Today I have done Nth Magical Number and leetcode's January LeetCoding Challenge with cpp.

Nth Magical Number

Description

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

Example 3:

Input: n = 5, a = 2, b = 4
Output: 10

Example 4:

Input: n = 3, a = 6, b = 4
Output: 8

Constraints:

• $1 \le n \le 10^9$
• $2 \le a, b \le 4 * 10^4$

Solution

class Solution {
    const long long MOD = 1e9 + 7;
    int gcd(int a, int b) {
        int c = a % b;
        while(c) {
            a = b;
            b = c;
            c = a % b;
        }
        return b;
    }
public:
    int nthMagicalNumber(int n, int a, int b) {
        int gcdAB = gcd(a, b);
        int lcmAB = a / gcdAB * b;
        long long roundNum = a / gcdAB + b / gcdAB - 1;
        long long answer = n / roundNum * lcmAB % MOD;
        int rest = n % roundNum;
        if(!rest) return answer;
        long long begin = 1, end = lcmAB-1;
        while(begin < end) {
            int mid = (begin + end) / 2;
            if(mid / a + mid / b < rest) {
                begin = mid + 1;
            } else {
                end = mid;
            }
        }
        return (answer + begin) % MOD;
    }
};

January LeetCoding Challenge 13

Description

Boats to Save People

The i-th person has weight people[i], and each boat can carry a maximum weight of limit.

Each boat carries at most 2 people at the same time, provided the sum of the weight of those people is at most limit.

Return the minimum number of boats to carry every given person. (It is guaranteed each person can be carried by a boat.)

Example 1:

Input: people = [1,2], limit = 3
Output: 1
Explanation: 1 boat (1, 2)

Example 2:

Input: people = [3,2,2,1], limit = 3
Output: 3
Explanation: 3 boats (1, 2), (2) and (3)

Example 3:

Input: people = [3,5,3,4], limit = 5
Output: 4
Explanation: 4 boats (3), (3), (4), (5)

Note:

• 1 <= people.length <= 50000
• 1 <= people[i] <= limit <= 30000

Solution

class Solution {
public:
    int numRescueBoats(vector<int>& people, int limit) {
        if(people.empty()) return 0;
        sort(people.begin(), people.end());
        int len = people.size();
        int begin = 0, end = len-1;
        while(begin < end) {
            int mid = (begin + end) / 2;
            if(people[mid] < limit) {
                begin = mid+1;
            } else {
                end = mid;
            }
        }
        int answer = len - end - 1;
        begin = 0;
        while(begin < end) {
            if(people[begin] + people[end] <= limit) {
                answer += 1;
                begin += 1;
                end -= 1;
            } else {
                answer += 1;
                end -= 1;
            }
        }
        if(begin == end) answer += 1;
        return answer;
    }
};