← Microsoft Interview Insights
My first instinct was just greedy from the top, grab the largest power of two that fits and subtract.
Recognize that this is a shortest path problem on an infinite graph where each move adds or subtracts a power of two. Use BFS from 0 to target, but optimize by considering only powers of two up to the next power above target. Alternatively, derive a greedy or DP solution based on binary representation.
Pro tip: Mention that the problem can be solved in O(log target) time using a greedy approach that examines the binary representation and handles carries, similar to counting set bits but with the option to subtract. This shows you can optimize beyond brute force.
Confirm that operations are adding or subtracting any power of two (including 2^0=1) and that target is non-negative. Ask if there are constraints on target size.
View each integer as a node, with edges to n ± 2^k for all k ≥ 0. The problem reduces to finding the shortest path from 0 to target.
Since powers of two grow exponentially, only powers up to the smallest power of two greater than target are needed. BFS from 0 will find the minimum operations, but may be inefficient for large targets.
Observe that the optimal sequence corresponds to representing target in binary with digits -1, 0, 1 (signed binary). Use a greedy algorithm from least significant bit to most, deciding whether to add or subtract based on the bit and carry.
The greedy approach runs in O(log target) time and O(1) space. Handle target=0 (0 operations) and ensure the algorithm works for all non-negative integers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.