Create product_except_self.py

Python/algorithms/mathematical/product_except_self.py

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+from typing import List
+
+def product_except_self(nums: List[int]) -> List[int]:
+    """
+    Returns an array `ans` where ans[i] is the product of all elements of
+    `nums` except nums[i], without using division and in O(n) time.
+
+    This implementation uses O(1) extra space (ignoring the output array)
+    by:
+      1. Building prefix products directly into the output array.
+      2. Scanning from right to left and multiplying by a running suffix product.
+
+    Time Complexity: O(n)
+    Space Complexity: O(1) extra (output array not counted)
+
+    Args:
+        nums: List[int] - input list of integers (length >= 1)
+
+    Returns:
+        List[int] - product array as described above
+
+    Example:
+        >>> product_except_self([1,2,3,4])
+        [24, 12, 8, 6]
+    """
+    n = len(nums)
+    if n == 0:
+        return []
+
+    # ans[i] will hold product of nums[0..i-1] after first pass
+    ans = [1] * n
+    for i in range(1, n):
+        ans[i] = ans[i - 1] * nums[i - 1]
+
+    # suffix holds product of nums[i+1..n-1]
+    suffix = 1
+    for i in range(n - 1, -1, -1):
+        ans[i] *= suffix
+        suffix *= nums[i]
+
+    return ans
+
+
+# Optional: straightforward version using explicit prefix and suffix arrays
+def product_except_self_extra_space(nums: List[int]) -> List[int]:
+    """
+    Alternate implementation that uses O(n) extra space for clarity.
+    """
+    n = len(nums)
+    if n == 0:
+        return []
+
+    pre = [1] * n
+    suf = [1] * n
+    ans = [1] * n
+
+    for i in range(1, n):
+        pre[i] = pre[i - 1] * nums[i - 1]
+
+    for i in range(n - 2, -1, -1):
+        suf[i] = suf[i + 1] * nums[i + 1]
+
+    for i in range(n):
+        ans[i] = pre[i] * suf[i]
+
+    return ans
+
+
+if __name__ == "__main__":
+    # quick manual checks
+    examples = [
+        ([1, 2, 3, 4], [24, 12, 8, 6]),
+        ([0, 0], [0, 0]),
+        ([0, 1, 2, 3], [6, 0, 0, 0]),
+        ([5], [5]),
+    ]
+    for arr, expected in examples:
+        out = product_except_self(arr)
+        print(f"{arr} -> {out} (expected {expected})")