Given an integer N, task is to find the numbers which when raised to the power of 2 and added finally, gives the integer N.
Input : 71307 Output : 0, 1, 3, 7, 9, 10, 12, 16 Explanation : 71307 = 2^0 + 2^1 + 2^3 + 2^7 + 2^9 + 2^10 + 2^12 + 2^16 Input : 1213 Output : 0, 2, 3, 4, 5, 7, 10 Explanation : 1213 = 2^0 + 2^2 + 2^3 + 2^4 + 2^5 + 2^7 + 2^10
Every number can be described in powers of 2.
Example : 29 = 2^0 + 2^2 + 2^3 + 2^4.
2^0 ( exponent of 2 is ‘0’) 0
2^2 ( exponent of 2 is ‘2’) 1
2^3 ( exponent of 2 is ‘3’) 3
2^4 ( exponent of 2 is ‘4’) 4
Convert each number into its binary equivalent by pushing remainder of given number, when divided by 2 till it is greater than 0, to vector. Now, Iterate through its binary equivalent and whenever there is set bit, just print the i-th value(iteration number).
Hamming Code : Hamming Code is an error correcting code which can detect and correct one bit error. This pattern is also used in Hamming code error detection where parity bits store the XOR of numbers on the basis of LSB(Least Significant bit), where numbers are assigned in blocks and you need to find the blocks where the sum of power of 2 resulting to given number exists. Below is the image to show the blocks with given numbers.
Below is the implementation of above approach :
Blocks for 71307 : 0, 1, 3, 7, 9, 10, 12, 16 Blocks for 1213 : 0, 2, 3, 4, 5, 7, 10 Blocks for 29 : 0, 2, 3, 4 Blocks for 100 : 2, 5, 6
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- Powers of 2 to required sum using Bit Masking
- Minimum number of given powers of 2 required to represent a number
- Minimum number of distinct powers of 2 required to express a given binary number
- Count of minimum reductions required to get the required sum K
- 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
- Find k numbers which are powers of 2 and have sum N | Set 1
- 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
- Represent n as the sum of exactly k powers of two | Set 2
- Print all integers that are sum of powers of two given numbers
- 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
- Count of numbers whose sum of increasing powers of digits is equal to the number itself
- Distinct powers of a number N such that the sum is equal to K
- Split N powers of 2 into two subsets such that their difference of sum is minimum
- Sum of first N natural numbers with all powers of 2 added twice
- Check if a number can be expressed as sum of two Perfect powers
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