From 813d8e0ccc16853b5b6e0b330d908ab35c311d1a Mon Sep 17 00:00:00 2001
From: Sangeeth Sudheer <sangeeth96@users.noreply.github.com>
Date: Fri, 1 Apr 2022 23:56:39 +0530
Subject: [PATCH] feat(18-4sum): add py3 solution

---
 0018_4sum/README.md           | 21 ++++++++++++++++++
 0018_4sum/python3/solution.py | 41 +++++++++++++++++++++++++++++++++++
 2 files changed, 62 insertions(+)
 create mode 100644 0018_4sum/README.md
 create mode 100644 0018_4sum/python3/solution.py

diff --git a/0018_4sum/README.md b/0018_4sum/README.md
new file mode 100644
index 0000000..bac4702
--- /dev/null
+++ b/0018_4sum/README.md
@@ -0,0 +1,21 @@
+Given an array `nums` of `n` integers, return _an array of all the unique quadruplets_ `[nums[a], nums[b], nums[c], nums[d]]` such that:
+
+* `0 <= a, b, c, d < n`
+* `a`, `b`, `c`, and `d` are distinct.
+* `nums[a] + nums[b] + nums[c] + nums[d] == target`
+
+You may return the answer in any order.
+
+Example 1:
+    
+    Input: nums = [1,0,-1,0,-2,2], target = 0 Output: [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]] 
+
+Example 2:
+    
+    Input: nums = [2,2,2,2,2], target = 8 Output: [[2,2,2,2]] 
+
+Constraints:
+
+* `1 <= nums.length <= 200`
+* `-109 <= nums[i] <= 109`
+* `-109 <= target <= 109`
diff --git a/0018_4sum/python3/solution.py b/0018_4sum/python3/solution.py
new file mode 100644
index 0000000..ece326f
--- /dev/null
+++ b/0018_4sum/python3/solution.py
@@ -0,0 +1,41 @@
+# NOTE: Far from the most optimal solution to the problem.
+# Time complexity: O(n^3)
+# Space complexity: O(n^2)  // NOTE: Really? And how?
+class Solution:
+    def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
+        arr_len = len(nums)
+        
+        # Helps keep out duplicates
+        nums.sort()
+        
+        # Will be a dict with each key storing a `set` of 2-tuples (pair of nums)
+        diff_cache = {}
+        
+        quadruplets = set()
+        
+        # No point in iterating with the last element since we won't be adding
+        # any new quadruplets at that point
+        for i in range(1, arr_len - 1):
+            for j in range(i + 1, arr_len):
+                current_sum = nums[i] + nums[j]
+                difference = target - current_sum
+                
+                if difference in diff_cache:
+                    # diff_cache could have multiple pairs that add up to the same
+                    # `difference`. We need to form quadruplets with all of them
+                    # and store them in `quadruplets`
+                    for pair in diff_cache[difference]:
+                        quadruplets.add(pair + (nums[i], nums[j]))
+                
+            # Compute sum with every element to the left of i and store
+            # in diff_cache. We do this at this later point to avoid duplicates
+            for k in range(0, i):
+                current_sum = nums[i] + nums[k]
+                
+                if current_sum in diff_cache:
+                    diff_cache[current_sum].add((nums[i], nums[k]))
+                else:
+                    # This has to be a set to avoid duplicates
+                    diff_cache[current_sum] = { (nums[i], nums[k]) }
+                    
+        return quadruplets