264. Ugly Number II - jiejackyzhang/leetcode-note GitHub Wiki

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 nth 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 Uk, the kth ugly number. Then Uk+1 must be Min(L1 * 2, L2 * 3, L3 * 5).

解题思路为将ugly number依次存入一个数组，并维护三个指针，分别代表*2，*3，*5。 每次取最小的那个加入数组，并使对应的指针前进一步。 需要注意的是，6即等于3*2，又等于2*3，此时应将*2，*3的指针都前进一步，因此三个判断的if语句都应运行。

public class Solution {
    public int nthUglyNumber(int n) {
        if(n == 0 || n == 1) return n;
        int[] ugly = new int[n];
        ugly[0] = 1;
        int p2 = 0, p3 = 0, p5 = 0, i = 1;
        while(i < n) {
            int min = Math.min(ugly[p2]*2, Math.min(ugly[p3]*3, ugly[p5]*5));
            if(min == ugly[p2]*2) p2++;
            if(min == ugly[p3]*3) p3++;
            if(min == ugly[p5]*5) p5++;
            ugly[i++] = min;
        }
        return ugly[n-1];
    }
}