add Three sum (#9177)

* add Three sum

* add Three sum

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* update

* update

* update

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* update

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* add documention

---------

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maths/three_sum.py

@@ -0,0 +1,47 @@
+"""
+https://en.wikipedia.org/wiki/3SUM
+"""
+
+
+def three_sum(nums: list[int]) -> list[list[int]]:
+    """
+    Find all unique triplets in a sorted array of integers that sum up to zero.
+
+    Args:
+        nums: A sorted list of integers.
+
+    Returns:
+        A list of lists containing unique triplets that sum up to zero.
+
+    >>> three_sum([-1, 0, 1, 2, -1, -4])
+    [[-1, -1, 2], [-1, 0, 1]]
+    >>> three_sum([1, 2, 3, 4])
+    []
+    """
+    nums.sort()
+    ans = []
+    for i in range(len(nums) - 2):
+        if i == 0 or (nums[i] != nums[i - 1]):
+            low, high, c = i + 1, len(nums) - 1, 0 - nums[i]
+            while low < high:
+                if nums[low] + nums[high] == c:
+                    ans.append([nums[i], nums[low], nums[high]])
+
+                    while low < high and nums[low] == nums[low + 1]:
+                        low += 1
+                    while low < high and nums[high] == nums[high - 1]:
+                        high -= 1
+
+                    low += 1
+                    high -= 1
+                elif nums[low] + nums[high] < c:
+                    low += 1
+                else:
+                    high -= 1
+    return ans
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()