: (1) S1 + S2 is the union of S1 and S2 (2) S1 - S2 is the set difference of S1 and S2, S1 - S2 (3) S1 * S2 is the set intersection of S1 and S2, S1 * S2 (4) S1 + e (or e +...
no other details are given, its asking for the invariant programming language: Java Question 3. [15...
no other details are given, its asking for the invariant
programming language: Java
Question 3. [15 marks in total Consider the following code fragment with missing statements at ????. Assume that A is a nonempty array of integers and has length N. Assume that it has already been initialised. Refer to this code in parts (a-e) below. A [0] int count 1; int i- 1 while (i< NI1 count> N/2 ) if (xAi]) count++ int x else ???? i+ if...
2. (25) [Rising trend] Textbook Exercise 17 in Chapter 6. The problem to solve is, in other words...
2. (25) [Rising trend] Textbook Exercise 17 in Chapter 6. The problem to solve is, in other words, to select from a sequence of n numbers a subset, including the first number, such that the selected numbers make a longest monotonously increasing sequence. In the exercise b, (i) write an optimal substructure (with an explanation),ii) write the iterative dynamic programming algorithm (pseudocode), and (iii) show the running-time analysis. Hints: the algorithm in the exercise a is a greedy algorithm; the...
Security is an important feature of information systems. Often, text is encrypted before being sent, and...
Security is an important feature of information systems. Often, text is encrypted before being sent, and then decrypted upon receipt. We want to build a class (or several classes) encapsulating the concept of encryption. You will need to test that class with a client program where the main method is located. For this project, encrypting consists of translating each character into another character. For instance, if we consider the English alphabet, including characters a through z, each character is randomly...
Must be done in Java. PROBLEM 2 INFORMATION AND THE CODE PROVIDED WITH IT AS WELL....
Must be done in Java.
PROBLEM 2 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
PROBLEM 1 INFORMATION IF YOU NEED IT AS
WELL:
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end, show the exact Output that's shown in
Problem3.
CODE PROVIDED FOR PROBLEM 2:
import java.util.Scanner;
public class Problem2
{
public static void main( String [] args )
{
//N...
Must be done in Java.
PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end, show the exact Output that's shown in
Problem 2.
CODE PROVIDED FOR PROBLEM 1:
import java.util.Scanner;
public class Problem1
{
public static void main( String [] args )
{
//N denoting the size of the
board
int n;
...
Must be done in Java.
PROBLEM 1 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end show the exact Output that's shown in the
Problem 2.
CODE PROVIDED FOR PROBLEM 1:
import java.util.Scanner;
public class Problem1
{
public static void main( String [] args )
{
//N denoting the size of the
board
int...
in this problem I have a problem understanding the
exact steps, can they be solved and simplified in a clearer and
smoother wayTo understand it .
Q/ How can I prove (in detailes) that the following examples match their definitions mentioned with each of them? 1. Definition 1.4[42]: (G-algebra) Let X be a nonempty set. Then, a family A of subsets of X is called a o-algebra if (1) XE 4. (2) if A € A, then A = X...
no other details are given, its asking for the invariant
programming language: Java
Question 3. [15 marks in total Consider the following code fragment with missing statements at ????. Assume that A is a nonempty array of integers and has length N. Assume that it has already been initialised. Refer to this code in parts (a-e) below. A [0] int count 1; int i- 1 while (i< NI1 count> N/2 ) if (xAi]) count++ int x else ???? i+ if...
2. (25) [Rising trend] Textbook Exercise 17 in Chapter 6. The problem to solve is, in other words, to select from a sequence of n numbers a subset, including the first number, such that the selected numbers make a longest monotonously increasing sequence. In the exercise b, (i) write an optimal substructure (with an explanation),ii) write the iterative dynamic programming algorithm (pseudocode), and (iii) show the running-time analysis. Hints: the algorithm in the exercise a is a greedy algorithm; the...
Must be done in Java.
PROBLEM 2 INFORMATION AND THE CODE PROVIDED WITH IT AS
WELL.
PROBLEM 1 INFORMATION IF YOU NEED IT AS
WELL:
Provide the rest of the code with full comments and
explanation and with proper indentation.
Use simple methods for better
understanding.
Must compile.
At the end, show the exact Output that's shown in
Problem3.
CODE PROVIDED FOR PROBLEM 2:
import java.util.Scanner;
public class Problem2
{
public static void main( String [] args )
{
//N...
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