Update maximum-of-absolute-value-expression.py

Author: kamyu104

Python/maximum-of-absolute-value-expression.py

@@ -8,6 +8,15 @@ def maxAbsValExpr(self, arr1, arr2):
         :type arr2: List[int]
         :rtype: int
         """
+        # 1. max(|arr1[i]-arr1[j]| + |arr2[i]-arr2[j]| + |i-j| for i > j)
+        #    = max(|arr1[i]-arr1[j]| + |arr2[i]-arr2[j]| + |i-j| for j > i)
+        # 2. for i > j:
+        #        (|arr1[i]-arr1[j]| + |arr2[i]-arr2[j]| + |i-j|)
+        #        >= c1*(arr1[i]-arr1[j]) + c2*(arr2[i]-arr2[j]) + i-j for c1 in (1, -1), c2 in (1, -1)
+        #        = (c1*arr1[i]+c2*arr2[i]+i) - (c1*arr1[j]+c2*arr2[j]+j) for c1 in (1, -1), c2 in (1, -1)
+        # 1 + 2 => max(|arr1[i]-arr1[j]| + |arr2[i]-arr2[j]| + |i-j| for i != j)
+        #          = max((c1*arr1[i]+c2*arr2[i]+i) - (c1*arr1[j]+c2*arr2[j]+j)
+        #                for c1 in (1, -1), c2 in (1, -1) for i > j)
         result = 0
         for c1 in [1, -1]:
             for c2 in [1, -1]: