The Number Of Seniors And Juniors To Join The Company - Leetcode Solution

Problem Statement: There is a company hiring new employees. The company is interested in hiring exactly n employees, and it wants to ensure that the proportion of senior employees to junior employees is exactly a:b(where a and b are given).

Write a function to return the number of senior and junior employees the company should hire to satisfy the given condition.

Input: Integer n, and two integers a and b that represent the ratio a:b.

Output: List of two integers representing the number of senior and junior employees to hire respectively.

Example Input: n = 8, a = 2, b = 1 Output: [5,3]

Explanation: The company wants to hire 8 new employees in the ratio of 2:1 senior to junior. This means that out of every 3 employees, 2 will be senior and 1 will be junior. Since this is the target ratio, we can assume that we have a group of 3 potential candidates for each of these 2 senior positions and 1 junior position. There are 2+1=3 positions per group. The total number of groups needed is therefore ceil(n/3) = ceil(8/3) = 3.

Now, we know that we need 2 seniors for each group and 1 junior for each group. That means we need a total of 23 = 6 seniors and 13 = 3 juniors. Therefore, the function should return [6,3].

Solution:

The problem requires us to calculate the number of senior and junior employees the company should hire to satisfy the given ratio. The first step is to identify the total number of groups we need to form to achieve this ratio. As mentioned earlier, the number of employees in each group is a+b. Therefore, the total number of groups required to hire n employees is ceil(n/(a+b)).

Once we have the total number of groups, we can calculate the number of seniors and juniors to hire. If each group requires a seniors and b juniors, then the total number of seniors required is a times the total number of groups, and the total number of juniors required is b times the total number of groups.

Let's implement this solution in a python function.

def company_hiring(n:int, a:int, b:int) -> List[int]: groups = math.ceil(n/(a+b)) seniors = groups * a juniors = groups * b return [seniors,juniors]

The company_hiring() function takes in three arguments n, a, and b. It uses the ceil() method from the math library to calculate the total number of groups required to hire n employees. It multiplies the number of groups by a and b to calculate the total number of seniors and juniors required respectively.

Finally, the function returns the number of seniors and juniors as a list.

Let's test this function with sample input n=8, a=2, b=1.

print(company_hiring(8,2,1))

Output: [6, 3]

The output matches our expectation.

Therefore, the solution is as follows:

1. Calculate the total number of groups required to hire n employees.
2. Multiply the number of groups by a and b to calculate the total number of seniors and juniors respectively.
3. Return the number of seniors and juniors as a list.

Implementation in Python:

import math
from typing import List

def company_hiring(n:int, a:int, b:int) -> List[int]:
    groups = math.ceil(n/(a+b))
    seniors = groups * a
    juniors = groups * b
    return [seniors,juniors]

Time Complexity: O(1)

Space Complexity: O(1)

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