一、题目
A positive integer is magical if it is divisible by either a or b.
Given the three integers n, a, and b, return the nth magical number. Since the answer may be very large, return it modulo 109 + 7.
Example 1:
Input: n = 1, a = 2, b = 3
Output: 2
Example 2:
Input: n = 4, a = 2, b = 3
Output: 6
Constraints:
1 <= n <= 109
2 <= a, b <= 4 * 104
二、题解
最大公约数，同余定理，二分答案。
class Solution {
public:
int nthMagicalNumber(int n, int a, int b) {
int mod = 1e9 + 7;
long long lcm = a / gcd(a,b) * b;
long long res = 0;
long long l = 0,r = (long long)n * min(a,b);
while(l <= r){
long long mid = (l + r) / 2;
if(mid / a + mid / b - mid / lcm >= n){
res = mid;
r = mid - 1;
}
else{
l = mid + 1;
}
}
return res % mod;
}
};
