The sequence first consists of all the odd numbers starting from 1 to n and then remaining even numbers starting 2 up to n. Let’s suppose we have n as 1000. Then the sequence becomes 1 3 5 7….999 2 4 6….1000
We are given a range (L, R), we need to find sum of numbers of this sequence in given range.
Note: Here the range is given as (L, R) L and R are included in the range
Input : n = 10 Range 1 6 Output : 27 Explanation: Sequence is 1 3 5 7 9 2 4 6 8 10 Sum in range (2, 6) = 1 + 3 + 5 + 7 + 9 + 2 = 27 Input : n = 5 Range 1 2 Output : 4 Explanation: sequence is 1 3 5 2 4 sum = 1 + 3 = 4
The idea is to first find sum of numbers before left(excluding left), then find sum of numbers before right (including right). We get result as second sum minus first sum.
How to find count of odd numbers?
- If n is odd then the number of odd numbers are ((n/2) + 1)
- If n is even then number of odd numbers are (n/2)
By simple observation, we get the number of odd numbers is ceil(n/2). So, the number of even numbers are n – ceil(n/2).
- Sum of first N odd numbers is (N^2)
- Sum of first N even numbers is (N^2) + N
For a given number x how will we find the sum in the sequence from 1 to x?
let’s suppose x is less than the number of odd numbers.
- Then we simply return (x*x)
If the x is greater then the number of odd numbers
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- Sum of cubes of first n odd natural numbers
- Sum of fourth powers of first n odd natural numbers
- Sum of fourth power of first n even natural numbers
- Check if a number has an odd count of odd divisors and even count of even divisors
- Count set bits in the Kth number after segregating even and odd from N natural numbers
- Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime
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- Sum of series formed by difference between product and sum of N natural numbers
- Sum of array elements that is first continuously increasing then decreasing
- Difference between sum of the squares of first n natural numbers and square of sum
- Sum of sum of all subsets of a set formed by first N natural numbers
- Difference between Sum of Cubes and Sum of First N Natural Numbers
- Check if a given number can be expressed as pair-sum of sum of first X natural numbers
- Count of N-digit Numbers having Sum of even and odd positioned digits divisible by given numbers