Given two integers N and K, the task is to find K distinct positive odd integers such that their sum is equal to the given number N.
Input: N = 10, K = 2
Output: 1 9
Two odd positive integers such that their sum is 10 can be (1, 9) or (3, 7).
Input: N = 10, K = 4
There does not exists four odd positive integers with sum 10.
The number N can be represented as the sum of K positive odd integers only is the following two conditions satisfies:
- If the square of K is less than or equal to N and,
- If the sum of N and K is an even number.
If these conditions are satisfied then there exist K positive odd integers whose sum is N.
To generate K such odd numbers:
- Print first K-1 odd numbers starting from 1, i.e. 1, 3, 5, 7, 9…….
- The last odd number will be : N – (Sum of first K-1 odd positive integers)
Below is the implementation of the above approach:
1 3 5 91
- Time Complexity: In the above-given approach, there is one loop which takes O(K) time in the worst case. Therefore, the time complexity for this approach will be O(K).
- Auxiliary Space: O(1)
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