leetcode 1201. Ugly Number III

Seawolf

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

Ugly numbers are positive integers which are divisible by a or b or c.

 

Example 1:

Input: n = 3, a = 2, b = 3, c = 5
Output: 4
Explanation: The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3rd is 4.
Example 2:

Input: n = 4, a = 2, b = 3, c = 4
Output: 6
Explanation: The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4th is 6.
Example 3:

Input: n = 5, a = 2, b = 11, c = 13
Output: 10
Explanation: The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5th is 10.
Example 4:

Input: n = 1000000000, a = 2, b = 217983653, c = 336916467
Output: 1999999984
 

Constraints:

1 <= n, a, b, c <= 10^9
1 <= a * b * c <= 10^18
It's guaranteed that the result will be in range [1, 2 * 10^9]

class Solution {
    public static int nthUglyNumber(int n, int a, int b, int c) {
        int start = 1,end = Integer.MAX_VALUE,mid;
        
        while(start < end){
            mid = start + (end - start) / 2; 
            if(count(a,b,c,mid) < n) start = mid + 1;
            else {
                end = mid;
            }
        }
        
        return end;
    }
    static long stein(long a, long b){
        int acc = 0;
    while ((a & 1) == 0 && (b & 1) == 0) {
        acc++;
        a >>= 1;
        b >>= 1;
    }
    while ((a & 1) == 0) a >>= 1;
    while ((b & 1) == 0) b >>= 1;
    if (a < b) { long t = a; a = b; b = t; }
    while ((a = (a - b) >> 1) != 0) {
        while ((a & 1) == 0) a >>= 1;
        if (a < b) { long t = a; a = b; b = t; }
    }
    return b << acc;

        
    }
    
    static long lcm(long a, long b){
        
        return a*b / stein(a,b);
    }
    
    static long count (long a, long b, long c, long num){
        
        return ((num / a) + (num / b) + (num / c)
                - (num / lcm(a, b))
                - (num / lcm(b, c))
                - (num / lcm(a, c))
                + (num / lcm(a, lcm(b, c))));
    }  
}