Given a number n. The task is to find the sum of numbers up to n, that are divisible by 2 or 5.
Examples:
Input: n = 2 Output: 2 Input: n = 5 Output: 11
A naive approach is to just iterate over the numbers up to n and check if it divisible by 2 or 5. If it is divisible then just add this number to our required sum. And finally, we got our total sum with a complexity of O(n).
Efficient Approach:
1. First find the numbers that are divisible by 2. So, these numbers for an AP, having
first term = 2, difference = 2, Number of terms = n/2
So, sum given by-
2. Secondly we find the numbers that are divisible by 5. So, these number for an AP, having
first term = 5, difference = 5, Number of terms = n/5
So, sum given by-
3. First we find the numbers that are divisible by 2 and 5.so, these number for an AP, having
first term =10, difference = 10, Number of terms = n / 10
So, sum given by-
4. As we have to find the sum of numbers divisible by 2 or 5. So, the required sum is given by-
sum = sum_2 + sum_5 – sum_10
Algorithm:
Step 1: Start
Step 2: Create a function with the return type of long and input parameter of int type, find sum will return the sum of numbers divisible by 2 or 5 up to N.
Step 3: Now create three variables of long type say sum2, sum5, sum10
Step 4: Now store the sum of all numbers divided by 2 in sum2 by using the formula : (n / 2) * (4 + (n / 2 – 1) * 2)) / 2
Step 5: Now store the sum of all numbers divided by 5 in sum5 by using the formula : ((n / 5) * (10 + (n / 5 – 1) * 5)) / 2
Step 6: Now store the sum of all numbers divided by 10 in sum10 by using the formula : ((n / 10) * (20 + (n / 10 – 1) * 10)) / 2
Step 7: Now return the sum2 + sum5 – sum10 because it will give sum of the number divisible by 2 or 5.
Step 8: End
Below is the implementation of the above approach:
// C++ implementation of above approach #include <bits/stdc++.h> #define ll long long int using namespace std;
// Function to find the sum ll findSum( int n)
{ ll sum2, sum5, sum10;
// sum2 is sum of numbers divisible by 2
sum2 = ((n / 2) * (4 + (n / 2 - 1) * 2)) / 2;
// sum5 is sum of number divisible by 5
sum5 = ((n / 5) * (10 + (n / 5 - 1) * 5)) / 2;
// sum10 of numbers divisible by 2 and 5
sum10 = ((n / 10) * (20 + (n / 10 - 1) * 10)) / 2;
return sum2 + sum5 - sum10;
} // Driver code int main()
{ int n = 5;
cout << findSum(n) << endl;
return 0;
} |
// Java implementation of // above approach import java.lang.*;
import java.util.*;
class GFG
{ // Function to find the sum static long findSum( int n)
{ long sum2, sum5, sum10;
// sum2 is sum of numbers
// divisible by 2
sum2 = ((n / 2 ) * ( 4 +
(n / 2 - 1 ) * 2 )) / 2 ;
// sum5 is sum of number
// divisible by 5
sum5 = ((n / 5 ) * ( 10 +
(n / 5 - 1 ) * 5 )) / 2 ;
// sum10 of numbers divisible
// by 2 and 5
sum10 = ((n / 10 ) * ( 20 +
(n / 10 - 1 ) * 10 )) / 2 ;
return sum2 + sum5 - sum10;
} // Driver code public static void main (String[] args)
{ int n = 5 ;
System.out.println(findSum(n));
} } // This code is contributed by Raj |
# Python3 implementation of # above approach # Function to find the sum def findSum(n):
# sum2 is sum of numbers divisible by 2
sum2 = ((n / / 2 ) * ( 4 + (n / / 2 - 1 ) * 2 )) / / 2
# sum5 is sum of number divisible by 5
sum5 = ((n / / 5 ) * ( 10 + (n / / 5 - 1 ) * 5 )) / / 2
# sum10 of numbers divisible by 2 and 5
sum10 = ((n / / 10 ) * ( 20 + (n / / 10 - 1 ) * 10 )) / / 2
return sum2 + sum5 - sum10;
# Driver code if __name__ = = '__main__' :
n = 5
print ( int (findSum(n)))
# this code is contributed by Shivi_Aggarwal |
// C# implementation of // above approach using System;
class GFG
{ // Function to find the sum static long findSum( int n)
{ long sum2, sum5, sum10;
// sum2 is sum of numbers
// divisible by 2
sum2 = ((n / 2) * (4 +
(n / 2 - 1) * 2)) / 2;
// sum5 is sum of number
// divisible by 5
sum5 = ((n / 5) * (10 +
(n / 5 - 1) * 5)) / 2;
// sum10 of numbers divisible
// by 2 and 5
sum10 = ((n / 10) * (20 +
(n / 10 - 1) * 10)) / 2;
return sum2 + sum5 - sum10;
} // Driver code public static void Main ()
{ int n = 5;
Console.WriteLine(findSum(n));
} } // This code is contributed by inder_verma |
<?php // PHP implementation of above approach // Function to find the sum function findSum( $n )
{ // sum2 is sum of numbers
// divisible by 2
$sum2 = ((int)( $n / 2) * (4 +
((int)( $n / 2) - 1) * 2)) / 2;
// sum5 is sum of number
// divisible by 5
$sum5 = ((int)( $n / 5) * (10 +
( $n / 5 - 1) * 5)) / 2;
// sum10 of numbers divisible
// by 2 and 5
$sum10 = ((int)( $n / 10) * (20 +
( $n / 10 - 1) * 10)) / 2;
return $sum2 + $sum5 - $sum10 ;
} // Driver Code $n = 5;
echo findSum( $n );
// This code is contributed by Raj ?> |
<script> // Javascript implementation of above approach // Function to find the sum function findSum(n)
{ var sum2, sum5, sum10;
// sum2 is sum of numbers divisible by 2
sum2 = parseInt((parseInt(n / 2) *
(4 + (parseInt(n / 2) - 1) * 2)) / 2);
// sum5 is sum of number divisible by 5
sum5 = parseInt((parseInt(n / 5) *
(10 + (parseInt(n / 5) - 1) * 5)) / 2);
// sum10 of numbers divisible by 2 and 5
sum10 = parseInt((parseInt(n / 10) *
(20 + (parseInt(n / 10) - 1) * 10)) / 2);
return sum2 + sum5 - sum10;
} // Driver code var n = 5;
document.write( findSum(n)); </script> |
Output
11
Time Complexity: O(1)
Auxiliary Space: O(1)