Find the nth ugly number

Generally, the ugly number: all factors are only 2, 3, or 5. For convenience, 1 is also an ugly number. For example, 100 = 2*2*5*5, 12 = 2*2*3

Ugly data in the first 11: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15 ,...

14 is not an ugly number, because 14 = 2*7, 7 is not in the range of 2, 3, 5

 

To determine whether a number is ugly:

Def isuugly (n): <br/> while (N % 2 = 0 ): <br/> N/= 2 <br/> while (N % 3 = 0 ): <br/> N/= 3 <br/> while (N % 5 = 0 ): <br/> N/= 5 <br/> If (n = 1): <br/> return true <br/> return false

 

1. Start from 1 and look up one by one. However, it is inefficient to judge whether a number is ugly:

Def getnthuglynumber (n): <br/> I = 1 <br/> CNT = 1 <br/> while (CNT <n ): <br/> I = I + 1 <br/> If (isuugly (I): <br/> CNT = CNT + 1 <br/> return I

An ugly number is the other ugly number multiplied by 2, multiplied by 3, or multiplied by 5 (except 1), such as 2 = 1*2, 3 = 1*3, 4 = 2*2, 5 = 1*5. We can generate an ugly number from small to big, put the N sequential ugly numbers in an array, and finally return the nth number. How to keep the array in order? For example, if we currently have the ugly number 1, which is the next ugly number? Currently, there is only 1, with 1*2 = 2, 1*3 = 3, 1*5 = 5, and the smallest of the three is greater than 1, so the second ugly number is 2, the current array is {1, 2}. What is the next ugly number? We can do this first:

Multiply the number of each number in the current array by 2, and take the number that is the smallest value greater than the maximum ugly number in the current array.

Multiply the number of each number in the current array by 3, and take the number that is the smallest value greater than the maximum ugly number in the current array.

Multiply the number of each number in the current array by 5, and take the number that is smaller than the maximum ugly number in the current array.

The last ugly number nextuugly = min (num2, num3, num5), such

1*2 = 2,2*2 = 4. Obtain num2 = 4.

1*3 = 3,2*3 = 5 get num3 = 3

1*5 = 5 5*5 = 10 get num5 = 5

Therefore, nextuugly = min (num2, num3, num5) = 3. In fact, there are many additional steps, which can be further improved:

Use Max to represent the current maximum ugly number. The initial max = 1, ptr2, ptr3, and ptr5 are all 0, pointing to the first element of the array, if nextuugly is obtained by uugly [ptr2] * 2, PTR 1 is added. To search forward, PTR + 1 points to the next big ugly number ~ Ptr3 and ptr5 are the same.

Def getnthuglynumber (n): <br/> uugly = [1] <br/> ptr2 = ptr3 = ptr5 = 0 <br/> for I in range (1, N ): <br/> num2 = uugly [ptr2] * 2 <br/> num3 = uugly [ptr3] * 3 <br/> num5 = uugly [ptr5] * 5 <br/> uugly. append (min (num2, num3, num5) <br/> If (uugly [I] = num2 ): <br/> ptr2 = ptr2 + 1 <br/> If (uugly [I] = num3 ): <br/> ptr3 = ptr3 + 1 <br/> If (uugly [I] = num5 ): <br/> ptr5 = ptr5 + 1 <br/> return uugly [-1]