Given two integers N and K, the task is to find K consecutive integers such that their sum if N.
Note: If there is no such K integers print -1.
Input: N = 15, K = 5
Output: 1 2 3 4 5
N can be represented as sum of 5 consecutive integers as follows –
=> N => 1 + 2 + 3 + 4 + 5 = 15
Input: N = 33, K = 6
Output: 3 4 5 6 7 8
N can be represented as sum of 6 consecutive integers as follows –
=> N => 3 + 4 + 5 + 6 + 7 + 8 = 33
Naive Approach: A simple solution is to run a loop from i = 0 to N – (K – 1) to check if K consecutive integers starting from i is having sum as N.
Efficient Approach: The idea is to use Arithmetic Progression to solve this problem, where sum of K terms of arithmetic progression with common difference is 1 can be defined as follows –
- Sum of K Terms –
- Solving the equation further to get the first term possible
- Here aK is the Kth term which can be written as a1 + K – 1
- Finally, check the first term computed is an integer, If yes then K consecutive number exists whose sum if N.
Below is the implementation of the above approach:
3 4 5 6 7 8
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.
- Find the first N integers such that the sum of their digits is equal to 10
- Find any K distinct odd integers such that their sum is equal to N
- Count pairs from 1 to N such that their Sum is divisible by their XOR
- Possible values of Q such that, for any value of R, their product is equal to X times their sum
- Find three integers less than or equal to N such that their LCM is maximum
- Count of pairs in a given range with sum of their product and sum equal to their concatenated number
- Print numbers such that no two consecutive numbers are co-prime and every three consecutive numbers are co-prime
- Sum of product of all integers upto N with their count of divisors
- Rearrange an Array such that Sum of same-indexed subsets differ from their Sum in the original Array
- Find the pair (a, b) with minimum LCM such that their sum is equal to N
- Check if a number can be written as sum of three consecutive integers
- Number expressed as sum of five consecutive integers
- Remove two consecutive integers from 1 to N to make sum equal to S
- Check if N can be represented as sum of squares of two consecutive integers
- Count integers in a range which are divisible by their euler totient value
- Sort integers in array according to their distance from the element K
- Pair of integers having difference of their fifth power as X
- Find K numbers with sum equal to N and sum of their squares maximized
- Count ordered pairs of positive numbers such that their sum is S and XOR is K
- Print n numbers such that their sum is a perfect square
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.