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++ 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 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. |
# 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# 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. |
<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>
|
3
Time Complexity: O(1)
Auxiliary Space: O(1)