Given an integer N, the task is to generate a matrix of dimensions N x N using positive integers from the range [1, N] such that the sum of the secondary diagonal is a perfect square.
Examples:
Input: N = 3
Output:
1 2 3
2 3 1
3 2 1
Explanation:
The sum of secondary diagonal = 3 + 3 + 3 = 9(= 32).Input: N = 7
Output:
1 2 3 4 5 6 7
2 3 4 5 6 7 1
3 4 5 6 7 1 2
4 5 6 7 1 2 3
5 6 7 1 2 3 4
6 7 1 2 3 4 5
7 1 2 3 4 5 6
Explanation:
The sum of secondary diagonal = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49(= 72).
Approach: Since the generated matrix needs to be of dimensions N x N, therefore, to make the sum of elements in the secondary diagonal a perfect square, the idea is to assign N at each index of the secondary diagonal. Therefore, the sum of all N elements in this diagonal is N2, which is a perfect square. Follow the steps below to solve the problem:
- Initialize a matrix mat[][] of dimension N x N.
- Initialize the first row of the matrix as {1 2 3 … N}.
- Now for the remaining rows of the matrix, fill each row by circular left shift of the arrangement of the previous row of the matrix by 1.
- Print the matrix after completing the above steps.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to print the matrix whose sum // of element in secondary diagonal is a // perfect square void diagonalSumPerfectSquare( int arr[], int N)
{ // Iterate for next N - 1 rows
for ( int i = 0; i < N; i++)
{
// Print the current row after
// the left shift
for ( int j = 0; j < N; j++)
{
cout << (arr[(j + i) % 7]) << " " ;
}
cout << endl;
}
} // Driver Code int main()
{ // Given N
int N = 7;
int arr[N];
// Fill the array with elements
// ranging from 1 to N
for ( int i = 0; i < N; i++)
{
arr[i] = i + 1;
}
// Function Call
diagonalSumPerfectSquare(arr, N);
} // This code is contributed by gauravrajput1 |
// Java program for the above approach class GFG {
// Function to print the matrix whose sum
// of element in secondary diagonal is a
// perfect square
static void diagonalSumPerfectSquare( int [] arr,
int N)
{
// Iterate for next N - 1 rows
for ( int i = 0 ; i < N; i++)
{
// Print the current row after
// the left shift
for ( int j = 0 ; j < N; j++)
{
System.out.print(arr[(j + i) % 7 ] + " " );
}
System.out.println();
}
}
// Driver Code
public static void main(String[] srgs)
{
// Given N
int N = 7 ;
int [] arr = new int [N];
// Fill the array with elements
// ranging from 1 to N
for ( int i = 0 ; i < N; i++)
{
arr[i] = i + 1 ;
}
// Function Call
diagonalSumPerfectSquare(arr, N);
}
} // This code is contributed by Amit Katiyar |
# Python3 program for the above approach # Function to print the matrix whose sum # of element in secondary diagonal is a # perfect square def diagonalSumPerfectSquare(arr, N):
# Print the current row
print ( * arr, sep = " " )
# Iterate for next N - 1 rows
for i in range (N - 1 ):
# Perform left shift by 1
arr = arr[i::] + arr[:i:]
# Print the current row after
# the left shift
print ( * arr, sep = " " )
# Driver Code # Given N N = 7
arr = []
# Fill the array with elements # ranging from 1 to N for i in range ( 1 , N + 1 ):
arr.append(i)
# Function Call diagonalSumPerfectSquare(arr, N) |
// C# program for the // above approach using System;
class GFG {
// Function to print the matrix whose sum
// of element in secondary diagonal is a
// perfect square
static void diagonalSumPerfectSquare( int [] arr,
int N)
{
// Iterate for next N - 1 rows
for ( int i = 0; i < N; i++)
{
// Print the current row after
// the left shift
for ( int j = 0; j < N; j++)
{
Console.Write(arr[(j + i) % 7] + " " );
}
Console.WriteLine();
}
}
// Driver Code
public static void Main(String[] srgs)
{
// Given N
int N = 7;
int [] arr = new int [N];
// Fill the array with elements
// ranging from 1 to N
for ( int i = 0; i < N; i++) {
arr[i] = i + 1;
}
// Function Call
diagonalSumPerfectSquare(arr, N);
}
} // This code is contributed by 29AjayKumar |
<script> // Javascript program to implement // the above approach // Function to print the matrix whose sum
// of element in secondary diagonal is a
// perfect square
function diagonalSumPerfectSquare( arr,N)
{
// Iterate for next N - 1 rows
for (let i = 0; i < N; i++)
{
// Print the current row after
// the left shift
for (let j = 0; j < N; j++)
{
document.write(arr[(j + i) % 7] + " " );
}
document.write( "<br/>" );
}
}
// Driver Code // Given N
let N = 7;
let arr = new Array(N).fill(0);
// Fill the array with elements
// ranging from 1 to N
for (let i = 0; i < N; i++)
{
arr[i] = i + 1;
}
// Function Call
diagonalSumPerfectSquare(arr, N);
// This code is contributed by avijitmondal1998.
</script> |
1 2 3 4 5 6 7 2 3 4 5 6 7 1 3 4 5 6 7 1 2 4 5 6 7 1 2 3 5 6 7 1 2 3 4 6 7 1 2 3 4 5 7 1 2 3 4 5 6
Time Complexity: O(N2)
Auxiliary Space: O(N)