Given two numbers N and K. The task is to print K numbers which are powers of 2 and their sum is N. Print -1 if not possible.
Input: N = 9, K = 4 Output: 4 2 2 1 4 + 2 + 2 + 1 = 9 Input: N = 4, K = 5 Output: -1
Approach: The below algorithm can be followed to solve the above problem:
- If the K is less than the number of set bits in N or more than the number of set bits in N, then it is not possible.
- Insert the powers of two at set bits into Priority Queue.
- Iterate in the Priority Queue till we get K elements, pop() the topmost element and
- Once K elements are achieved, print them.
element/2 twice into the Priority Queue again.
Below is the implementation of the above approach:
4 2 2 1
- Sum of first N natural numbers which are not powers of K
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- Count numbers in a range having GCD of powers of prime factors equal to 1
- Powers of 2 to required sum
- Represent n as the sum of exactly k powers of two | Set 2
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- Sum of largest divisible powers of p (a prime number) in a range
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