Maximum Absolute Difference

Author: anantkaushik

Python/Interviewbit/Arrays/maximum-absolute-difference.py

@@ -0,0 +1,29 @@
+"""
+Problem Link: https://www.interviewbit.com/problems/maximum-absolute-difference/
+
+You are given an array of N integers, A1, A2 ,…, AN. Return maximum value of f(i, j) 
+for all 1 ≤ i, j ≤ N. 
+f(i, j) is defined as |A[i] - A[j]| + |i - j|, where |x| denotes absolute value of x.
+
+For example,
+A=[1, 3, -1]
+f(1, 1) = f(2, 2) = f(3, 3) = 0
+f(1, 2) = f(2, 1) = |1 - 3| + |1 - 2| = 3
+f(1, 3) = f(3, 1) = |1 - (-1)| + |1 - 3| = 4
+f(2, 3) = f(3, 2) = |3 - (-1)| + |2 - 3| = 5
+So, we return 5.
+"""
+class Solution:
+    # @param A : list of integers
+    # @return an integer
+    def maxArr(self, A):
+        min_pair1 = min_pair2 = float('inf')
+        max_pair1 = max_pair2 = float('-inf')
+        for i in range(len(A)):
+            min_pair1 = min(min_pair1, A[i] + i)
+            max_pair1 = max(max_pair1, A[i] + i)
+            
+            min_pair2 =  min(min_pair2, A[i] - i)
+            max_pair2 = max(max_pair2, A[i] - i)
+            
+        return max(max_pair1 - min_pair1, max_pair2 - min_pair2)