LeetCode-in-Java
1201. Ugly Number III
Medium
An ugly number is a positive integer that is divisible by a, b, or c.
Given four integers n, a, b, and c, return the nth ugly number.
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.
Constraints:
1 <= n, a, b, c <= 1091 <= a * b * c <= 1018- It is guaranteed that the result will be in range
[1, 2 * 109].
Solution
public class Solution {
private long getLcm(long a, long b) {
long mx = a;
long mn = b;
if (a < b) {
mx = b;
mn = a;
}
while (mn != 0) {
long tmp = mn;
mn = mx % mn;
mx = tmp;
}
return (a * b) / mx;
}
public int nthUglyNumber(int n, int a, int b, int c) {
long ab = getLcm(a, b);
long ac = getLcm(a, c);
long bc = getLcm(b, c);
long abc = getLcm(a, bc);
long left = 1;
long right = 2000000001;
if (a != 0 && b != 0 && c != 0 && bc != 0) {
while (left < right) {
long mid = left + (right - left) / 2;
if (mid / a + mid / b + mid / c - mid / ab - mid / ac - mid / bc + mid / abc >= n) {
right = mid;
} else {
left = mid + 1;
}
}
}
return (int) left;
}
}