检查矩阵的两个元素是否在同一对角线上

给定矩阵mat [] []以及两个整数X和Y ，任务是检查X和Y是否在给定矩阵的同一对角线上。

例子：

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

方法：解决该问题的关键观察结果是，只有两个索引的总和或两个元素的索引的绝对差相等时，矩阵的两个元素才在同一对角线上。请按照以下步骤解决问题：

• 遍历矩阵并找到矩阵元素的索引。
• 检查元素是否在同一对角线上。
  假设矩阵元素的索引为(P，Q)和(X，Y)，则两个元素在同一对角线上的条件由以下方程式给出：

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

• 如果满足以上条件，则打印“是”。否则，打印“否”。

下面是上述方法的实现：

C++

// C++ program for
// the above approach
#include 
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

Java

// 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

Python3

# 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)

C#

// 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

Javascript

 
// JavaScript program for
// the above approach
   
// Function to check if two
// letegers are on the same
// diagonal of the matrix
function checkSameDiag(li, x,
                          y, m, n)
{
      
    // Storing indexes of x in I, J
    let I = 0, J = 0;
      
    // Storing Indexes of y in P, Q
    let P = 0, Q = 0;
      
    for(let i = 0; i < m; i++)
    {
        for(let 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)
    {
        document.write("YES");
    }
    else
        document.write("NO");
}
 
// Driver code
 
    // Dimensions of Matrix
    let m = 6;
    let n = 5;
  
    // Given Matrix
    let 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
    let x = 42;
    let y = 80;
  
    // Function call
    checkSameDiag(li, x, y, m, n);
     
    // This code is contributed by splevel62.

输出：

YES

时间复杂度： O(N * M)
辅助空间： O(1)