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My first instinct was to just iterate from each query index to the end and track the max and count.
Clarify the problem and constraints, then propose an efficient solution using a monotonic stack to compute for each index the range where it is the maximum, and a hash map to count occurrences of each value. For each query, return the count associated with the maximum value in the subarray starting at that index, which can be precomputed by processing indices from right to left.
Pro tip: Mention that the solution can be optimized to O(n) preprocessing and O(1) per query by leveraging the fact that the maximum of a suffix starting at i is non-increasing as i increases, and using a monotonic stack to find the next greater element. This shows you can handle large inputs efficiently.
Restate the problem in your own words and ask clarifying questions about constraints, input size, and expected output format. Confirm that queries are 0-indexed and that the subarray starts at the given index and extends to the end of the array.
Acknowledge that a naive approach would iterate over each query, find the maximum in the subarray, and count its occurrences, resulting in O(n) per query and O(n*q) overall. This is acceptable only for small inputs.
Use a monotonic stack to compute for each index the range where it is the maximum (or the next greater element to the right). Then, for each index, determine the maximum value of the suffix starting there and the count of that maximum in the suffix. Precompute these for all indices in O(n) time.
Process indices from right to left. Maintain a stack of indices with decreasing values. For each index i, pop elements smaller than arr[i] to find the next greater element. The maximum of the suffix starting at i is either arr[i] (if it's greater than the next greater element's value) or the maximum of the suffix starting at the next greater index. The count is updated accordingly. Store the result for each index.
The preprocessing takes O(n) time and O(n) space. Each query is answered in O(1) by looking up the precomputed result. Discuss edge cases such as empty array, single element, all equal elements, and queries out of bounds.
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