add Three sum

maths/three_sum.py

@@ -0,0 +1,55 @@
+"""
+The "Three Sum" problem is a commonly encountered problem in computer
+science and data analysis.the Three Sum problem has practical applications
+in various fields, including data analysis, optimization, algorithmic research,
+pattern recognition, and cryptography. Its versatility makes it a valuable problem
+for both theoretical analysis and real-world problem-solving.
+
+"""
+
+
+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.
+
+    Example:
+        >>> 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
+
+
+# Run the doctests
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()