Ugly Number II

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于 2015-11-01 11:43:02 发布

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本文介绍了一种高效算法来找到序列中的第N个丑数。丑数定义为仅包含质因数2、3和5的正整数，例如1、2、3、4、5等。文章提供了一个Java实现示例，通过动态规划方法逐步构建丑数序列，并最终返回指定位置的数值。

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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.

public class Solution {
	public int nthUglyNumber(int n) {
        int[] ugly = new int[n];
        ugly[0] = 1;
        int i2 = 0;
        int i3 = 0;
        int i5 = 0;
        for (int i = 1; i < n; i++) {
			int cur = Math.min(ugly[i2] * 2, Math.min(ugly[i3] * 3, ugly[i5] * 5));
			ugly[i] = cur;
			if (cur == ugly[i2] * 2) {
				i2++;
			}
			if (cur == ugly[i3] * 3) {
				i3++;
			}
			if (cur == ugly[i5] * 5) {
				i5++;
			}
		}
        return ugly[n-1];
    }
}