Overlay number

/**
 *  Cover numbers 
 * 
 *  Given an integer interval [a,b] And integer interval [x,y], You can use it any number of times a,b Add integers between , How many can be made up [x,y] An integer in an interval ？  Input 
 * a,b,x,y, among 1<= a < b <= 1000000000, 1 <= x < y <= 1000000000.  Output ：
 *  use [a,b] Add integers in any number of times , How many can you get [x,y] The whole number inside .  for example a = 8, b = 10, x = 3 , y = 20  We can get 
 * [3..20] Integer between  8, 9, 10, 16 （ 8 + 8）, 17（8 + 9）, 18（9 + 9）, 19（9 + 10）, 20（10 +
 * 10）, So output 8.  ask ：2+3=5 1+4=5  Is this a 1 One is still 2 individual ？  answer ： count 1 Time   Ask how many different numbers you can cover  [x,y] If it is completely covered   Namely y - x +
 * 1.
 * 
 * @author zoyation
 * 
 */
public class OverWriteNumber {
	public static int howmany(int a, int b, int x, int y) {
		/*
		 * Scanner sc = new Scanner(System.in);  Get input abcd Input ,1<= a < b <=
		 * 1000000000,1 <= x < y <= 1000000000 while (a <= 0 || a >= 999999999
		 * || b <= a || b >= 1000000000 || x <= 0 || x >= 999999999 || y <= x ||
		 * y >= 1000000000) { if (a <= 0 || a >= 999999999) {
		 * System.out.print(" Please enter a Value （[1,999999999]）："); a = sc.nextInt(); if (a
		 * <= 0 || a >= 999999999) {
		 * System.out.println("a The value of is not in the interval [1,999999999] Inside , Please re-enter ！"); } } else if (b <=
		 * a || b >= 1000000000) { System.out.print(" Please enter b Value （[a+1=" + (a + 1) +
		 * ",999999999]）："); b = sc.nextInt();
		 * 
		 * if (b <= a || b >= 1000000000) { System.out.println("b The value of is not in the interval [a+1=" +
		 * (a + 1)+ ",999999999] Inside , Please re-enter ！"); } } else if (x <= 0 || x >=
		 * 999999999) { System.out.print(" Please enter x Value （[1,999999999]）："); x =
		 * sc.nextInt();
		 * 
		 * if (x <= 0 || x >= 999999999) {
		 * System.out.println("x The value of is not in the interval [1,999999999] Inside , Please re-enter ！"); } } else if (y <=
		 * x || y >= 1000000000) { System.out.print(" Please enter y Value （[x+1=" + (x + 1) +
		 * ",999999999]）："); y = sc.nextInt();
		 * 
		 * if (y <= x || y >= 1000000000) { System.out.println("y The value of is not in the interval [x+1=" +
		 * (x + 1)+ ",999999999] Inside , Please re-enter ！"); } } } System.out.println("a=" + a +
		 * ",b=" + b + ",x=" + x + ",y=" + y);
		 */
		/* count  Record how many different numbers can be covered  */
		int count = 0;
		if (a > y) {
			count = 0;
		} else if (a == y) {
			count = 1;
		} else {
			int i = a >= x ? a : x;//  Record the beginning of traversal [x,y] value 

			if (b >= y) {
				/* b Than y Big , Direct calculation  */
				count = y - i + 1;
			} else {
				int k = 0;/*  The record starts in the interval [x,y] Calculate the minimum number of statistics through circulation  */
				if (b < x) { /* a<b<x */
					count = 0;
					k = x;
				} else {
					count = b - i + 1;
					k = b + 1;
				}
				/*  Next, traverse the statistical coverage figures  */
				int t1 = a;
				int t2 = b;
				do {
					int m1 = k % t1;
					if (m1 >= a || m1 == 0) {
						/* Current statistics and t1 Seeking remainder , If 0 Or not a Small , In the interval [a,t1) Inside ,k=t1*n+m1(n=k/t1)*/
						count++;
						// System.out.println("m1="+m1+",t1="+t1+",k="+k);
						t1 = a;
						t2 = b;
						k++;
					} else {
						int m2 = k % t2;

						if (m2 >= a || m2 == 0) {
							/* Current statistics and t1 Seeking remainder , If 0 Or not a Small , In the interval [a,t2) Inside ,k=t2*n+m2 (n=k/t2)*/
							count++;
							// System.out.println("m2="+m2+",t2="+t2+",k="+k);
							t1 = a;
							t2 = b;
							k++;
						} else {
							t1++;
							t2--;
							/* t1 Greater than t2 when ,[a,b] The interval values have been taken , Restart the verification of the next number  */
							if (t1 > t2) {
								t1 = a;
								t2 = b;
								k++;
							}
						}
					}

				} while (k <= y);
			}
		}

		return count;
	}

	public static void main(String args[]) {
		System.out.println(howmany(51, 52, 50, 999999999));// 57315234
	}
}