Given a number N, write a function to express N as sum of two or more consecutive positive numbers. If there is no solution, output -1. If there are multiple solution, then print one of them.
Input : N = 10 Output : 4 + 3 + 2 + 1 Input : N = 8 Output : -1 Input : N = 24 Output : 9 + 8 + 7
Sum of first n natural numbers = n * (n + 1)/2 Sum of first (n + k) numbers = (n + k) * (n + k + 1)/2 If N is sum of k consecutive numbers, then following must be true. N = [(n+k)(n+k+1) - n(n+1)] / 2 OR 2 * N = [(n+k)(n+k+1) - n(n+1)]
Below is the implementation based on above idea.
12 = 3 + 4 + 5
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Improved By : nitin mittal