Given two numbers n and k, we need to find the minimum number of flips required to maximize given number by flipping its bits such that the resulting number has exactly k set bits.
Note : K must be less than number of bits in n.
Input : n = 14, k = 2 Output : Min Flips = 1 Explanation : Binary representation of 14 = 1110 Largest 4-digit Binary number with 2 set bit = 1100 Conversion from 1110 to 1100 requires 1 flipping Input : n = 145, k = 4 Output : Min Flips = 3 Explanation : Binary representation of 145 = 10010001 Largest 8-digit Binary number with 4 set bit = 11110000 Conversion from 10010001 to 11110000 requires 3 flipping
For the given number n and k find the largest number possible with k-set bits and having exactly same number of bits as n has as :
- size = log2(n) + 1 gives the number of bits of n.
- max = pow(2, k) – 1 gives largest possible number with k bits.
- max = max << (size – k) gives the largest number possible with k-set bits and having exactly same number of bits as n has
- Number of set bit in (n XOR max ) is our required number of flipping.
Illustration of above approach :
let n = 145 (10010001), k = 4 size = log2(n) + 1 = log2(145) + 1 = 7 + 1 = 8 max = pow(2, k) -1 = pow(2, 4) - 1 = 16 - 1 = 15 (1111) max = max << (size - k) = 15 << (8 - 4) = 240 (11110000) number of set bit in = no. of set bit in (n XOR max ) (145 ^ 240 ) = 3
Min Flips = 3
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