Started with divide and conquer, recursively narrowing down ranges using the query function.
Clarify the problem constraints and the nature of the query function, then propose an efficient algorithm that leverages the query to locate all 1s without scanning the entire array. Discuss trade-offs between different approaches and analyze time and space complexity.
Pro tip: Demonstrate awareness of real-world constraints by discussing how to handle large sparse arrays and the cost of queries, and mention that the optimal strategy depends on the sparsity and query cost.
Ask about the size of the bit array, the number of 1s, the cost of the query function, and whether the array is static or dynamic. Confirm that the query function returns a boolean indicating if any 1 exists in a given subrange.
Discuss the naive linear scan and its inefficiency for sparse arrays. Then propose a divide-and-conquer or binary search approach that uses the query function to prune empty ranges.
Outline a recursive algorithm: for a given range, if the query returns false, stop; if true and the range is a single element, record the position; otherwise, split the range and recurse on both halves. Alternatively, use binary search to find the next 1.
Derive the time complexity in terms of the number of queries and the number of 1s. For divide-and-conquer, it's O(k log n) queries where k is the number of 1s. Discuss space complexity of recursion.
Compare with other methods like segment trees or bitset operations. Address edge cases: no 1s, all 1s, single element, and large ranges. Mention potential optimizations like iterative deepening or using the query to skip large empty blocks.
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