Ugly Number II

题目描述：

Write a program to find the n-th ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.

Note that 1 is typically treated as an ugly number.

Hint:

1. The naive approach is to call isUgly for every number until you reach the n^th one. Most numbers are not ugly. Try to focus your effort on generating only the ugly ones.
2. An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.
3. The key is how to maintain the order of the ugly numbers. Try a similar approach of merging from three sorted lists: L₁, L₂, and L₃.
4. Assume you have U_k, the k^th ugly number. Then U_k+1 must be Min(L₁ * 2, L₂ * 3, L₃ * 5).

维护3个队列，分别是2,3,5的倍数，队列开头都是最小的元素，一直往里面放入元素，用外层的循环来控制个数。

public class Solution {
    public int nthUglyNumber(int n) {  
        int u = 0;  
        Deque<Integer> l1 = new ArrayDeque<Integer>();  
        Deque<Integer> l2 = new ArrayDeque<Integer>();  
        Deque<Integer> l3 = new ArrayDeque<Integer>();  
        l1.offer(1);  
        l2.offer(1);  
        l3.offer(1);  
          
        for(int i=0; i<n; i++) {  
            u = Math.min( Math.min(l1.peek(), l2.peek()), l3.peek());  
              
            if(l1.peek() == u) l1.poll();  
            if(l2.peek() == u) l2.poll();  
            if(l3.peek() == u) l3.poll();  
              
            l1.offer(u*2);  
            l2.offer(u*3);  
            l3.offer(u*5);  
        }  
        return u;  
    }  
}