Sum of count of persons still performing the job whenever a person finishes job
Last Updated :
18 Nov, 2021
Given two integers P denoting the number of people and a positive integer K. Each person is assigned with the same job which takes exactly K hours to finish. A condition is given that all of them can start performing their jobs exactly in X hours of interval. Count the number of persons still performing the job whenever a prior person finishes his/her job. The task is to find the sum of such counts.
Examples:
Input: P = 4, K = 6, X = 3
Output: 5
Explanation: Let the four persons be P1, P2, P3, P4
- P1 starts at 0 and finishes at 6
- P2 starts at 3 and finishes at 9
- P3 starts at 6 and finishes at 12
- P4 starts at 9 and finishes at 15
So, when P1 finishes, P2 and P3 started performing their respective job, count for P1 = 2
when P2 finishes, P3 and P4 started performing their respective job, count for P2 = 2
when P3 finishes, only P4 started performing the job, count for P3 = 1
when P4 finishes, there is no person who starts at this point, so count for P4 = 0
Therefore, Total counts = (2 + 2 + 1 + 0) = 5
Input: P = 9, K = 72, X = 8
Output: 36
Approach: The given problem can be solved by analyzing the problem with the concept of math. Follow the steps below to solve the problem:
- Find the minimum of total persons excluding the first one(because P1 always starts at 0) and K/X, store it in a variable say a.
- Check if a is equal to 0
- if yes, return 0.
- else, calculate the total sum of count by making mathematical formula.
- Return the final sum of count as the required answer.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int countPersons( int P, int K, int X)
{
int a = min(P - 1, K / X);
if (a == 0) {
return 0;
}
int ans = max(0,
a * (a - 1) / 2)
+ a * (P - a);
return ans;
}
int main()
{
int P = 22, K = 9, X = 1;
cout << countPersons(P, K, X);
return 0;
}
|
Java
import java.util.*;
public class GFG {
static int countPersons( int P, int K, int X)
{
int a = Math.min(P - 1 , K / X);
if (a == 0 ) {
return 0 ;
}
int ans = Math.max( 0 ,
a * (a - 1 ) / 2 )
+ a * (P - a);
return ans;
}
public static void main(String args[])
{
int P = 22 , K = 9 , X = 1 ;
System.out.println(countPersons(P, K, X));
}
}
|
Python3
def countPersons(P, K, X):
a = min (P - 1 , K / X)
if a = = 0 :
return 0
ans = max ( 0 ,
a * (a - 1 ) / 2 )
return ans + a * (P - a)
if __name__ = = "__main__" :
P = 22
K = 9
X = 1
print ( int (countPersons(P, K, X)))
|
C#
using System;
class GFG {
static int countPersons( int P, int K, int X)
{
int a = Math.Min(P - 1, K / X);
if (a == 0) {
return 0;
}
int ans = Math.Max(0,
a * (a - 1) / 2)
+ a * (P - a);
return ans;
}
public static void Main()
{
int P = 22, K = 9, X = 1;
Console.Write(countPersons(P, K, X));
}
}
|
Javascript
<script>
function countPersons(P, K, X)
{
let a = Math.min(P - 1, K / X);
if (a == 0) {
return 0;
}
let ans = Math.max(0,
a * (a - 1) / 2)
+ a * (P - a);
return ans;
}
let P = 22, K = 9, X = 1;
document.write(countPersons(P, K, X));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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