Given a series of numbers 1, 2, 4, 3, 5, 7, 9, 6, 8, 10, 11, 13… The task is to find the sum of all the numbers in series till N-th number.
Examples:
Input: N = 4
Output: 10
1 + 2 + 4 + 3 = 10
Input: N = 10
Output: 55
Approach: The series is basically 20 odd numbers, 21 even numbers, 22 even numbers…. The sum of first N odd numbers is N * N and sum of first N even numbers is (N * (N+1)). Calculate the summation for 2i odd or even numbers and keep adding them to the sum.
Iterate for every power of 2, till the number of iterations exceeds N, and keep adding the respective summation of odd or even numbers according to the parity. For every segment the sum of the segment will be, (current sum of X odd/even numbers – previous sum of Y odd/even numbers), where X is the total sum of odd/even numbers till this segment and Y is the summation of odd/even numbers till the previous when odd/even numbers occurred.
Below is the implementation of the above approach:
// C++ program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the // sum of first N odd numbers int sumodd( int n)
{ return (n * n);
} // Function to find the // sum of first N even numbers int sumeven( int n)
{ return (n * (n + 1));
} // Function to overall // find the sum of series int findSum( int num)
{ // Initial odd numbers
int sumo = 0;
// Initial even numbers
int sume = 0;
// First power of 2
int x = 1;
// Check for parity
// for odd/even
int cur = 0;
// Counts the sum
int ans = 0;
while (num > 0) {
// Get the minimum
// out of remaining num
// or power of 2
int inc = min(x, num);
// Decrease that much numbers
// from num
num -= inc;
// If the segment has odd numbers
if (cur == 0) {
// Summate the odd numbers
// By exclusion
ans = ans + sumodd(sumo + inc) - sumodd(sumo);
// Increase number of odd numbers
sumo += inc;
}
// If the segment has even numbers
else {
// Summate the even numbers
// By exclusion
ans = ans + sumeven(sume + inc) - sumeven(sume);
// Increase number of even numbers
sume += inc;
}
// Next set of numbers
x *= 2;
// Change parity for odd/even
cur ^= 1;
}
return ans;
} // Driver code int main()
{ int n = 4;
cout << findSum(n);
return 0;
} |
// Java program to implement // the above approach class GFG
{ // Function to find the
// sum of first N odd numbers
static int sumodd( int n)
{
return (n * n);
}
// Function to find the
// sum of first N even numbers
static int sumeven( int n)
{
return (n * (n + 1 ));
}
// Function to overall
// find the sum of series
static int findSum( int num)
{
// Initial odd numbers
int sumo = 0 ;
// Initial even numbers
int sume = 0 ;
// First power of 2
int x = 1 ;
// Check for parity
// for odd/even
int cur = 0 ;
// Counts the sum
int ans = 0 ;
while (num > 0 )
{
// Get the minimum
// out of remaining num
// or power of 2
int inc = Math.min(x, num);
// Decrease that much numbers
// from num
num -= inc;
// If the segment has odd numbers
if (cur == 0 )
{
// Summate the odd numbers
// By exclusion
ans = ans + sumodd(sumo + inc) - sumodd(sumo);
// Increase number of odd numbers
sumo += inc;
}
// If the segment has even numbers
else
{
// Summate the even numbers
// By exclusion
ans = ans + sumeven(sume + inc) - sumeven(sume);
// Increase number of even numbers
sume += inc;
}
// Next set of numbers
x *= 2 ;
// Change parity for odd/even
cur ^= 1 ;
}
return ans;
}
// Driver code
public static void main(String[] args)
{
int n = 4 ;
System.out.println(findSum(n));
}
} // This code contributed by Rajput-Ji |
# Python3 program to implement # the above approach # Function to find the # sum of first N odd numbers def sumodd(n):
return (n * n)
# Function to find the # sum of first N even numbers def sumeven(n):
return (n * (n + 1 ))
# Function to overall # find the sum of series def findSum(num):
# Initial odd numbers
sumo = 0
# Initial even numbers
sume = 0
# First power of 2
x = 1
# Check for parity
# for odd/even
cur = 0
# Counts the sum
ans = 0
while (num > 0 ):
# Get the minimum
# out of remaining num
# or power of 2
inc = min (x, num)
# Decrease that much numbers
# from num
num - = inc
# If the segment has odd numbers
if (cur = = 0 ):
# Summate the odd numbers
# By exclusion
ans = ans + sumodd(sumo + inc) - sumodd(sumo)
# Increase number of odd numbers
sumo + = inc
# If the segment has even numbers
else :
# Summate the even numbers
# By exclusion
ans = ans + sumeven(sume + inc) - sumeven(sume)
# Increase number of even numbers
sume + = inc
# Next set of numbers
x * = 2
# Change parity for odd/even
cur ^ = 1
return ans
# Driver code n = 4
print (findSum(n))
# This code is contributed by mohit kumar |
// C# program to implement // the above approach using System;
class GFG
{ // Function to find the
// sum of first N odd numbers
static int sumodd( int n)
{
return (n * n);
}
// Function to find the
// sum of first N even numbers
static int sumeven( int n)
{
return (n * (n + 1));
}
// Function to overall
// find the sum of series
static int findSum( int num)
{
// Initial odd numbers
int sumo = 0;
// Initial even numbers
int sume = 0;
// First power of 2
int x = 1;
// Check for parity
// for odd/even
int cur = 0;
// Counts the sum
int ans = 0;
while (num > 0)
{
// Get the minimum
// out of remaining num
// or power of 2
int inc = Math.Min(x, num);
// Decrease that much numbers
// from num
num -= inc;
// If the segment has odd numbers
if (cur == 0)
{
// Summate the odd numbers
// By exclusion
ans = ans + sumodd(sumo + inc) - sumodd(sumo);
// Increase number of odd numbers
sumo += inc;
}
// If the segment has even numbers
else
{
// Summate the even numbers
// By exclusion
ans = ans + sumeven(sume + inc) - sumeven(sume);
// Increase number of even numbers
sume += inc;
}
// Next set of numbers
x *= 2;
// Change parity for odd/even
cur ^= 1;
}
return ans;
}
// Driver code
public static void Main(String[] args)
{
int n = 4;
Console.WriteLine(findSum(n));
}
} // This code has been contributed by 29AjayKumar |
<?php // PHP program to implement // the above approach // Function to find the // sum of first N odd numbers function sumodd( $n )
{ return ( $n * $n );
} // Function to find the // sum of first N even numbers function sumeven( $n )
{ return ( $n * ( $n + 1));
} // Function to overall // find the sum of series function findSum( $num )
{ // Initial odd numbers
$sumo = 0;
// Initial even numbers
$sume = 0;
// First power of 2
$x = 1;
// Check for parity
// for odd/even
$cur = 0;
// Counts the sum
$ans = 0;
while ( $num > 0)
{
// Get the minimum
// out of remaining num
// or power of 2
$inc = min( $x , $num );
// Decrease that much numbers
// from num
$num -= $inc ;
// If the segment has odd numbers
if ( $cur == 0)
{
// Summate the odd numbers
// By exclusion
$ans = $ans + sumodd( $sumo + $inc ) -
sumodd( $sumo );
// Increase number of odd numbers
$sumo += $inc ;
}
// If the segment has even numbers
else
{
// Summate the even numbers
// By exclusion
$ans = $ans + sumeven( $sume + $inc ) -
sumeven( $sume );
// Increase number of even numbers
$sume += $inc ;
}
// Next set of numbers
$x *= 2;
// Change parity for odd/even
$cur ^= 1;
}
return $ans ;
} // Driver code $n = 4;
echo findSum( $n );
// This code contributed by princiraj1992 ?> |
<script> // javascript program to implement // the above approach // Function to find the // sum of first N odd numbers function sumodd( n)
{ return (n * n);
} // Function to find the // sum of first N even numbers function sumeven( n)
{ return (n * (n + 1));
} // Function to overall // find the sum of series function findSum( num)
{ // Initial odd numbers
let sumo = 0;
// Initial even numbers
let sume = 0;
// First power of 2
let x = 1;
// Check for parity
// for odd/even
let cur = 0;
// Counts the sum
let ans = 0;
while (num > 0) {
// Get the minimum
// out of remaining num
// or power of 2
let inc = Math.min(x, num);
// Decrease that much numbers
// from num
num -= inc;
// If the segment has odd numbers
if (cur == 0) {
// Summate the odd numbers
// By exclusion
ans = ans + sumodd(sumo + inc) - sumodd(sumo);
// Increase number of odd numbers
sumo += inc;
}
// If the segment has even numbers
else {
// Summate the even numbers
// By exclusion
ans = ans + sumeven(sume + inc) - sumeven(sume);
// Increase number of even numbers
sume += inc;
}
// Next set of numbers
x *= 2;
// Change parity for odd/even
cur ^= 1;
}
return ans;
} // Driver code let n = 4;
document.write( findSum(n));
// This code is contributed by todaysgaurav </script> |
10
Time Complexity: O(n) because using inbuilt function min
Auxiliary Space: O(1)