Maximum Absolute Difference - The Coding Shala

Home >> Programming Questions >> Maximum Absolute Difference

Maximum Absolute Difference InterviewBit Solution

You are given an array of N integers, A1, A2,…, AN. Return maximum value of f(i, j) for all 1 ≤ i, j ≤ N.
Maximum Absolute Difference - The Coding Shala
f(i, j) is defined as |A[i] - A[j]| + |i - j|, where |x| denotes the 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.

Solution

Here function f(i, j) = |A[i] - A[j]| + |i-j] can be written in four ways - 

 
(A[i] + i) - (A[j] + j)
-(A[i] - i) + (A[j] - j) 
(A[i] - i) - (A[j] - j) 
(-A[i] - i) + (A[j] + j) = -(A[i] + i) + (A[j] + j)
we just have to store minimum and maximum values of expressions A[i] + i and A[i] - i for all i.

 Java Code::
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
public class Solution {
    public int maxArr(ArrayList<Integer> A) {
        int max1 = Integer.MIN_VALUE;
        int max2 = Integer.MIN_VALUE;
        int min1 = Integer.MAX_VALUE;
        int min2 = Integer.MAX_VALUE;
        for(int i=0;i<A.size();i++){
            max1 = Math.max(max1, A.get(i)+i);
            max2 = Math.max(max2, A.get(i)-i);
            min1 = Math.min(min1, A.get(i)+i);
            min2 = Math.min(min2, A.get(i)-i);
        }
        return Math.max(max1-min1, max2-min2);
    }
}



Other Posts You May Like
Please leave a comment below if you like this post or found some error, it will help me to improve my content.
By

Comments

  1. VaibhavJuly 8, 2020 at 9:40 PM

    This question can be solved in O(N) Time and O(1) space complexity by using simple mathematics concepts of absolute operator.

    We can deduce this express into 4 different forms after removing the absolute operator and applying specific conditions.

    Cases can be A[i]>A[j] or A[i]<=A[j] and simultaneously i>j and i<=j can be the cases so using these conditions we can formulate 4 different expressions which do not involve use of absolute operator.
    After that we just need to find the maximum value possible through each expression by iterating on array of numbers only once.

    If you still face any difficulties while solving this question then you can refer to the video solution

    Video Link:- https://youtu.be/Ov4weYCIipg

    ReplyDelete
    Replies
    1. Akshay KumarJuly 10, 2020 at 10:07 AM

      Nice Explanation.

      Delete
    2. D.PrashanthApril 16, 2021 at 11:34 PM

      Code is very simple once we understand the logic. Thanks Vaibhav. Breaking down the modulus operation into all possibilities made it clear.

      Delete

Post a Comment

Popular Posts from this Blog

Shell Script to find sum, product and average of given numbers - The Coding Shala

Home >> Scripting >> Sum, product and average Shell Script to find the sum, product, and the average of given numbers Read four integer numbers from the user and find the sum, product, and average of these four numbers? Code:  #! / bin / bash echo "enter four integers" read a b c d sum =$(echo "$a + $b + $c + $d" | bc - l) average=$(echo "$sum / 4" | bc - l) product=$(echo "$a * $b * $c * $d" | bc - l) echo "sum = $sum" echo "Average = $average" echo "Product = $product" Other Posts You May Like Shell script to print sum of the digits of a number Shell Script to print number in descending order Shell script to find out biggest number from three numbers Shell script to find out factorial of a number Shell Script to create a simple calculator Please leave a comment below if you like this post or found some error, it will help me to improve my content.
Read more

Shell Script to Create a Simple Calculator - The Coding Shala

Home >> Scripting >> simple calculator Shell Script to Create a Simple Calculator Write a shell script to create a simple calculator using a switch-case statement? Code:  #! / bin / bash echo "simple calculator" sum = 0 i = "y" echo "enter first number" read n1 echo "enter second number" read n2 while [ $ i = "y" ] do echo "1.Addition" echo "2.Subtraction" echo "3.Multiplication" echo "4.Division" echo "Enter choice" read ch case $ch in 1 ) sum =$(echo " $n1 + $n2" | bc - l) echo "Addition is =" $ sum ;; 2 ) sum =$(echo "$n1 - $n2" | bc - l) echo "Sub is =" $ sum ;; 3 ) sum =$(echo "$n1 * $n2" | bc - l) echo "Mul is =" $ sum ;; 4 ) sum =$(echo "$n1 / $n2" | bc - l) echo "div is =" $ sum ;; * )echo "invalid choice" esac echo "Do y
Read more

Add two numbers in Scala - The Coding Shala

Home >> Learn Scala >> Add Two Numbers  In this post, we will learn how to write a Scala program to Add Two Numbers. Add Two Numbers in Scala The following is the Scala program to Add two Numbers. Scala Program:  //add two numbers in scala //the coding shala object Main { def main ( args : Array [ String ]){ //we can take user input also val num1 = 10 ; val num2 = 20 ; //add both numbers val result = num1 + num2 ; println ( "Sum of " + num1 + " + " + num2 + " = " + result ); } } Other Posts You May Like Scala - Hello World Program Java - Hello World Program Power of Two Simple XML Validator Fibonacci Series Please leave a comment below if you like this post or found some errors, it will help me to improve my content.
Read more

New Year Chaos Solution - The Coding Shala

Home >> Programming Questions >> New Year Chaos New Year Chaos Problem Solution In this post, you will learn how to solve New Year Chaos Problem and implement its solution in Java. Problem:   It's New Year's Day and everyone's in line for the Wonderland rollercoaster ride! There are a number of people queued up, and each person wears a sticker indicating their initial position in the queue. Initial positions increment from at the front of the line to at the back.  Any person in the queue can bribe the person directly in front of them to swap positions. If two people swap positions, they still wear the same sticker denoting their original places in line. One person can bribe at most two others.  For Example, if n=8 and Person 5 bribes Person 4, the queue will look like this: 1,2,3,5,4,6,7,8. Fascinated by this chaotic queue, you decide you must know the minimum number of bribes that took place to get the queue into its current state. Input:
Read more

Richest Customer Wealth LeetCode Solution - The Coding Shala

Home >> LeetCode >> Richest Customer Wealth  In this post, we will learn how to solve LeetCode's Richest Customer Wealth problem and will implement its solution in Java. Richest Customer Wealth Problem You are given an m x n integer grid accounts where accounts[i][j] is the amount of money i​​​​​​​​​​​th​​​​ customer has in the j​​​​​​​​​​​th​​​​ bank. Return the wealth that the richest customer has.  A customer's wealth is the amount of money they have in all their bank accounts. The richest customer is the customer that has the maximum wealth. Example 1: Input: accounts = [[1,2,3],[3,2,1]] Output: 6 Explanation: 1st customer has wealth = 1 + 2 + 3 = 6 2nd customer has wealth = 3 + 2 + 1 = 6 Both customers are considered the richest with a wealth of 6 each, so return 6. Example 2: Input: accounts = [[1,5],[7,3],[3,5]] Output: 10 Example 3: Input: accounts = [[2,8,7],[7,1,3],[1,9,5]] Output: 17 Practice this problem on LeetCode . LeetCode - Richest Customer
Read more