The Complete Guide to Solving Question 1: Methods, Code, and Logic

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Q1: Why is Question 1 usually solved with a hash map instead of two pointers?
A1: Two-pointer solutions require a sorted array. If the initial input is unsorted, sorting it scrambles the original array indexing. Preserving those original indices requires creating an array of index pairs, which uses O(n) memory and runs in O(n log n) time, slower than the O(n) hash map technique.

Q2: Can hash collisions degrade the time complexity of the optimal solution?
A2: Yes, in theoretical worst-case scenarios where all keys collide into the same bucket, lookup degrades to O(n), pushing overall time complexity to O(n²). However, standard Python dictionaries and modern hash tables use randomized seeding and robin-hood or open-addressing strategies that make this practically impossible under normal execution.

Q3: Does the single-pass solution work if the array contains multiple pairs that equal the target?
A3: The standard problem specification guarantees exactly one valid solution. If multiple pairs exist, the single-pass algorithm returns the first complete pair it encounters in traversal order. Handling all pairs requires returning a list of tuples and continuing the iteration across the entire array.