Skip to content
Related Articles
Remove two consecutive integers from 1 to N to make sum equal to S
• Last Updated : 10 Jan, 2020

Given a sum S and an integer N, The task is to remove two consecutive integers from 1 to N to make sum equal to S.

Examples:

```Input: N = 4, S = 3
Output: Yes
sum(1, 2, 3, 4) = 10,
remove 3 and 4 from 1 to N
now sum(1, 2) = 3 = S
Hence by removing 3 and 4 we got sum = S

Input: N = 5, S =3
Output: No
Its not possible to remove two elements
from 1 to N such that new sum is 3
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

• Method 1:
• Create an array with elements from 1 to N.
• Each time remove two consecutive elements and check the difference between sum of N natural numbers and sum of two removed elements is S.
• sum of N natural numbers can be calculated using formula
`sum = (n)(n + 1) / 2`
```Time complexity: O(n)
Space complexity: O(n)
```
• Method 2:
• We know that, sum of N natural numbers can be calculated using formula
`sum = (n)(n + 1) / 2`
• According to the problem statement, we need to remove two integers from 1 to N such that the sum of remaining integers is S.
• Let the two consecutive integers to be removed be i and i + 1.
• Therefore,
```required sum = S = (n)(n + 1) / 2 - (i) - (i + 1)
S = (n)(n + 1) / 2 - (2i - 1)

Therefore,
i = ((n)(n + 1) / 4) - ((S + 1) / 2)
```
• Hence find i using above formula
• if i is an integer, then answer is Yes else No

Below is the implementation of the above approach:

## C++

 `// C++ program remove two consecutive integers``// from 1 to N to make sum equal to S`` ` `#include ``using` `namespace` `std;`` ` `// Function to find the numbers``// to be removed``float` `findNumber(``int` `N, ``int` `S)``{`` ` `    ``// typecast appropriately``    ``// so that answer is float``    ``float` `i = (((``float``)(N) * (``float``)(N + 1)) / 4)``              ``- ((``float``)(S + 1) / 2);`` ` `    ``// return the obtained result``    ``return` `i;``}`` ` `void` `check(``int` `N, ``int` `S)``{`` ` `    ``float` `i = findNumber(N, S);`` ` `    ``// Convert i to integer``    ``int` `integerI = (``int``)i;`` ` `    ``// If i is an integer is 0``    ``// then answer is Yes``    ``if` `(i - integerI == 0)``        ``cout << ``"Yes: "``             ``<< integerI << ``", "``             ``<< integerI + 1``             ``<< endl;``    ``else``        ``cout << ``"No"``             ``<< endl;``}`` ` `// Driver code``int` `main()``{`` ` `    ``int` `N = 4, S = 3;``    ``check(N, S);`` ` `    ``N = 5, S = 3;``    ``check(N, S);`` ` `    ``return` `0;``}`

## Java

 `// Java program remove two consecutive integers ``// from 1 to N to make sum equal to S `` ` `class` `GFG ``{``     ` `    ``// Function to find the numbers ``    ``// to be removed ``    ``static` `float` `findNumber(``int` `N, ``int` `S) ``    ``{ ``     ` `        ``// typecast appropriately ``        ``// so that answer is float ``        ``float` `i = (((``float``)(N) * (``float``)(N + ``1``)) / ``4``) ``                ``- ((``float``)(S + ``1``) / ``2``); ``     ` `        ``// return the obtained result ``        ``return` `i; ``    ``} ``     ` `    ``static` `void` `check(``int` `N, ``int` `S) ``    ``{ ``     ` `        ``float` `i = findNumber(N, S); ``     ` `        ``// Convert i to integer ``        ``int` `integerI = (``int``)i; ``     ` `        ``// If i is an integer is 0 ``        ``// then answer is Yes ``        ``if` `(i - integerI == ``0``) ``            ``System.out.println(``"Yes: "` `+ integerI + ``                                ``", "` `+ (integerI + ``1``)) ;``        ``else``            ``System.out.println(``"No"``);``    ``} ``     ` `    ``// Driver code ``    ``public` `static` `void` `main (String[] args)``    ``{ ``     ` `        ``int` `N = ``4``, S = ``3``; ``        ``check(N, S); ``     ` `        ``N = ``5``; S = ``3``; ``        ``check(N, S); `` ` `    ``} ``}`` ` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program remove two consecutive integers ``# from 1 to N to make sum equal to S `` ` `# Function to find the numbers ``# to be removed ``def` `findNumber(N, S) :`` ` `    ``# typecast appropriately ``    ``# so that answer is float ``    ``i ``=` `(((N) ``*` `(N ``+` `1``)) ``/` `4``) ``-` `((S ``+` `1``) ``/` `2``); `` ` `    ``# return the obtained result ``    ``return` `i; `` ` `def` `check(N, S) :`` ` `    ``i ``=` `findNumber(N, S); `` ` `    ``# Convert i to integer ``    ``integerI ``=` `int``(i); `` ` `    ``# If i is an integer is 0 ``    ``# then answer is Yes ``    ``if` `(i ``-` `integerI ``=``=` `0``) :``        ``print``(``"Yes:"``, integerI,``                 ``","``, integerI ``+` `1``); ``    ``else` `:``        ``print``(``"No"``);`` ` `# Driver code ``if` `__name__ ``=``=` `"__main__"` `: `` ` `    ``N ``=` `4``;``    ``S ``=` `3``; ``    ``check(N, S); `` ` `    ``N ``=` `5``;``    ``S ``=` `3``; ``    ``check(N, S); `` ` `# This code is contributed by AnkitRai01`

## C#

 `// C# program remove two consecutive integers ``// from 1 to N to make sum equal to S ``using` `System;`` ` `class` `GFG ``{ ``     ` `    ``// Function to find the numbers ``    ``// to be removed ``    ``static` `float` `findNumber(``int` `N, ``int` `S) ``    ``{ ``     ` `        ``// typecast appropriately ``        ``// so that answer is float ``        ``float` `i = (((``float``)(N) * (``float``)(N + 1)) / 4) ``                ``- ((``float``)(S + 1) / 2); ``     ` `        ``// return the obtained result ``        ``return` `i; ``    ``} ``     ` `    ``static` `void` `check(``int` `N, ``int` `S) ``    ``{ ``        ``float` `i = findNumber(N, S); ``     ` `        ``// Convert i to integer ``        ``int` `integerI = (``int``)i; ``     ` `        ``// If i is an integer is 0 ``        ``// then answer is Yes ``        ``if` `(i - integerI == 0) ``            ``Console.WriteLine(``"Yes: "` `+ integerI + ``                                ``", "` `+ (integerI + 1)) ; ``        ``else``            ``Console.WriteLine(``"No"``); ``    ``} ``     ` `    ``// Driver code ``    ``public` `static` `void` `Main() ``    ``{ ``     ` `        ``int` `N = 4, S = 3; ``        ``check(N, S); ``     ` `        ``N = 5; S = 3; ``        ``check(N, S); ``    ``} ``} `` ` `// This code is contributed by AnkitRai01 `
Output:
```Yes: 3, 4
No
```

Time complexity: O(1)
Space complexity: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up