Ugly Number II

一、问题描述

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.

二、思路

生成丑数的数组中是从小到大有序排列的，每次都选当前最小的丑数。

采用DP思想，即动态规划，递归式：ugleNumbers[i] = min{ugleNumbers[i2]  * 2,ugleNumbers[i3] *3,ugleNumbers[i5]  * 5},根据递归式找到最小的丑数，同时相应的将i2、i3、i5加一。

三、代码

class Solution {public:    int nthUglyNumber(int n) {        if(n <= 0)            return 0;        int i2 = 0, i3 = 0, i5 = 0;        int c1 = 0, c2 = 0, c3 = 0;        vector<int> ugleNums(n, 0);        ugleNums[0] = 1;        for(int i = 1; i < n; ++i ){            c1 = ugleNums[i2] * 2;            c2 = ugleNums[i3] * 3;            c3 = ugleNums[i5] * 5;            int min = c1;            if(c2 < min)                min = c2;            if(c3 < min)                min = c3;            ugleNums[i] = min;            if(min == c1)                i2++;            if(min == c2)                i3++;            if(min == c3)                i5++;        }        return ugleNums[n - 1];    }};