Ugly Number II

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.

Analyse: We can divide the ugly numbers into three categories:

2: 1*2, 2*2, 3*2, 4*2, 5*2...

3: 1*3, 2*3, 3*3, 4*3, 5*3...

5: 1*5, 2*5, 3*5, 4*5, 5*5...

So our job is to find the first n number in these three arrays. If we already find the i-th smallest number, the next number should be min(l1*2, l2*3, l3*5). The point is that we need to mark the current position of the three arrays, which means that the factor that we want to multiply is the smallest one in the result array. Thus, if the element in one array is selected, then we increase this index.

Runtime: 8ms.

class Solution {
public:
int nthUglyNumber(int n) {
if(n <= 1) return n;

const int len = n;
int ugly
= {1};
int l1 = 0, l2 = 0, l3 = 0;//to represent the current location of the arrays respectively
int f1 = 2, f2 = 3, f3 = 5;//to represent the current ugly factors

for(int i = 1; i < n; i++){
int least = min(min(f1, f2), f3);
if(least == f1) {
ugly[i] = f1;
f1 = 2 * ugly[++l1];
}
if(least == f2){
ugly[i] = f2;
f2 = 3 * ugly[++l2];
}
if(least == f3){
ugly[i] = f3;
f3 = 5 * ugly[++l3];
}
}
return ugly[n - 1];
}
};