Given two integers n and k, the task is to find whether it is possible to represent n as the sum of exactly k powers of 2. If possible then print k positive integers such that they are powers of 2 and their sum is exactly equal to n else print Impossible.
Input: n = 9, k = 4
Output: 1 2 2 4
1, 2 and 4 are all powers of 2 and 1 + 2 + 2 + 4 = 9.
Input: n = 3, k = 7
It is impossible since 3 cannot be represented as sum of 7 numbers which are powers of 2.
We have discussed one approach to solve this problem in Find k numbers which are powers of 2 and have sum N. In this post, a different approach is being discussed.
- Create an array arr of size k with all elements initialized to 1 and create a variable sum = k.
- Now starting from the last element of arr
- If sum + arr[i] ≤ n then update sum = sum + arr[i] and arr[i] = arr[i] * 2.
- Else skip the current element.
- If sum = n then the contents of arr are the required elements.
- Else it is impossible to represent n as exactly k powers of 2.
Below is the implementation of the above approach:
1 1 1 1 4 4
- Minimum number of given powers of 2 required to represent a number
- Represent K^N as the sum of exactly N numbers
- Add two integers of different base and represent sum in smaller base of the two
- Print all integers that are sum of powers of two given numbers
- Split N powers of 2 into two subsets such that their difference of sum is minimum
- Check if a number can be expressed as sum of two Perfect powers
- Represent the given number as the sum of two composite numbers
- Find k numbers which are powers of 2 and have sum N | Set 1
- Powers of two and subsequences
- Last two digits of powers of 7
- Represent the fraction of two numbers in the string format
- Sum of fourth powers of the first n natural numbers
- Sum of fifth powers of the first n natural numbers
- Sum of fourth powers of first n odd natural numbers
- Sum of largest divisible powers of p (a prime number) in a range
- Powers of 2 to required sum
- Sum of first N natural numbers by taking powers of 2 as negative number
- Sum of first N natural numbers which are not powers of K
- Check if a number can be represented as sum of non zero powers of 2
- Find the sum of numbers from 1 to n excluding those which are powers of K
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