Maintain pair-sum counts under replacements
Problem Description
You are given two integer arrays, A and B, and a list of operations to perform.
The supported operations are:
- Query(T): Return the number of pairs
(i, j)such thatA[i] + B[j] = T. - Replace(idx, val): Update the array
Bby settingB[idx] = val.
You must design a data structure that efficiently supports these operations for very large inputs. After processing all operations, return an array containing the results of each Query operation in the order they were performed.
Example
A = [1, 3]B = [2, 4]- Operations:
Query(5),Replace(0, 3),Query(6)
Expected Output: [2, 1]
Requirements
- Design a data structure to support very large inputs efficiently.
- State the time and space complexity of your approach.
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Core dilemma
Balancing efficient query performance (finding sum pairs) with the cost of updates to one of the contributing arrays. The challenge is to maintain pre-computed information or an optimized lookup structure for B's values, while ensuring that 'Replace' operations don't invalidate or make that structure prohibitively expensive to update.
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Maintain pair-sum counts under replacements
Problem Description
You are given two integer arrays, A and B, and a list of operations to perform.
The supported operations are:
- Query(T): Return the number of pairs
(i, j)such thatA[i] + B[j] = T. - Replace(idx, val): Update the array
Bby settingB[idx] = val.
You must design a data structure that efficiently supports these operations for very large inputs. After processing all operations, return an array containing the results of each Query operation in the order they were performed.
Example
A = [1, 3]B = [2, 4]- Operations:
Query(5),Replace(0, 3),Query(6)
Expected Output: [2, 1]
Requirements
- Design a data structure to support very large inputs efficiently.
- State the time and space complexity of your approach.