x402 Gateway – OpenAI o4-mini (Fast Reasoning)

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    {
      "role": "user",
      "content": "Given a list of integers [3, 1, 4, 1, 5, 9], write a Python function that returns all pairs summing to 10 and explain the time complexity."
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  "content": "Here’s a simple O(n)-time, O(n)-space solution using a hash set to find all unique pairs that sum to a given target (10 in your example):\n\n```python\ndef find_pairs(arr, target):\n    seen = set()      # numbers we’ve seen so far\n    pairs = set()     # store result pairs as (small, large) to avoid dupes\n\n    for x in arr:\n        y = target - x\n        if y in seen:\n            # order the pair so (1,9) and (9,1) aren’t counted separately\n            pairs.add((min(x, y), max(x, y)))\n        seen.add(x)\n\n    # convert set of tuples to a list if you like\n    return list(pairs)\n\n# Example\nnums = [3, 1, 4, 1, 5, 9]\nprint(find_pairs(nums, 10))   # [(1, 9)]\n```\n\nExplanation of time complexity:\n\n- We loop over the list once: O(n) iterations.\n- Each iteration does at most two set operations (`in`-check and `add`), each O(1) on average.\n- So total time is O(n).  \n- We use O(n) extra space for the `seen` set (and up to O(n) for the result set in the worst"
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