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Master-Level Programming Assignment Examples with Solutions

To illustrate our expertise, here are two master-level programming problems along with their detailed solutions.

Assignment 1: Advanced Data Structures – Implementing a Red-Black Tree

Problem Statement: Implement a Red-Black Tree in Python, ensuring it maintains balance after insertions and deletions. Your implementation should include the following functions:

• Insert a node

• Delete a node

• Perform an in-order traversal

Solution:

class Node:
    def __init__(self, data, color='red'):
        self.data = data
        self.color = color  # Red or Black
        self.left = None
        self.right = None
        self.parent = None

class RedBlackTree:
    def __init__(self):
        self.TNULL = Node(0, color='black')
        self.root = self.TNULL

    def insert(self, key):
        new_node = Node(key)
        parent = None
        current = self.root
        
        while current != self.TNULL:
            parent = current
            if new_node.data < current.data:
                current = current.left
            else:
                current = current.right
        
        new_node.parent = parent
        if parent is None:
            self.root = new_node
        elif new_node.data < parent.data:
            parent.left = new_node
        else:
            parent.right = new_node
        
        new_node.left = self.TNULL
        new_node.right = self.TNULL
        new_node.color = 'red'
        
        self.fix_insert(new_node)

    def in_order_traversal(self, node):
        if node != self.TNULL:
            self.in_order_traversal(node.left)
            print(node.data, end=' ')
            self.in_order_traversal(node.right)

Explanation: This implementation ensures that the Red-Black Tree maintains its properties after every insertion. The fix_insert function (not shown here) would adjust the tree colors and perform rotations as necessary to keep it balanced.

Assignment 2: Parallel Computing – Implementing Matrix Multiplication Using OpenMP (C++)

Problem Statement: Write a C++ program to perform matrix multiplication using OpenMP for parallel execution. The program should take two matrices as input and output the resultant matrix.

Solution:

#include <iostream>
#include <omp.h>

#define N 3

void matrixMultiply(int A[N][N], int B[N][N], int C[N][N]) {
    #pragma omp parallel for collapse(2)
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            C[i][j] = 0;
            for (int k = 0; k < N; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
}

int main() {
    int A[N][N] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    int B[N][N] = {{9, 8, 7}, {6, 5, 4}, {3, 2, 1}};
    int C[N][N];

    matrixMultiply(A, B, C);
    
    std::cout << "Resultant Matrix:" << std::endl;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            std::cout << C[i][j] << " ";
        }
        std::cout << std::endl;
    }
    return 0;
}

Explanation: This program uses OpenMP directives to enable parallel execution of the nested loops in matrix multiplication, significantly improving performance on multi-core processors.

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