Given two positive integers A and B, we can change at most K bits in both the numbers to make OR of them equal to a given target number T. In the case of multiple solutions try to keep A as small as possible.
Input : A = 175, B = 66, T = 100, K = 5 Output : A = 36 B = 64 Initial bits of A = 1010 1111 Changed bits of A = 0010 0100 Initial bits of B = 0100 0010 Changed bits of B = 0100 0000 OR of changed Bits = 0110 0100 Which has decimal value equal to Target T. Input : A = 175, B = 66, T = 100, K = 4 Output : Not Possible It is not possible to get OR of A and B as T, just by changing K bits.
We can solve this problem by iterating over all bits of A and B and greedily changing them that is,
- If i-th bit of Target T is 0 then set i-th bits of A and B to 0 (if not already)
- If i-th bit of Target T is 1 then we will try to set one of the bits to 1 and we will change i-th bit of B only to 1(if not already) to minimize A.
After above procedure, if changed bits are more than K, then it is not possible to get OR of A and B as T by changing at most K bits.
If changed bits are less than k, then we can further minimize the value of A by using remaining value of K for which we will loop over bits one more time and if at any time,
- i-th A bit is 1 and i-th B bit is 0 then we will make 2 changes and flip both.
- i-th A and B bits are 1 then again we will make 1 change and flip A’s bit.
Total time complexity of above solution will be O(max number of bits).
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Improved By : jit_t