Check if two elements of a matrix are on the same diagonal or not

Given a matrix mat[][], and two integers X and Y, the task is to check if X and Y are on the same diagonal of the given matrix or not.

Examples:

Input: mat[][]= {{1, 2}. {3, 4}}, X = 1, Y = 4 
Output: Yes
Explanation:
Both X and Y lie on the same diagonal.

Input: mat[][]= {{1, 2}. {3, 4}}, X = 2, Y = 4
Output: No

Approach: The key observation to solve the problem is that the two elements of the matrix are on the same diagonal only if the sum of the indices or the absolute difference of the indices of the elements are equal. Follow the steps below to solve the problem:



  • Traverse the matrix and find the indices of the elements of the matrix.
  • Check if the elements are on the same diagonal.
    Let the indices of the elements of the matrix are (P, Q) and (X, Y), then the condition that both the elements are on the same diagonal is given by the following equation:

abs(P – Q) == abs(X – Y) or P + Q == X + Y

  • If the above condition is satisfied, print “Yes”. Otherwise, print “No”.

Below is the implementation of the above approach:

C++

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// C++ program for
// the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if two
// integers are on the same
// diagonal of the matrix
void checkSameDiag(int li[6][5], int x,
                   int y, int m, int n)
{
  // Storing indexes of x in I, J
  int I = 0, J = 0;
 
  // Storing Indexes of y in P, Q
  int P = 0, Q = 0;
 
  for(int i = 0; i < m; i++)
  {
    for(int j = 0; j < n; j++)
    {
      if (li[i][j] == x)
      {
        I = i;
        J = j;
      }
      if (li[i][j] == y)
      {
        P = i;
        Q = j;
      }
    }
  }
 
  // Condition to check if the
  // both the elements are in
  // same diagonal of a matrix
  if (abs(P - Q) == abs(I - J) ||
      P + Q == I + J)
  {
    cout << "YES";
  }
  else
    cout << "NO";
}
 
// Driver code
int main()
{
  // Dimensions of Matrix
  int m = 6;
  int n = 5;
 
  // Given Matrix
  int li[6][5] = {{32, 94, 99, 26, 82},
                  {51, 69, 52, 63, 17},
                  {90, 36, 88, 55, 33},
                  {93, 42, 73, 39, 28},
                  {81, 31, 83, 53, 10},
                  {12, 29, 85, 80, 87}};
 
  // Elements to be checked
  int x = 42;
  int y = 80;
 
  // Function call
  checkSameDiag(li, x, y, m, n);
  return 0;
}
 
//This code is contributed by 29AjayKumar

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Java

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// Java implementation of the
// above approach
class GFG{
     
// Function to check if two
// integers are on the same
// diagonal of the matrix
static void checkSameDiag(int li[][], int x,
                          int y, int m, int n)
{
     
    // Storing indexes of x in I, J
    int I = 0, J = 0;
     
    // Storing Indexes of y in P, Q
    int P = 0, Q = 0;
     
    for(int i = 0; i < m; i++)
    {
        for(int j = 0; j < n; j++)
        {
            if (li[i][j] == x)
            {
                I = i;
                J = j;
            }
            if (li[i][j] == y)
            {
                P = i;
                Q = j;
            }
        }
    }
     
    // Condition to check if the
    // both the elements are in
    // same diagonal of a matrix
    if (Math.abs(P - Q) == Math.abs(I - J) ||
        P + Q == I + J)
    {
        System.out.println("YES");
    }
    else
        System.out.println("NO");
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Dimensions of Matrix
    int m = 6;
    int n = 5;
 
    // Given Matrix
    int[][] li = { { 32, 94, 99, 26, 82 },
                   { 51, 69, 52, 63, 17 },
                   { 90, 36, 88, 55, 33 },
                   { 93, 42, 73, 39, 28 },
                   { 81, 31, 83, 53, 10 },
                   { 12, 29, 85, 80, 87 } };
 
    // Elements to be checked
    int x = 42;
    int y = 80;
 
    // Function call
    checkSameDiag(li, x, y, m, n);
}
}
 
// This code is contributed by Amit Katiyar

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Python3

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# Python3 implementation of the
# above approach
 
# Function to check if two
# integers are on the same
# diagonal of the matrix
def checkSameDiag(x, y):
     
    # Storing indexes of x in I, J
    # Storing Indexes of y in P, Q
    for i in range(m):
        for j in range(n):
            if li[i][j] == x:
                I, J = i, j
            if li[i][j] == y:
                P, Q = i, j
                 
    # Condition to check if the
    # both the elements are in
    # same diagonal of a matrix
    if abs(P-Q) == abs(I-J) or P + Q == I + J:
        print("YES")
    else:
        print("NO")
 
 
# Driver Code
if __name__ == "__main__":
     
    # Dimensions of Matrix
    m, n = 6, 5
     
    # Given Matrix
    li = [[32, 94, 99, 26, 82],
        [51, 69, 52, 63, 17],
        [90, 36, 88, 55, 33],
        [93, 42, 73, 39, 28],
        [81, 31, 83, 53, 10],
        [12, 29, 85, 80, 87]]
     
    # elements to be checked
    x, y = 42, 80
     
    # Function Call
    checkSameDiag(x, y)

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C#

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// C# implementation of the
// above approach
using System;
class GFG{
     
// Function to check if two
// integers are on the same
// diagonal of the matrix
static void checkSameDiag(int [,]li, int x,
                          int y, int m, int n)
{
  // Storing indexes of x in I, J
  int I = 0, J = 0;
 
  // Storing Indexes of y in P, Q
  int P = 0, Q = 0;
 
  for(int i = 0; i < m; i++)
  {
    for(int j = 0; j < n; j++)
    {
      if (li[i, j] == x)
      {
        I = i;
        J = j;
      }
      if (li[i, j] == y)
      {
        P = i;
        Q = j;
      }
    }
  }
 
  // Condition to check if the
  // both the elements are in
  // same diagonal of a matrix
  if (Math.Abs(P - Q) == Math.Abs(I - J) ||
                         P + Q == I + J)
  {
    Console.WriteLine("YES");
  }
  else
    Console.WriteLine("NO");
}
 
// Driver Code
public static void Main(String[] args)
{
  // Dimensions of Matrix
  int m = 6;
  int n = 5;
 
  // Given Matrix
  int [,]li = {{32, 94, 99, 26, 82},
               {51, 69, 52, 63, 17},
               {90, 36, 88, 55, 33},
               {93, 42, 73, 39, 28},
               {81, 31, 83, 53, 10},
               {12, 29, 85, 80, 87}};
 
  // Elements to be checked
  int x = 42;
  int y = 80;
 
  // Function call
  checkSameDiag(li, x, y, m, n);
}
}
 
// This code is contributed by 29AjayKumar

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Output: 

YES







 

Time Complexity: O(N * M) 
Auxiliary Space: O(1)

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