Given a squared matrix M[ ][ ] of N * N dimensions, the task is to find the Kth diagonal of the matrix, starting from the top-left towards the bottom-right, and print its contents.
Examples:
Input: N = 3, K = 2, M[ ][ ] = {{4, 7, 8}, {9, 2, 3}, {0, 4, 1}
Output: 9 7
Explanation:
5 possible diagonals starting from the top left to the bottom right for the given matrix are:
1 -> {4}
2 -> {9, 7}
3 -> {0, 2, 8}
4 -> {4, 3}
5 -> {1}
Since K = 2, the required diagonal is (9, 7).
Input: N = 2, K = 2, M[ ][ ] = {1, 5}, {9, 4}}
Output: 1
Explanation:
3 possible diagonals starting from the bottom left to the top right for the given matrix are:
1 -> {1}
2 -> {9, 5}
3 -> {4}
Since K = 2, the required diagonal is (9, 5).
Naive Approach:
The simplest approach to solve this problem is to generate all diagonals starting from the top-left to the bottom right of the given matrix. After generating the Kth diagonal, print its contents.
Time complexity: O(N2)
Auxiliary Space: O(N)
Efficient Approach:
The above approach can be optimized by avoiding the traversal of the matrix. Instead, find the boundaries of the Kth diagonal i.e. bottom-left and top-right indices. Once these indices are obtained, print the required diagonal by just traversing the indices of the diagonal.
The following observations are needed to find the position of the diagonal:
If ((K – 1) < N): The diagonal is an upper diagonal
Bottom-left boundary = M[K – 1][0]
Top-right boundary = M[0][K – 1]
If (K ? N): The diagonal is a lower diagonal.
Bottom-left boundary = M[N-1][K-N]
Top-right boundary = M[K-N][N-1]
Follow the steps below to solve the problem:
- If (K – 1) < N, set the starting row, startRow as K – 1 and column, startCol as 0.
- Otherwise, set startRow as N – 1 and startCol as K – N.
- Finally, print the elements of diagonal starting from M[startRow][startCol].
Below is the implementation of the above approach:
// C++ implementation of // the above approach #include <bits/stdc++.h> using namespace std;
// Function returns required diagonal void printDiagonal( int K, int N,
vector<vector< int > >& M)
{ int startrow, startcol;
// Initialize values to
// print upper diagonals
if (K - 1 < N) {
startrow = K - 1;
startcol = 0;
}
// Initialize values to
// print lower diagonals
else {
startrow = N - 1;
startcol = K - N;
}
// Traverse the diagonal
for (; startrow >= 0 && startcol < N;
startrow--, startcol++) {
// Print its contents
cout << M[startrow][startcol]
<< " " ;
}
} // Driver Code int main()
{ int N = 3, K = 4;
vector<vector< int > > M = { { 4, 7, 8 },
{ 9, 2, 3 },
{ 0, 4, 1 } };
printDiagonal(K, N, M);
return 0;
} |
// Java implementation of // the above approach import java.util.*;
class GFG{
// Function returns required diagonal static void printDiagonal( int K, int N,
int [][]M)
{ int startrow, startcol;
// Initialize values to
// print upper diagonals
if (K - 1 < N)
{
startrow = K - 1 ;
startcol = 0 ;
}
// Initialize values to
// print lower diagonals
else
{
startrow = N - 1 ;
startcol = K - N;
}
// Traverse the diagonal
for (; startrow >= 0 && startcol < N;
startrow--, startcol++)
{
// Print its contents
System.out.print(M[startrow][startcol] + " " );
}
} // Driver Code public static void main(String[] args)
{ int N = 3 , K = 4 ;
int [][] M = { { 4 , 7 , 8 },
{ 9 , 2 , 3 },
{ 0 , 4 , 1 } };
printDiagonal(K, N, M);
} } // This code is contributed by PrinciRaj1992 |
# Python3 implementation of the # above approach def printDiagonal(K, N, M):
startrow, startcol = 0 , 0
# Initialize values to prupper
# diagonals
if K - 1 < N:
startrow = K - 1
startcol = 0
else :
startrow = N - 1
startcol = K - N
# Traverse the diagonals
while startrow > = 0 and startcol < N:
# Print its contents
print (M[startrow][startcol], end = " " )
startrow - = 1
startcol + = 1
# Driver code if __name__ = = '__main__' :
N, K = 3 , 4
M = [ [ 4 , 7 , 8 ],
[ 9 , 2 , 3 ],
[ 0 , 4 , 1 ] ]
printDiagonal(K, N, M)
# This code is contributed by mohit kumar 29 |
// C# implementation of // the above approach using System;
class GFG{
// Function returns required diagonal static void printDiagonal( int K, int N,
int [,]M)
{ int startrow, startcol;
// Initialize values to
// print upper diagonals
if (K - 1 < N)
{
startrow = K - 1;
startcol = 0;
}
// Initialize values to
// print lower diagonals
else
{
startrow = N - 1;
startcol = K - N;
}
// Traverse the diagonal
for (; startrow >= 0 && startcol < N;
startrow--, startcol++)
{
// Print its contents
Console.Write(M[startrow,startcol] + " " );
}
} // Driver Code public static void Main(String[] args)
{ int N = 3, K = 4;
int [,] M = { { 4, 7, 8 },
{ 9, 2, 3 },
{ 0, 4, 1 } };
printDiagonal(K, N, M);
} } // This code is contributed by PrinciRaj1992 |
<script> // JavaScript implementation of // the above approach // Function returns required diagonal function printDiagonal(K,N,M)
{ let startrow, startcol;
// Initialize values to
// print upper diagonals
if (K - 1 < N)
{
startrow = K - 1;
startcol = 0;
}
// Initialize values to
// print lower diagonals
else
{
startrow = N - 1;
startcol = K - N;
}
// Traverse the diagonal
for (; startrow >= 0 && startcol < N;
startrow--, startcol++)
{
// Print its contents
document.write(M[startrow][startcol] + " " );
}
} // Driver Code let N = 3, K = 4; let M = [[ 4, 7, 8 ], [ 9, 2, 3 ],
[ 0, 4, 1 ]];
printDiagonal(K, N, M); // This code is contributed by patel2127 </script> |
Output:
4 3
Time complexity: O(N)
Auxiliary Space: O(1)