1201. Ugly Number III

Given four integers `n`, `a`, `b`, and `c`, return the `nth` ugly number.

Ugly numbers are positive integers that are divisible by `a`, `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 <= 109`
• `1 <= a * b * c <= 1018`
• It is guaranteed that the result will be in range `[1, 2 * 109]`.

1201. Ugly Number III
``````struct Solution;

impl Solution {
fn nth_ugly_number(n: i32, a: i32, b: i32, c: i32) -> i32 {
let mut left = 0;
let mut right = 2_000_000_000;
while left < right {
let mid = left + (right - left) / 2;
if Self::count(mid, a as u64, b as u64, c as u64) < n as u64 {
left = mid + 1;
} else {
right = mid
}
}
left as i32
}

fn count(num: u64, a: u64, b: u64, c: u64) -> u64 {
num / a + num / b + num / c
- num / Self::lcm(a, b)
- num / Self::lcm(b, c)
- num / Self::lcm(a, c)
+ num / Self::lcm(a, Self::lcm(b, c))
}

fn lcm(a: u64, b: u64) -> u64 {
a * b / Self::gcd(a, b)
}

fn gcd(a: u64, b: u64) -> u64 {
if a == 0 {
b
} else {
Self::gcd(b % a, a)
}
}
}

#[test]
fn test() {
let n = 3;
let a = 2;
let b = 3;
let c = 5;
let res = 4;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 4;
let a = 2;
let b = 3;
let c = 4;
let res = 6;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 5;
let a = 2;
let b = 11;
let c = 13;
let res = 10;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 1000000000;
let a = 2;
let b = 217983653;
let c = 336916467;
let res = 1999999984;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
}
``````