264. Ugly Number II

sysu_jiang

于 2017-06-21 16:45:14 发布

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本文链接：https://blog.youkuaiyun.com/sysu_jiang/article/details/73550646

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。文中提供了一个C++实现的例子，展示了如何通过动态规划的方法构建丑数序列。

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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, and n does not exceed 1690.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

class Solution {
public:
    int nthUglyNumber(int n) {
        vector<int> res(1, 1);
        int i2 = 0, i3 = 0, i5 = 0;
        while (res.size() < n) {
            int m2 = res[i2] * 2, m3 = res[i3] * 3, m5 = res[i5] * 5;
            int mn = min(m2, min(m3, m5));
            if (mn == m2) ++i2;
            if (mn == m3) ++i3;
            if (mn == m5) ++i5;
            res.push_back(mn);
        }
        return res.back();
    }
};