【leetcode】878. Nth Magical Number

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

 

暴力法：用set接收数据，然后两个数字依次累加，超时了。

class Solution {
public:
    int nthMagicalNumber(int n, int a, int b) {
        // 用set去重
        long M=10e9+7;
        set<long>dp;
        long tmpa=a,tmpb=b;
        while(dp.size()<n){
            if(tmpa<tmpb){
                dp.insert(tmpa);
                tmpa=(tmpa+a)%M;
            }
            else if(tmpa>tmpb){
                dp.insert(tmpb);
                tmpb=(tmpb+b)%M;
            }
            else{
                dp.insert(tmpa);
                tmpa=(tmpa+a)%M;
                tmpb=(tmpb+b)%M;
            }
        }
        auto zz=--dp.end();
        return *(zz);
        
    }
};

用二分法来求解，参考了大佬的帖子。

class Solution {
public:
    int nthMagicalNumber(int N, int A, int B) {
        long lcm = A * B / gcd(A, B), left = 2, right = 1e14, M = 1e9 + 7;
        while (left < right) {
            long mid = left + (right - left) / 2;
            if (mid / A + mid / B - mid / lcm < N) left = mid + 1;
            else right = mid;
        }
        return right % M;
    }
    int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }
};