Master

data_structures/arrays/find_triplets_with_0_sum.py

@@ -81,7 +81,82 @@
     return output_arr
 
 
+# Two pointer approach to find triplets with zero sum
+
+"""
+Why is it the best?
+1. Faster than brute force due to sorting and then two pointers scanning.
+
+2. No extra space needed (except for sorting).
+
+3. Handles Duplicate efficiently by skipping repeated values.
+"""
+def find_triplets_with_0_sum_two_pointer(arr: list[int]) -> list[list[int]]:
+    """
+    Function for finding the triplets with a given sum in the array using hashing.
+
+    Given a list of integers, return elements a, b, c such that a + b + c = 0.
+
+    Args:
+        nums: list of integers
+    Returns:
+        list of lists of integers where sum(each_list) == 0
+    Examples:
+        >>> find_triplets_with_0_sum_two_pointer([-1, 0, 1, 2, -1, -4])
+        [[-1, 0, 1], [-1, -1, 2]]
+        >>> find_triplets_with_0_sum_two_pointer([])
+        []
+        >>> find_triplets_with_0_sum_two_pointer([0, 0, 0])
+        [[0, 0, 0]]
+        >>> find_triplets_with_0_sum_two_pointer([1, 2, 3, 0, -1, -2, -3])
+        [[-1, 0, 1], [-3, 1, 2], [-2, 0, 2], [-2, -1, 3], [-3, 0, 3]]
+
+    Time complexity: O(N^2)
+    Auxiliary Space: O(1) (excluding output storage)
+
+    """
+
+    # Step 1: Sort the array to facilitate the two pointer approach
+    nums.sort()
+    triplets = []  # list to store the valid triplets
+    n = len(nums)
+
+    # Step 2: iterate through the array, fixing one number at a time
+    for i in range(n - 2):      # We need atleast 3 elements for a triplet
+        # skip duplicate elements for the first number
+        if i > 0 and nums[i] == nums[i - 1]:
+            continue        #Move to the distinct number
+
+        # Step 3: Use the two pointer technique to find pairs that sum up to -nums[i]
+        left, right = i + 1, n - 1  # Initialize two pointers
+        while left < right:
+            total = nums[i] + nums[left] + nums[right]      #Calculate sum of three numbers
+
+            if total == 0:
+                # If the sum is zero, we found a valid triplet
+                triplets.append([nums[i], nums[left], nums[right]])
+
+                # Move both pointers to look for the next unique pair
+                left += 1
+                right -= 1
+
+                # skip duplicate values for the second and third numbers
+                while left < right and nums[left] == nums[left - 1]:
+                    left += 1
+                while left < right and nums[right] == nums[right + 1]:
+                    right -= 1
+
+            elif total < 0:
+                # If sum is less than zero, move the left pointer to the right
+                left += 1
+            else:
+                # If sum is greater than zero, move the right pointer to the left
+                right -= 1
+    return triplets
+
+
 if __name__ == "__main__":
     from doctest import testmod
 
     testmod()
+