#include <stdio.h>
#include <conio.h>
#include <math.h>

int main()
{   
	//kiem tra chinh phuong 

	int n;
	 nhapthongtin:
	do
	{
		printf("\nhay nhap vao so n : ");
		scanf("%d",&n);

		if(n <= 0)
		{
		    printf("\nso ban nhap khong hop le xin hay nhap lai cam on!");
		}
	} while (n <= 0);



	if (sqrt((double)n) == (int)sqrt((double)n))
	{
		printf("\nla so chinh phuong ");
	}
	else
	{
		printf("\nkhong phai la so chinh phuong");
	}

	/*so nguyen to la so bat dau tu 2 va chi co the chia het duy nhat cho 1 va chinh no
	  co rat nhieu cach giai tu cach do nhat den cach hay nhat 
	  giai thuat & lap trinh cua thay le minh hoang */
	/*cach 1 : ta di theo dung nghia cua so nguyen to chi chia het cho 1 va chinh no , thanh ra neu trong doan tu 2 cho den 
	nho hon no thi no se khong chia het cho so nao ca 
	vd: so n 
	n se goi la so nguyen to neu nhu trong doan tu 2 => n -1 thi n khong chia het cho so nao ca 
	vd: so 7 thi trong doan	tu 2 => 6  so 7 khong chia het cho so nao ca => 7 la so nguyen to 
	vd : so 8 khong goi la so nguyen to vi chia het cho 2 , 4 
	
	cach chung minh 1 : cho vong lap for chay tu 2 => n -1 . neu gap 1 so nao bat ky ma n chia het cho no
	=> khong thoa la nguyen to 
	*/
	if (n < 2)
	{
	   printf("\nkhong phai la nguyen to");
	}
	else
	{    
		int check = 1;// true 
		int solanchaycach1 = 1;
		for (int i = 2; i < n; i++)
		{
			if (n % i == 0)
			{
				check = 0;//false 
				break; //thoat ra 
			}
			solanchaycach1++;
		}
		printf("\nso lan chay cua cach 1 la %d lan",solanchaycach1);
		if (check == 1)
		{
			printf("\nla so nguyen to cach 1");
		}
		else
		{
			printf("\nkhong phai la so nguyen to cach 1");
		}
	}
	/*
	cach 2 : ta thay 1 so n se khong the nao chia het cho cac so trong doan tu n/2 + 1 cho toi n -1 
	=>cai tien cach 1 :ta chi can chay vong lap xet cac so chia het tu 2 toi n/2 la duoc roi 
	*/
	if (n < 2)
	{
	   printf("\nkhong phai la nguyen to");
	}
	else
	{    
		int check = 1;// true 
		int solanchaycach2 = 1;
		for (int i = 2; i < n/2; i++)
		{
			if (n % i == 0)
			{
				check = 0;//false 
				break; //thoat ra 
			}
			solanchaycach2++;
		}
		printf("\nso lan chay cua cach 2 la %d lan",solanchaycach2);
		if (check == 1)
		{
			printf("\nla so nguyen to cach 2");
		}
		else
		{
			printf("\nkhong phai la so nguyen to cach 2");
		}
	}
	/*
	cach 3: cai tien len tu cach 2 , ta thay khong can phai chay tu 2 cho toi n /2 ma chi can 
	chay cho toi sqrt(n) la duoc roi (toan hoc chung minh )
	*/
	if (n < 2)
	{
	   printf("\nkhong phai la nguyen to");
	}
	else
	{    
		int check = 1;// true 
		int solanchaycach3 = 1;
		for (int i = 2; i < sqrt((double)n); i++)
		{
			if (n % i == 0)
			{
				check = 0;//false 
				break; //thoat ra 
			}
			solanchaycach3++;
		}
		printf("\nso lan chay cua cach 3 la %d lan",solanchaycach3);
		if (check == 1)
		{
			printf("\nla so nguyen to cach 3");
		}
		else
		{
			printf("\nkhong phai la so nguyen to cach 3");
		}
	}
	/*
	cach 4 : cai tien tu cach 3 va ta thay mot dieu sau : so 2 la so nguyen to chan duy nhat , ngoai ra 
	khong co so chan nao ngoai so 2 ma la so nguyen to 
	*/
		if (n < 2)
	{
	   printf("\nkhong phai la nguyen to");
	}
	else
	{    
		int check = 1;// true 
		int solanchaycach4 = 1;
		for (int i = 3; i < sqrt((double)n); i+=2)
		{
			if (n % i == 0)
			{
				check = 0;//false 
				break; //thoat ra 
			}
			solanchaycach4++;
		}
		printf("\nso lan chay cua cach 4 la %d lan",solanchaycach4);
		if (check == 1)
		{
			printf("\nla so nguyen to cach 4");
		}
		else
		{
			printf("\nkhong phai la so nguyen to cach 4");
		}
	}
	
	//d: kiem tra tang dan giam dan va khong tang khong giam 

		int temp = n;
		int checktang = 1;//co hieu 
		int checkgiam = 1;

		while (temp > 9)
		{
			int chuso1 = temp % 10;//5
			temp /=10;
			int chuso2 = temp %10;//4

			if(chuso1 <= chuso2)
			{
			   checktang = 0;
			   //BREAK;
			}

			if(chuso1 >= chuso2)
			{
			   checkgiam = 0;
			}
						
		}
		
		if (checktang == 1 )
		{
			printf("\nso tang dan");
		}
		else if (checkgiam == 1)
		{
			printf("\nso giam dan");
		}
		else
		{
			printf("\nkhong tang khong giam");
		}
	


	getch();
	return 0;



}