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Linked List Optimization Research

Key Focus Areas

1. Cache-optimized traversal
2. Batch insertion patterns
3. Memory pool allocation
4. Performance measurement infrastructure

Complete Runnable Code

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To prove that every ( k )-regular graph on ( 2k + 1 ) vertices is Hamiltonian, we’ll use some concepts and arguments from graph theory. A ( k )-regular graph means that every vertex has exactly ( k ) edges.

Here's how we can approach the proof step-by-step:

Key Definitions and Theorem

1. ( k )-regular Graph: A graph where every vertex has exactly ( k ) edges.
2. Number of Vertices: ( 2k + 1 ) vertices.
3. Hamiltonian Cycle: A cycle that visits each vertex exactly once and returns to the starting vertex.

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/* eslint-disable react-native/no-inline-styles */
import React from 'react';
import {
  View,
  Text,
  StyleSheet,
  SafeAreaView,
  FlatList,
  TouchableOpacity,
  Modal,

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import React from 'react';
import { View, Text, Dimensions, StyleSheet } from 'react-native';

const Dev_Height = Dimensions.get('window').height;
const Dev_Width = Dimensions.get('window').width;

class App extends React.Component {
  render() {
    return (
      <View style={styles.container}>

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/* Single Linked List */

#include <stdio.h>
#include <stdlib.h>
#include <conio.h>
#include <process.h>
#include <string.h>

struct node
{

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num1 = int(input("Enter the first number - "))
num2 = int(input("Enter the second number - "))

sum = num1+num2
sub = num1-num2
prod = num1*num2
div = num1/num2

print("Sum of ",num1 , "and ",num2 ,"is ", sum)
print("Sub of ",num1 , "and ",num2 ,"is ", sub)

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import math 
n1 = int(input("Number1 ->"))
n2 = int(input("Number2 ->"))
print (math.gcd(n1,n2)) 

# or

def gcd(n1,n2): 
    if(n2==0): 
        return n1 

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import PySimpleGUI as sg
from utlis import get_meaning, get_antonyms, get_synonyms

greeting = "Hi. I am word bot. I can help you with words.\n\n"

layout = [
    [sg.Multiline(greeting, font=("Arial", 14), size=(70, 15), key='output')],
    [sg.InputText("", font=("Arial", 14), size=(50, 1), key='input', enable_events=True)],
    [sg.Button("Meaning", font=("Arial", 14), bind_return_key=True, key="meaning"),
     sg.Button("Synonyms", font=("Arial", 14), key='synonyms'),

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# Importing Python MongoDB Connector
# Can Be Installed By -> "pip install pymongo"
import pymongo

# For Working With Date And Time
import datetime

# This Is The Connector With The URL From MongoDB Atlas
client = pymongo.MongoClient('...') # Enter Your URL From MongoDB Atlas 

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# We have seen how to search for a particular file extension and also how to get files modified within a 
# date range. For assignment, you need to combine both. User should 
# be able to search for python files modified in a date range

import os
import datetime

def file_extension_finder(pat,start_date,end_date):
    file_extension = input("Enter The File Extension's -> ")
    for (root,directory,files) in os.walk(pat.strip()):