Calculate the Manhattan Distance between two cells of given 2D array

Given a 2D array of size M * N and two points in the form (X₁, Y₁) and (X₂ , Y₂) where X₁ and X₂ represents the rows and Y₁ and Y₂ represents the column. The task is to calculate the Manhattan distance between the given points. 

Examples:

Input: M = 5, N = 5, X₁ = 1, Y₁ = 2, X₂ = 3, Y₂ = 3
Output: 3
Explanation: As per the definition, the Manhattan the distance is same as sum of the absolute difference of the coordinates.

Input: M = 5, N = 5, X₁ = 4, Y₁ = 2, X₂ = 4, Y₂ = 2
Output: 0

Approach: The approach is based on mathematical observation. The Manhattan distance between two points is the sum of absolute difference of the coordinates.

Manhattan distance = |X₁ – X₂| + |Y₁ – Y₂|

Below is the implementation of the above approach.

C++

// C++ code to implement above approach
#include <bits/stdc++.h>
using namespace std;

// Code to calculate Manhattan distance
int manhattanDist(int M, int N, int X1,
                  int Y1, int X2, int Y2)
{
    int dist = abs(X2 - X1) + abs(Y2 - Y1);
    return dist;
}

// Driver code
int main()
{
    // Define size of 2-D array
    int M = 5, N = 5;

    // First point
    int X1 = 1, Y1 = 2;

    // Second point
    int X2 = 3, Y2 = 3;

    cout << manhattanDist(M, N, X1, Y1, X2, Y2);
    return 0;
}

Java

// java code to implement above approach

class GFG
{

  // Code to calculate Manhattan distance
  static int manhattanDist(int M, int N, int X1,
                           int Y1, int X2, int Y2) {
    int dist = Math.abs(X2 - X1) + Math.abs(Y2 - Y1);
    return dist;
  }

  // Driver code
  public static void main(String args[])
  {

    // Define size of 2-D array
    int M = 5, N = 5;

    // First point
    int X1 = 1, Y1 = 2;

    // Second point
    int X2 = 3, Y2 = 3;

    System.out.println(manhattanDist(M, N, X1, Y1, X2, Y2));
  }
}

// This code is contributed by gfgking.

Python3

# Python code for the above approach
import math as Math

# Code to calculate Manhattan distance
def manhattanDist(M, N, X1, Y1, X2, Y2):
    dist = Math.fabs(X2 - X1) + Math.fabs(Y2 - Y1)
    return (int)(dist)

# Driver code

# Define size of 2-D array
M = 5
N = 5

# First point
X1 = 1
Y1 = 2

# Second point
X2 = 3
Y2 = 3

print(manhattanDist(M, N, X1, Y1, X2, Y2))

# This code is contributed by Saurabh Jaiswal

C#

// C# code to implement above approach
using System;
class GFG {

  // Code to calculate Manhattan distance
  static int manhattanDist(int M, int N, int X1, int Y1,
                           int X2, int Y2)
  {
    int dist = Math.Abs(X2 - X1) + Math.Abs(Y2 - Y1);
    return dist;
  }

  // Driver code
  public static void Main()
  {

    // Define size of 2-D array
    int M = 5, N = 5;

    // First point
    int X1 = 1, Y1 = 2;

    // Second point
    int X2 = 3, Y2 = 3;

    Console.WriteLine(
      manhattanDist(M, N, X1, Y1, X2, Y2));
  }
}

// This code is contributed by ukasp.

Javascript

<script>
       // JavaScript code for the above approach

       // Code to calculate Manhattan distance
       function manhattanDist(M, N, X1,
           Y1, X2, Y2) {
           let dist = Math.abs(X2 - X1) + Math.abs(Y2 - Y1);
           return dist;
       }

       // Driver code

       // Define size of 2-D array
       let M = 5, N = 5;

       // First point
       let X1 = 1, Y1 = 2;

       // Second point
       let X2 = 3, Y2 = 3;

       document.write(manhattanDist(M, N, X1, Y1, X2, Y2));

 // This code is contributed by Potta Lokesh
   </script>

Output

3

Time Complexity: O(1)
Auxiliary Space: O(1)