#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;
}

/*
Good morning! Here's your coding interview problem for today.

This problem was asked by Stripe.

Given an array of integers, find the first missing positive integer in linear time and constant space. In other words, find the lowest positive integer that does not exist in the array. The array can contain duplicates and negative numbers as well.

For example, the input [3, 4, -1, 1] should give 2. The input [1, 2, 0] should give 3.

You can modify the input array in-place.
*/
#include <iostream>
using namespace std;

int calcMissing(int* input, int size)
{
	int sum = 0;
	int n = 1; //add one to account for missing value
	for(int i = 0; i < size; i++)
	{
	if(input[i] > 0)
	{
	sum += input[i];
	n++;
	}
	}

	//If no numbers higher than 0, answer is 1
	if(sum == 0)
	return 1;

	return (n*(n+1)/2) - sum; //Formula is expectedSum - actualSum
	/* expectedSum = n*(n+1)/2, the formula for sum(1, n) */
}

int main()
{

	cout << calcMissing(new int[4]{3, 4, -1, 1}, 4) << endl;
	cout << calcMissing(new int[3]{1, 2, 0}, 3) << endl;

	//No positive numbers
	cout << calcMissing(new int[1]{0}, 1) << endl;
}

#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 <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.
	}

	}
	
}

//Leif Messinger
//Compile with C++ 20
#include <iostream>
#include <ranges>
#include <vector>
#include <functional>
#include <cctype> //toupper
#include <cxxabi.h>

template <typename T>
void printType(){
    std::cout << abi::__cxa_demangle(typeid(T).name(), NULL, NULL, NULL) << std::endl;
}

template <typename T>
class Slicer{
    public:
        T begin_;
        T end_;
        T trueEnd;
        Slicer(T begin, T end): begin_(begin), end_(begin), trueEnd(end){}
        template<typename U>
        Slicer(U&& vec) : begin_(vec.begin()), end_(vec.begin()), trueEnd(vec.end()){}
        Slicer& finish(){
            begin_ = end_;
            end_ = trueEnd;
            return (*this);
        }
        Slicer& to(long int index){
            begin_ = end_;
            if(index > 0){
                end_ = (begin_ + index);
            }else{
                index *= -1;
                end_ = (trueEnd - index);
            }
            return (*this);
        }
        Slicer& operator[](long int index){
            return to(index);
        }
        T begin(){
            return this->begin_;
        }
        T end(){
            return this->end_;
        }
        Slicer& operator()(std::function<void(decltype(*begin_))> func) {
            for(decltype(*begin_) thing : (*this)){
                func(thing);
            }
            return (*this);
        }
};
static_assert(std::ranges::range< Slicer<std::vector<int>::const_iterator> >);

int main(){
    std::string vec = "abcdefghijklmnopqrstuvwxyz";
    Slicer<std::string::const_iterator> bruh(vec);
    
    //printType<decltype(bruh)>();

    bruh.to(3)([](char yeet){
        std::cout << yeet;
    })
    .to(-1)([](char yeet){
        std::cout << char(std::toupper(yeet));
    }).finish()([](char yeet){
        std::cout << yeet << yeet << yeet << yeet << yeet;
    });
    
    std::cout << std::endl << std::endl;
    
    int arr[] = {1, 2, 3, 4, 5, 6, 7, 8};
    Slicer<int*> arrSlicer(arr, arr + (sizeof(arr)/sizeof(int)));
    
    std::cout << "[";
    arrSlicer.to(-1)([](int yeet){
        std::cout << yeet << ", ";
    }).finish()([](int yeet){
        std::cout << yeet << "]" << std::endl;
    });

    return 0;
}

#include <iostream>
using namespace std;

int main {
   cout << 1; 
}