Given a number n, find the number of ways to represent this number as a sum of 2 or more consecutive natural numbers.
Input : n = 15 Output : 3 15 can be represented as: 1 + 2 + 3 + 4 + 5 4 + 5 + 6 7 + 8 Input :10 Output :2 10 can only be represented as: 1 + 2 + 3 + 4
We have already discussed one approach in below post.
Count ways to express a number as sum of consecutive numbers
Here a new approach is discussed. Suppose that we are talking about the sum of numbers from X to Y ie [X, X+1, …, Y-1, Y]
Then the arithmetic sum is
If this should be N, then
2N = (Y+X)(Y-X+1)
Note that one of the factors should be even and the other should be odd because Y-X+1 and Y+X should have opposite parity because Y-X and Y+X have the same parity. Since 2N is anyways even, we find the number of odd factors of N.
For example, n = 15 all odd factors of 15 are 1 3 and 5 so the answer is 3.
The Time complexity for this program is O(N^0.5).
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.
- Expressing factorial n as sum of consecutive numbers
- Expressing a fraction as a natural number under modulo 'm'
- Print all numbers whose set of prime factors is a subset of the set of the prime factors of X
- Maximum number of prime factors a number can have with exactly x factors
- Find number of factors of N when location of its two factors whose product is N is given
- Check if a number exists having exactly N factors and K prime factors
- Queries on sum of odd number digit sums of all the factors of a number
- Find sum of odd factors of a number
- Sum of all odd factors of numbers in the range [l, r]
- Number of elements with odd factors in given range
- Check whether count of odd and even factors of a number are equal
- First element of every K sets having consecutive elements with exactly K prime factors less than N
- Sum of Factors of a Number using Prime Factorization
- Generate an alternate odd-even sequence having sum of all consecutive pairs as a perfect square
- Count of integers in a range which have even number of odd digits and odd number of even digits
- Number of factors of very large number N modulo M where M is any prime number
- Sum of M maximum distinct digit sum from 1 to N that are factors of K
- Print numbers such that no two consecutive numbers are co-prime and every three consecutive numbers are co-prime
- Generate a Binary String without any consecutive 0's and at most K consecutive 1's
- Count possible binary strings of length N without P consecutive 0s and Q consecutive 1s
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.
Improved By : manishshaw1