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Consecutive Numbers Sum - Leetcode Solution
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LeetCode: Consecutive Numbers Sum Leetcode Solution
Difficulty: Hard
Topics: math
Problem Statement: Given an integer N, you need to find the number of ways to represent it as a sum of two or more consecutive positive integers.
Example:
Input: N = 15
Output: 4
Explanation: 15 can be represented as: 1+2+3+4+5 = 15 4+5+6 = 15 7+8 = 15 15 = 15
Solution:
We can solve this problem efficiently by using the concept of arithmetic progression. An arithmetic progression is a sequence of numbers in which each element differs from the previous one by a constant value called the common difference.
Suppose we want to represent N as the sum of a consecutive sequence of k numbers, starting from x. Then the sum of this sequence can be represented as:
sum = kx + k(k-1)/2
We need to find the values of x and k such that this equation is satisfied and the sum is equal to N. Rearranging the equation, we get:
x = (N - k*(k-1)/2)/k
We can iterate over all possible values of k and calculate the corresponding value of x. If x is an integer, we have found a valid sequence.
Here is the code to implement this solution:
class Solution:
def consecutiveNumbersSum(self, N: int) -> int:
count = 0
for k in range(1, N+1):
# calculate x using the formula
x = (N - k*(k-1)//2) / k
# check if x is an integer and greater than 0
if x.is_integer() and x > 0:
count += 1
return count
Time Complexity: O(N) as we are iterating over all possible values of k.
Space Complexity: O(1) as we are not using any extra space.
This solution gives us the number of ways to represent N as the sum of two or more consecutive positive integers.
Consecutive Numbers Sum Solution Code
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