Create Reverse Pairs - using Merge Sort.py

Author: SamirPaulb

03_Sorting-Algorithms/Reverse Pairs - using Merge Sort.py

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+# https://leetcode.com/problems/reverse-pairs/
+
+class Solution:
+    def __init__(self):
+        self.count = 0
+    
+    def reversePairs(self, nums: List[int]) -> int:
+        self.mergeSort(nums)
+        return self.count
+    
+    def mergeSort(self, nums):
+        if len(nums) > 1:
+            # calculate mid
+            mid = len(nums) // 2
+            # divide the input array in to right and left
+            left = nums[:mid]
+            right = nums[mid:]
+            
+            self.mergeSort(left)
+            self.mergeSort(right)
+            
+            # the tricky part - updating the count of number of possible pairs
+            j = 0
+            for i in range(len(left)):
+                while j < len(right) and left[i] > 2 * right[j]:
+                    j += 1
+                self.count += j
+            
+            # merge two sorted array
+            i = j = k = 0
+            while i < len(left) and j < len(right):
+                if left[i] <= right[j]:
+                    nums[k] = left[i]
+                    k += 1
+                    i += 1
+                else:
+                    nums[k] = right[j]
+                    k += 1
+                    j += 1
+            while i < len(left):
+                nums[k] = left[i]
+                k += 1
+                i += 1
+            while j < len(right):
+                nums[k] = right[j]
+                k += 1
+                j += 1
+
+# Time: O(n log(n))
+# Space: O(n)