//Constant prefix notation solver using bruh
//Could make it infix or postfix later
#include<string>
#include<vector>
#include<iostream>

std::vector<long double> bruhBuff;

long double operator ""bruh(long double a){
    bruhBuff.push_back(a);
    return a;
}

long double operator ""bruh(const char op){
    if(bruhBuff.size() < 2) throw "Bruh weak";
    
    long double b = bruhBuff.back();
    bruhBuff.pop_back();
    long double a = bruhBuff.back();
    bruhBuff.pop_back();
    
    
    switch(op){
        case (int)('+'):
            return a + b;
        case (int)('-'):
            return a - b;
        case (int)('*'):
            return a * b;
        case (int)('/'):
            return a / b;
    }
    return 69l;
}
 
int main(){
    1.0bruh;
    2.0bruh;
    std::cout << '+'bruh << std::endl;
    
    return 0;
}

using namespace std; 
  
class Hash 
{ 
    int BUCKET;    // No. of buckets 
  
    // Pointer to an array containing buckets 
    list<int> *table; 
public: 
    Hash(int V);  // Constructor 
  
    // inserts a key into hash table 
    void insertItem(int x); 
  
    // deletes a key from hash table 
    void deleteItem(int key); 
  
    // hash function to map values to key 
    int hashFunction(int x) { 
        return (x % BUCKET); 
    } 
  
    void displayHash(); 
}; 
  
Hash::Hash(int b) 
{ 
    this->BUCKET = b; 
    table = new list<int>[BUCKET]; 
} 
  
void Hash::insertItem(int key) 
{ 
    int index = hashFunction(key); 
    table[index].push_back(key);  
} 
  
void Hash::deleteItem(int key) 
{ 
  // get the hash index of key 
  int index = hashFunction(key); 
  
  // find the key in (inex)th list 
  list <int> :: iterator i; 
  for (i = table[index].begin(); 
           i != table[index].end(); i++) { 
    if (*i == key) 
      break; 
  } 
  
  // if key is found in hash table, remove it 
  if (i != table[index].end()) 
    table[index].erase(i); 
} 
  
// function to display hash table 
void Hash::displayHash() { 
  for (int i = 0; i < BUCKET; i++) { 
    cout << i; 
    for (auto x : table[i]) 
      cout << " --> " << x; 
    cout << endl; 
  } 
} 
  
// Driver program  
int main() 
{ 
  // array that contains keys to be mapped 
  int a[] = {15, 11, 27, 8, 12}; 
  int n = sizeof(a)/sizeof(a[0]); 
  
  // insert the keys into the hash table 
  Hash h(7);   // 7 is count of buckets in 
               // hash table 
  for (int i = 0; i < n; i++)  
    h.insertItem(a[i]);   
  
  // delete 12 from hash table 
  h.deleteItem(12); 
  
  // display the Hash table 
  h.displayHash(); 
  
  return 0; 
}

#include <iostream>
using namespace std;

int main() {


    int arr[5];
    
    for(int i = 0; i < 5; i++) {
        arr[i] = i;
    }

    for(int i = 0; i < 5; i++) {
        cout << "Outputting array info at position " << i + 1 << ": " << arr[i] << endl;
    }

    for(int i=0;i<5;i++)
	{		
		for(int j=i+1;j<5;j++)
		{
			if(arr[i]>arr[j])
			{
				int temp=arr[i];
				arr[i]=arr[j];
				arr[j]=temp;
			}
		}
	}

    cout << endl;

    for(int i = 0; i < 5; i++) {
        cout << "Outputting sorted array info at position " << i + 1 << ": " << arr[i] << endl;
    }

    return 0;
}

#include <iostream>
#include <vector>
#include <limits>

#define DEBUG_TRIAL false

class Trial{
    public:
        const size_t HEIGHT;
        std::string record;
        
        //Breaking height is the index of the floor, so 0 is the bottom floor, height-1 is the top floor.
        //Eggs is the eggs remaining.
        //Start is the bottom floor.
        //End is one above the top floor.
        const size_t BREAKING_HEIGHT;
        size_t eggs;
        size_t start;
        size_t end;
        
        
        size_t floorsLeft(){
            return (end-start);
        }
        
        size_t middle(){
            return start + (floorsLeft()/2UL);
        }
        
        size_t drops = 0;
        Trial(const size_t BREAKING_HEIGHT, size_t eggs, size_t start, size_t end): BREAKING_HEIGHT(BREAKING_HEIGHT), eggs(eggs), start(start), end(end), HEIGHT(end), record(end, '_'){
            record[BREAKING_HEIGHT] = 'B'; //Marking the breaking point
        }
        
        bool foundAnswer(){
            return ((record[0] == 'X') || (record.find("OX")!=std::string::npos));
        }
        
        //returns true if the egg broke.
        //height is the index of the floor, so 0 is the bottom floor, height-1 is the top floor.
        bool drop(size_t height){
            
            #if DEBUG_TRIAL
                std::cout << "Start: " << start << ". End: " << end << ". Floors Left: " << floorsLeft() << ". Middle Index: " << middle() << std::endl;
            #endif
            
            drops++;
            bool cracked = height >= BREAKING_HEIGHT;
            if(cracked) --eggs;
            
            //Update the record
            record[height] = (height >= BREAKING_HEIGHT)? 'X' : 'O';
            
            #if DEBUG_TRIAL
                //Print the record
                std::cout << record << std::endl;
            #endif
        
            return cracked;
        }
        
        size_t nowWhat(){
            if(foundAnswer()){
                return drops;
            }else if(eggs <= 0){ //Ran out of eggs
                throw "Algorithm failed! No more eggs!";
                return 1UL;
            }else if(eggs > 1){
                return wrecklessSearch();
            }else{
                return safeSearch();
            }
        }
        
        size_t safeSearch(){
            if(drop(start)){
                --end;
            }else{
                ++start;
            }
            
            return nowWhat();
        }
        
        size_t wrecklessSearch(){
            //If the egg breaks
            if(drop(middle())){
                end -= (floorsLeft()/2UL);
            }else{ //egg doesn't crack
                start += (floorsLeft()/2UL);
            }
            
            return nowWhat();
        }
        
        //returns the amount of drops needed to find the answer
        size_t search(){
            return nowWhat();
        }
};

//Height is the height of the building in floors.
//Breaking height is the index of the floor, so 0 is the bottom floor, height-1 is the top floor.
//Eggs is the eggs given.
//returns the amount of drops needed to find the answer
size_t search(const size_t height, const size_t BREAKING_HEIGHT, size_t eggs){
    Trial trial(BREAKING_HEIGHT, eggs, 0, height);
    return trial.search();
}

class TrialStats {
    public:
        size_t min = std::numeric_limits<size_t>::max();
        size_t max = 0;
        double mean = -1.0;
        
        void printStats(){
            // Print the results
            std::cout << "Minimum drops: " << min << std::endl;
            std::cout << "Maximum drops: " << max << std::endl;
            std::cout << "Mean drops: " << mean << std::endl;
        }
};

//Benchmarks all the possible breaking points of a single building height with a number of eggs.
TrialStats trial(const size_t HEIGHT, const size_t eggs){
    
    TrialStats stats;
    int totaldrops = 0;

    //Test every possible breaking point
    //Breaking height is the index of the floor, so 0 is the bottom floor, height-1 is the top floor.
    for (int breakingHeight = 0; breakingHeight < HEIGHT; ++breakingHeight) {
        size_t drops = search(HEIGHT, breakingHeight, eggs);

        stats.min = std::min(stats.min, drops);
        stats.max = std::max(stats.max, drops);
        totaldrops += drops;
    }

    // Calculate the mean number of drops
    stats.mean = static_cast<double>(totaldrops) / HEIGHT;
    
    return stats;
}

//Benchmarks a single building height from 1 egg to MAX_EGGS
void testTower(const size_t height, const size_t MAX_EGGS){
    //Drop every amount of eggs that you'd need.
    for (int eggs = 1; eggs <= MAX_EGGS; ++eggs) {
        std::cout << "Building height: " << height << ". Num eggs: " << eggs << std::endl;
        
        TrialStats stats = trial(height, eggs);
        stats.printStats();
        
        std::cout << std::endl << std::endl;
    }
}

//Benchmarks all buildings from 0 to MAX_HEIGHT
void benchmark(const size_t MAX_HEIGHT){
    const size_t MAX_EGGS = 2;
    //Test every building
    for (size_t height = 1; height <= MAX_HEIGHT; ++height) {
        testTower(height, std::min(height, MAX_EGGS));
    }
}

int main() {
    constexpr size_t MAX_HEIGHT = 36;
    
    benchmark(MAX_HEIGHT);

    return 0;
}

//Leif Messinger
//Finds all sets of 5 5 letter words that don't have duplicate letters in either themselves or each other.
//First it reads the words in and puts them in groups of their bitmasks
//After that, we recurse on each group. Before doing that, we remove the group from the set of other groups to check it against.
#include <cstdio> //getchar, printf
#include <cassert> //assert
#include <vector>
#include <set>
#include <algorithm> //std::copy_if
#include <iterator> //std::back_inserter

#define CHECK_FOR_CRLF true
#define MIN_WORDS 5
#define MAX_WORDS 5
#define WORD_TOO_LONG(len) (len != 5)

const unsigned int charToBitmask(const char bruh){
	assert(bruh >= 'a' && bruh <= 'z');
	return (1 << (bruh - 'a'));
}

void printBitmask(unsigned int bitmask){
	char start = 'a';
	while(bitmask != 0){
		if(bitmask & 1){
			putchar(start);
		}

		bitmask >>= 1;
		++start;
	}
}

//Pointer needs to be deleted
const std::set<unsigned int>* getBitmasks(){
	std::set<unsigned int>* bitmasksPointer = new std::set<unsigned int>;
	std::set<unsigned int>& bitmasks = (*bitmasksPointer);

	unsigned int bitmask = 0;
	unsigned int wordLength = 0;
	bool duplicateLetters = false;
	for(char c = getchar(); c >= 0; c = getchar()){
		if(CHECK_FOR_CRLF && c == '\r'){
			continue;
		}
		if(c == '\n'){
			if(!(WORD_TOO_LONG(wordLength) || duplicateLetters)) bitmasks.insert(bitmask);
			bitmask = 0;
			wordLength = 0;
			duplicateLetters = false;
			continue;
		}
		if((bitmask & charToBitmask(c)) != 0) duplicateLetters = true;
		bitmask |= charToBitmask(c);
		++wordLength;
	}

	return bitmasksPointer;
}

void printBitmasks(const std::vector<unsigned int>& bitmasks){
	for(unsigned int bruh : bitmasks){
		printBitmask(bruh);
		putchar(','); putchar(' ');
	}
	puts("");
}

//Just to be clear, when I mean "word", I mean a group of words with the same letters.
void recurse(std::vector<unsigned int>& oldBitmasks, std::vector<unsigned int> history, const unsigned int currentBitmask){
	//If there's not enough words left
	if(oldBitmasks.size() + (-(history.size())) + (-MIN_WORDS) <= 0){
		//If there's enough words
		if(history.size() >= MIN_WORDS){
			//Print the list
			printBitmasks(history);
		}
		return;
	//To make it faster, we can stop it after 5 words too
	}else if(history.size() >= MAX_WORDS){
		//Print the list
		printBitmasks(history);
		return;
	}

	//Thin out the array with only stuff that matches the currentBitmask.
	std::vector<unsigned int> newBitmasks;
	std::copy_if(oldBitmasks.begin(), oldBitmasks.end(), std::back_inserter(newBitmasks), [&currentBitmask](unsigned int bruh){
		return (bruh & currentBitmask) == 0;
	});

	while(newBitmasks.size() > 0){
		//I know this modifies 'oldBitmasks' too. It's intentional.
		//This makes it so that the word is never involved in any of the child serches or any of the later searches in this while loop.
		const unsigned int word = newBitmasks.back(); newBitmasks.pop_back();

		std::vector<unsigned int> newHistory = history;
		newHistory.push_back(word);

		recurse(newBitmasks, newHistory, currentBitmask | word);
	}
}

int main(){
	const std::set<unsigned int>* bitmasksSet = getBitmasks();
	std::vector<unsigned int> bitmasks(bitmasksSet->begin(), bitmasksSet->end());
	delete bitmasksSet;

	recurse(bitmasks, std::vector<unsigned int>(), 0);

	return 0;
}

#include <bits/stdc++.h>
#define MAXSIZE 50000
#define INF 100000

using namespace std;

vector<int> adj[MAXSIZE]; //Adjacency List

bool visited[MAXSIZE]; //Checks if a node is visited or not in BFS and DFS
bool isConnected = true; //Checks if the input graph is connected or not

int dist[MAXSIZE], discover[MAXSIZE], finish[MAXSIZE]; //Distance for BFS, in time and out time for DFS
int t = 1; //Time used for DFS
int u, v, i, j, k, N = 0;

stack<int> st; //Stack for TopSort

multiset<pair<int, int>> s; //collection of pairs to sort by distance
pair<int, int> current; //pointer variable to a position in the multiset

void BFS()
{
	queue<int> q; //queue for BFS
	q.push(1); //pushing the source
	dist[1] = 0; //assign the distance of source as 0
	visited[1] = 1; //marking as visited
	
	while(!q.empty())
	{
	u = q.front();
	q.pop();

	for(i=0; i < adj[u].size(); i++)
	{
	v = adj[u][i]; //Adjacent vertex

	if(!visited[v]) //if not visited, update the distance and push onto queue
	{
	visited[v] = 1;
	dist[v] = dist[u]+1;
	q.push(v);
	}

	}

	}
	
	for(i = 1; i <= N; i++)
	{
	s.insert(make_pair(dist[i], i)); //for sorted distance
	}
	
	cout << "BFS results:" << endl;
	
	//prints BFS results and checks if the graph is connected
	while(!s.empty())
	{
	current = *s.begin(); 
	s.erase(s.begin());

	i = current.second; 
	j = current.first;

	if(j == INF) //if any infinite value, graph is not connected
	{
	cout << i << " INF" << endl;
	isConnected = false;
	}
	else
	{
	cout << i << " " << j << endl;
	}

	}

	//marks blocks of memory as visited
	memset(visited, 0, sizeof visited);
}


void dfsSearch(int s)
{
	visited[s] = 1; //marking it visited
	discover[s] = t++; //assigning and incrementing time

	int i, v;

	for(i = 0; i < adj[s].size(); i++)
	{
	v = adj[s][i];

	if(!visited[v]) //if vertex is not visited then visit, else continue
	{
	dfsSearch(v);
	}

	}

	st.push(s); //pushed onto stack for TopSort if it was called
	finish[s] = t++; //out time
}

void DFS()
{

	for(i = 1; i <= N; i++)
	{
	if(visited[i]) //if visited continue, else visit it with DFS
	{
	continue;
	}

	dfsSearch(i); //embedded function to actually perform DFS
	}

	for(i=1;i<=N;i++)
	{
	s.insert(make_pair(discover[i], i)); //minheap for sorted discovery time
	}
	
	cout << "DFS results:" << endl;

	while(!s.empty()) //Prints DFS results as long as the multiset is not empty
	{
	current = *s.begin(); //duplicates the pointer to first object in the multiset
	s.erase(s.begin()); //erases the first object in multiset

	i = current.second;
	cout << i << " " << discover[i] << " " << finish[i] << endl; //prints discover times and finish times
	}

}

void TopSort()
{
	//call DFS so we can have a sorted stack to print
	for(i=1;i<=N;i++)
	{
	if(visited[i])
	{
	continue;
	}

	dfsSearch(i);
	}

	cout<<"Topological Sort results:"<<endl;

	//print sorted results from DFS
	while(!st.empty())
	{
	i = st.top(); 
	st.pop();

	cout << i << endl;
	}

	//declare blocks of memory as visited
	memset(visited, 0, sizeof visited);

}


int main()
{
	string str, num, input;
	int selection, connectedChoice = 0;


	//get to input any file, more freedom than declaring file in command line
	cout << "Enter the exact name of your input file [case sensitive]: ";
	cin >> input;
	
	ifstream inputFile(input); //Read the input file

	//checks if the ifstream cannot open
	if(inputFile.fail())
	{
	cout << endl << "No input files matching that name. Terminating..." << endl;
	return 0;
	}

	//Read until the end of file
	while(!inputFile.eof())
	{
	getline(inputFile, str); //read the current line

	if(str == "")
	{
	continue;
	}

	if(!isdigit(str[0])) //checks to see if the first item in a line is a digit or not
	{
	cout << "Invalid file format. You have a line beginning with a non-digit. Terminating..." << endl;
	return 0;
	}

	stringstream ss;
	ss << str; //convert the line to stream of strings
	
	ss >> num; //read the line num
	stringstream(num) >> u;
	
	while(!ss.eof())
	{
	ss>>num;
	if(stringstream(num) >> v)
	{
	adj[u].push_back(v); //read the adjacent vertices
	}
	}

	N++; //calculate the number of vertices
	sort(adj[u].begin(), adj[u].end()); //sort the adjacency list in case it is not sorted
	}
	
	//creates arbitrary values for distance, will check later if INF remain
	for(i = 1; i <= N; i++)
	{
	dist[i] = INF;
	}

	cout << endl << "Valid Input file loaded!" << endl;

	while(selection != 4)
	{
	cout << "************************************************" << endl;
	cout << "What type of analysis would you like to perform?" << endl;
	cout << "1: Breadth-First Search" << endl;
	cout << "2: Depth-First Search" << endl;
	cout << "3: Topological Sort" << endl;
	cout << "4: Quit" << endl;
	cout << "************************************************" << endl;
	
	//read user input and execute selection
	cin >> selection;

	switch(selection)
	{
	case 1:
	cout << endl;
	BFS();
	cout << endl;
	cout << "Would you like to know if the graph is connected?" << endl;
	cout << "1: Yes" << endl;
	cout << "Any other key: No" << endl;
	cin >> connectedChoice;

	switch(connectedChoice)
	{
	case 1:
	if(!isConnected)
	{
	cout << "The graph is not connected." << endl << endl;
	}
	else
	{
	cout << "The graph is connected!" << endl << endl;
	}
	break;
	default:
	break;
	}
	break;
	case 2:
	cout << endl;
	DFS();
	cout << endl;
	break;
	case 3:
	cout << endl;
	TopSort();
	cout << endl;
	break;
	case 4:
	return 0;
	default:
	cout << endl << "Invalid selection." << endl; //loops the selection prompt until a valid selection is input.
	}

	}
	
}