Ugly Numbers

Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...
shows the first 11 ugly numbers. By convention, 1 is included.

Write a program to find and print the 1500'th ugly number.

Input and Output：
There is no input to this program. Output should consist of a single line as shown below, with <number> replaced by the number computed.

Sample output：
The 1500'th ugly number is <number>.

  

Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence


1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...



shows the first 11 ugly numbers. By convention, 1 is included.


Write a program to find and print the 1500'th ugly number.


Input and Output
There is no input to this program. Output should consist of a single line as shown below, with <number> replaced by the number computed.


Sample output
The 1500'th ugly number is <number>.





public class UglyNumber {
   public static void main(String[] args){
       int m2 = 0;
       int m3 = 0;
       int m5 = 0;
       int[] a = new int[1500];
 
       int temp = 1;
       a[0] = 1;
 
       for(int i = 1; i < 1500;i++){
         temp = 2*a[m2] > 3*a[m3] ? 3*a[m3] : 2*a[m2];
         temp = temp > 5*a[m5] ? 5*a[m5] : temp;

         if(temp == 2*a[m2])
            m2++;
         if(temp == 3*a[m3])
            m3++;
         if(temp == 5*a[m5])
            m5++;
  
         a[i] = temp;
  }
  System.out.println("The 1500'th ugly number is: " + a[1499]);
}
}

算法思想：满足条件的数一定是2或3或5的倍数（包括1）。设置三个变量m2,m3,m5,表示下一个满足条件的数是2*a[m2],3*a[m3]和5*a[m5]这三个数中的最小者。满足条件的 m 值加1.下次从新的 m 值乘以相应的倍数。如要求a[8]时,m2 = 4,m3 = 3, m5 = 1，由于2 * a[4] = 10 及5 * a[1] = 10 小于 3 * a[3] = 12,这时可得a[8] = 10,同时
m2 = m2 + 1 = 5, m5 = m5 + 1 = 2.