[LeetCode] 264. Ugly Number II 丑陋数之二
LeetCode number II 之二
2023-09-11 14:21:39 时间
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 first10
ugly numbers.
Note:
1
is typically treated as an ugly number.n
does not exceed 1690.
Hint:
- 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. - An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.
- 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.
- Assume you have Uk, the kth ugly number. Then Uk+1 must be Min(L1 * 2, L2 * 3, L3 * 5).
这道题是之前那道 Ugly Number 的拓展,这里让找到第n个丑陋数,还好题目中给了很多提示,基本上相当于告诉我们解法了,根据提示中的信息,丑陋数序列可以拆分为下面3个子列表:
(1) 1x2, 2x2, 2x2, 3x2, 3x2, 4x2, 5x2...
(2) 1x3, 1x3, 2x3, 2x3, 2x3, 3x3, 3x3...
(3) 1x5, 1x5, 1x5, 1x5, 2x5, 2x5, 2x5...
仔细观察上述三个列表,可以发现每个子列表都是一个丑陋数分别乘以 2,3,5,而要求的丑陋数就是从已经生成的序列中取出来的,每次都从三个列表中取出当前最小的那个加入序列,请参见代码如下:
解法一:
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(); } };
我们也可以使用最小堆来做,首先放进去一个1,然后从1遍历到n,每次取出堆顶元素,为了确保没有重复数字,进行一次 while 循环,将此时和堆顶元素相同的都取出来,然后分别将这个取出的数字乘以 2,3,5,并分别加入最小堆。这样最终 for 循环退出后,堆顶元素就是所求的第n个丑陋数,参见代码如下:
解法二:
class Solution { public: int nthUglyNumber(int n) { priority_queue<long, vector<long>, greater<long>> pq; pq.push(1); for (long i = 1; i < n; ++i) { long t = pq.top(); pq.pop(); while (!pq.empty() && pq.top() == t) { t = pq.top(); pq.pop(); } pq.push(t * 2); pq.push(t * 3); pq.push(t * 5); } return pq.top(); } };
Github 同步地址:
https://github.com/grandyang/leetcode/issues/264
类似题目:
参考资料:
https://leetcode.com/problems/ugly-number-ii/
https://leetcode.com/problems/ugly-number-ii/discuss/69372/Java-solution-using-PriorityQueue
相关文章
- Java实现 LeetCode 792 自定义字符串排序(暴力)
- Java实现 LeetCode 780 到达终点(逻辑题)
- Java实现 LeetCode 762 二进制表示中质数个计算置位(位运算+JDK的方法)
- Java实现 LeetCode 515 在每个树行中找最大值
- Java实现 LeetCode 470 用 Rand7() 实现 Rand10()
- Java实现 LeetCode 388 文件的最长绝对路径
- Java实现 LeetCode 16 最接近的三数之和
- 【链表】leetcode 19. 删除链表的倒数第 N 个结点【中等】
- [LeetCode] Single Number II
- [LeetCode] Single Number
- [LeetCode] Number of 1 Bits
- [LeetCode] Excel Sheet Column Number
- Python 刷Leetcode题库,顺带学英语单词(29)
- Leetcode 2169. 得到 0 的操作数
- leetcode 374. Guess Number Higher or Lower
- leetcode 263. Ugly Number
- leetcode 747. Largest Number At Least Twice of Others
- leetcode 202. Happy Number
- leetcode 136. Single Number
- leetcode 476. Number Complement
- 【Leetcode刷题Python】216. 组合总和 III
- 【Leetcode刷题Python】33. 搜索旋转排序数组
- 【LeetCode】62. 不同路径