Given a matrix mat[][] of size N*N, the task is to rotate the matrix by 45 degrees and print the matrix.
Examples:
Input: N = 6,
mat[][] = {{3, 4, 5, 1, 5, 9, 5},
{6, 9, 8, 7, 2, 5, 2},
{1, 5, 9, 7, 5, 3, 2},
{4, 7, 8, 9, 3, 5, 2},
{4, 5, 2, 9, 5, 6, 2},
{4, 5, 7, 2, 9, 8, 3}}
Output:
3
6 4
1 9 5
4 5 8 1
4 7 9 7 5
4 5 8 7 2 9
5 2 9 5 5
7 9 3 3
2 5 5
9 6
8Input: N = 4,
mat[][] = {{2, 5, 7, 2},
{9, 1, 4, 3},
{5, 8, 2, 3},
{6, 4, 6, 3}}Output:
2
9 5
5 1 7
6 8 4 2
4 2 3
6 3
3
Approach: Follow the steps given below in order to solve the problem:
- Store the diagonal elements in a list using a counter variable.
- Print the number of spaces required to make the output look like the desired pattern.
- Print the list elements after reversing the list.
- Traverse through only diagonal elements to optimize the time taken by the operation.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to rotate matrix by 45 degree void matrix( int n, int m, vector<vector< int >> li)
{ // Counter Variable
int ctr = 0;
while (ctr < 2 * n - 1)
{
for ( int i = 0;
i < abs (n - ctr - 1);
i++)
{
cout << " " ;
}
vector< int > lst;
// Iterate [0, m]
for ( int i = 0; i < m; i++)
{
// Iterate [0, n]
for ( int j = 0; j < n; j++)
{
// Diagonal Elements
// Condition
if (i + j == ctr)
{
// Appending the
// Diagonal Elements
lst.push_back(li[i][j]);
}
}
}
// Printing reversed Diagonal
// Elements
for ( int i = lst.size() - 1; i >= 0; i--)
{
cout << lst[i] << " " ;
}
cout << endl;
ctr += 1;
}
} // Driver code int main()
{ // Dimensions of Matrix
int n = 8;
int m = n;
// Given matrix
vector<vector< int >> li{
{ 4, 5, 6, 9, 8, 7, 1, 4 },
{ 1, 5, 9, 7, 5, 3, 1, 6 },
{ 7, 5, 3, 1, 5, 9, 8, 0 },
{ 6, 5, 4, 7, 8, 9, 3, 7 },
{ 3, 5, 6, 4, 8, 9, 2, 1 },
{ 3, 1, 6, 4, 7, 9, 5, 0 },
{ 8, 0, 7, 2, 3, 1, 0, 8 },
{ 7, 5, 3, 1, 5, 9, 8, 5 } };
// Function call
matrix(n, m, li);
return 0;
} // This code is contributed by divyeshrabadiya07 |
4 1 5 7 5 6 6 5 9 9 3 5 3 7 8 3 5 4 1 5 7 8 1 6 7 5 3 1 7 0 6 4 8 9 1 4 5 7 4 8 9 8 6 3 2 7 9 3 0 1 3 9 2 7 5 1 5 1 9 0 0 8 8 5
Time Complexity: O(N2)
Auxiliary Space: O(N) since using auxiliary space for vector
Please refer complete article on Rotate matrix by 45 degrees for more details!