Count integers up to N which can be represented as sum of two or more consecutive numbers

Given a positive integer N, the task is to count the number of integers upto N which can be represented as the sum of two or more consecutive numbers.

Examples:

Input: N = 7
Output: 4
Explanation: In the range [1, 7]: {3, 5, 6, 7} can be represented as sum of consecutive numbers.

• 3 = 1 + 2
• 5 = 2 + 3
• 6 = 1 + 2 + 3
• 7 = 3 + 4

Input: N = 15
Output: 11

Naive Approach: Follow the steps below to solve the problem:

1. Iterate over all integers in the range [1, N] and for each integer, check if it can be represented as the sum of two or more consecutive integers or not.
2. To check whether a number can be expressed as the sum of two or more consecutive numbers or not, refer to this article.

Below is the implementation of the above approach:

C++

// C++ Program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to check if the number N
// can be expressed as sum of 2 or
// more consecutive numbers or not
bool isPossible(int N)
{
    return ((N & (N - 1)) && N);
}

// Function to count integers in the range
// [1, N] that can be expressed as sum of
// 2 or more consecutive numbers
void countElements(int N)
{
    // Stores the required count
    int count = 0;

    for (int i = 1; i <= N; i++) {

        if (isPossible(i))
            count++;
    }
    cout << count;
}
// Driver Code
int main()
{
    int N = 15;
    countElements(N);

    return 0;
}

Java

// Java program of the above approach
import java.io.*;
class GFG
{

// Function to check if the number N
// can be expressed as sum of 2 or
// more consecutive numbers or not
static int isPossible(int N)
{
    return (((N & (N - 1)) & N));
}

// Function to count integers in the range
// [1, N] that can be expressed as sum of
// 2 or more consecutive numbers
static void countElements(int N)
{

    // Stores the required count
    int count = 0;
    for (int i = 1; i <= N; i++)
    {
        if (isPossible(i) != 0)
            count++;
    }
    System.out.println(count);
}

// Driver Code
    public static void main(String[] args)
{
    int N = 15;
    countElements(N);
}
}

// This code is contributed by jana_sayantan.

Python3

# Python3 Program to implement
# the above approach

# Function to check if the number N
# can be expressed as sum of 2 or
# more consecutive numbers or not
def isPossible(N):
    return ((N & (N - 1)) and N)

# Function to count integers in the range
# [1, N] that can be expressed as sum of
# 2 or more consecutive numbers
def countElements(N):

    # Stores the required count
    count = 0
    for i in range(1, N + 1):
        if (isPossible(i)):
            count += 1

    print (count)

# Driver Code
if __name__ == '__main__':
    N = 15
    countElements(N)

    # This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
class GFG
{

// Function to check if the number N
// can be expressed as sum of 2 or
// more consecutive numbers or not
static int isPossible(int N)
{
    return (((N & (N - 1)) & N));
}

// Function to count integers in the range
// [1, N] that can be expressed as sum of
// 2 or more consecutive numbers
static void countElements(int N)
{

    // Stores the required count
    int count = 0;
    for (int i = 1; i <= N; i++)
    {
        if (isPossible(i) != 0)
            count++;
    }
    Console.Write(count);
}

// Driver Code
static public void Main()
{
    int N = 15;
    countElements(N);
}
}

// This code is contributed by code_hunt.

Javascript

<script>

// JavaScript program of the above approach

    // Function to check if the number N
    // can be expressed as sum of 2 or
    // more consecutive numbers or not
    function isPossible(N) {
        return (((N & (N - 1)) & N));
    }

    // Function to count integers in the range
    // [1, N] that can be expressed as sum of
    // 2 or more consecutive numbers
    function countElements(N) {

        // Stores the required count
        var count = 0;
        for (i = 1; i <= N; i++) {
            if (isPossible(i) != 0)
                count++;
        }
        document.write(count);
    }

    // Driver Code

        var N = 15;
        countElements(N);

// This code contributed by Rajput-Ji

</script>

Output:

11

Time Complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, follow the steps below to solve the problem 

1. All numbers except the ones which are powers of 2 can be expressed as a sum of consecutive numbers.
2. Count the number of powers of 2 ≤ N and store it in a variable, k say Count
3. Print (N – Count) as the required answer.

Below is the implementation of the above approach:

C++

// C++ implementation
// of the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to count integers in the range
// [1, N] that can be expressed as sum of
// 2 or more consecutive numbers
void countElements(int N)
{
    int Cur_Ele = 1;
    int Count = 0;

    // Count powers of 2 up to N
    while (Cur_Ele <= N) {

        // Increment count
        Count++;

        // Update current power of 2
        Cur_Ele = Cur_Ele * 2;
    }

    cout << N - Count;
}

// Driver Code
int main()
{
    int N = 15;
    countElements(N);

    return 0;
}

Java

// Java implementation
// of the above approach
import java.util.*;
class GFG
{

  // Function to count integers in the range
  // [1, N] that can be expressed as sum of
  // 2 or more consecutive numbers
  static void countElements(int N)
  {
    int Cur_Ele = 1;
    int Count = 0;

    // Count powers of 2 up to N
    while (Cur_Ele <= N)
    {

      // Increment count
      Count++;

      // Update current power of 2
      Cur_Ele = Cur_Ele * 2;
    }

    System.out.print(N - Count);
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 15;
    countElements(N);
  }
}

// This code is contributed by shikhasingrajput

Python3

# python 3 implementation
# of the above approach

# Function to count integers in the range
# [1, N] that can be expressed as sum of
# 2 or more consecutive numbers
def countElements(N):
    Cur_Ele = 1
    Count = 0

    # Count powers of 2 up to N
    while (Cur_Ele <= N):
        # Increment count
        Count += 1

        # Update current power of 2
        Cur_Ele = Cur_Ele * 2

    print(N - Count)

# Driver Code
if __name__ == '__main__':
    N = 15
    countElements(N)

C#

// C# implementation
// of the above approach
using System;

public class GFG
{

  // Function to count integers in the range
  // [1, N] that can be expressed as sum of
  // 2 or more consecutive numbers
  static void countElements(int N)
  {
    int Cur_Ele = 1;
    int Count = 0;

    // Count powers of 2 up to N
    while (Cur_Ele <= N)
    {

      // Increment count
      Count++;

      // Update current power of 2
      Cur_Ele = Cur_Ele * 2;
    }

    Console.Write(N - Count);
  }

  // Driver Code
  public static void Main(String[] args)
  {
    int N = 15;
    countElements(N);
  }
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript implementation
// of the above approach

// Function to count integers in the range
// [1, N] that can be expressed as sum of
// 2 or more consecutive numbers
function countElements(N)
{
    var Cur_Ele = 1;
    var Count = 0;

    // Count powers of 2 up to N
    while (Cur_Ele <= N)
    {

        // Increment count
        Count++;

        // Update current power of 2
        Cur_Ele = Cur_Ele * 2;
    }
    document.write(N - Count);
}

// Driver Code
var N = 15;

countElements(N);

// This code is contributed by todaysgaurav

</script>

Output:

11

Time Complexity: O(log(N))
Auxiliary Space: O(1)