Ugly Number II

[leetcode]Ugly Number

链接：https://leetcode.com/problems/ugly-number/description/

Question

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

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5.

Example

Input: n = 10
Output: 12
Explanation: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.

Note:  

1 is typically treated as an ugly number.
n does not exceed 1690.

Solution

class Solution {
public:
  typedef long long int ll;
  int nthUglyNumber(int n) {
    // i2指向的位置专门乘以2，i3专门乘以3，i5专门乘以5
    int i2, i3, i5;
    i2 = i3 = i5 = 0;
    vector<int> ugly;
    ugly.resize(n);
    ugly[0] = 1;
    ll next_2 = 2;
    ll next_3 = 3;
    ll next_5 = 5;
    for (int i = 1; i < n; i++) {
      ll next_min = min(next_2, next_3);
      next_min = min(next_min, next_5);
      ugly[i] = next_min;
      // 可能会出现一个两个同时最小值，但是这样也没关系
      if (next_min == next_2) {
        i2 += 1;
        next_2 = ugly[i2]*2;
      }
      if (next_min == next_3) {
        i3 += 1;
        next_3 = ugly[i3]*3;
      }
      if (next_min == next_5) {
        i5 += 1;
        next_5 = ugly[i5]*5;
      }
    }
    return ugly[n-1];
  }
};

思路：维护三个数，分别只能乘以2，3，5，每次拿最小的数【允许多个同时最小】，然后进行进一步的更新。