Sort the major diagonal of the matrix
Given a matrix mat[][], the task is to sort the main diagonal elements of the matrix in increasing order.
Main Diagonal: Main diagonal or major diagonal of a matrix is the collection of elements mati, j, where i == j.
Examples:
Input: mat[][] = {{4, 2}, {3, 1}}
Output:
1 2
3 4
Explanation:
In the given matrix, the diagonal elements are -
=> {mat[0][0], mat[1][1]}
=> {4, 1}
=> Sorted Order = {1, 4}
Input: mat[][] = {{9, 4}, {3, 4}}
Output:
4 4
3 9
Explanation:
In the given matrix, the diagonal elements are -
=> {mat[0][0], mat[1][1]}
=> {9, 4}
=> Sorted Order = {4, 9}
Approach: The idea is modify the selection sort to sort the diagonal elements of the matrix. Count of the diangonal elements of matrix M*N will be min(M, N). As we know the major diagonal elements of the matrix are mati, j where i == j. Therefore, the ith element of the major diagonal of the matrix will be mat[i][i]. Hence, repeatedly find the minimum element from the major diagonal of the matrix and put it at the beginning.
Below is the implementation of the above approach:
C++
// C++ implementation to sort the // major diagonal of the matrix #include <bits/stdc++.h> using namespace std; // Function to sort the major // diagonal of the matrix void sortDiagonal(int a[2][2], int M, int N) { // Loop to find the ith minimum // element from the major diagonal for (int i = 0; i < M; i++) { int sm = a[i][i]; int pos = i; // Loop to find the minimum // element from the unsorted matrix for (int j = i + 1; j < N; j++) { if (sm > a[j][j]) { sm = a[j][j]; pos = j; } } // Swap to put the minimum // element at the beginning of // the major diagonal of matrix swap(a[i][i], a[pos][pos]); } // Loop to print the matrix for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) cout << a[i][j] << " "; cout << endl; } } // Driven Code int main() { int a[2][2] = { { 4, 2 }, { 3, 1 } }; // Sort the major Diagonal sortDiagonal(a, 2, 2); return 0; } |
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Java
// Java implementation to sort the // major diagonal of the matrix class GFG{ // Function to sort the major // diagonal of the matrix static void sortDiagonal(int a[][], int M, int N) { // Loop to find the ith minimum // element from the major diagonal for (int i = 0; i < M; i++) { int sm = a[i][i]; int pos = i; // Loop to find the minimum // element from the unsorted matrix for (int j = i + 1; j < N; j++) { if (sm > a[j][j]) { sm = a[j][j]; pos = j; } } // Swap to put the minimum // element at the beginning of // the major diagonal of matrix swap(a, i, i, pos, pos); } // Loop to print the matrix for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) System.out.print(a[i][j]+ " "); System.out.println(); } } static void swap(int[][] a, int i, int i2, int pos, int pos2) { int temp = a[i][i2]; a[i][i2] = a[pos][pos2]; a[pos][pos2] = temp; } // Driven Code public static void main(String[] args) { int a[][] = { { 4, 2 }, { 3, 1 } }; // Sort the major Diagonal sortDiagonal(a, 2, 2); } } // This code is contributed by 29AjayKumar |
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Python3
# Python3 implementation to sort the # major diagonal of the matrix # Function to sort the major # diagonal of the matrix def sortDiagonal(a, M, N): # Loop to find the ith minimum # element from the major diagonal for i in range(M): sm = a[i][i] pos = i # Loop to find the minimum # element from the unsorted matrix for j in range(i + 1 , N): if (sm > a[j][j]): sm = a[j][j] pos = j # Swap to put the minimum # element at the beginning of # the major diagonal of matrix a[i][i], a[pos][pos] = a[pos][pos] , a[i][i] # Loop to print the matrix for i in range(M): for j in range(N): print(a[i][j],end=" ") print() # Driven Code a = [[4, 2],[3, 1]] # Sort the major Diagonal sortDiagonal(a, 2, 2) # This code is contributed by shubhamsingh10 |
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C#
// C# implementation to sort the // major diagonal of the matrix using System; class GFG{ // Function to sort the major // diagonal of the matrix static void sortDiagonal(int[,]a, int M, int N) { // Loop to find the ith minimum // element from the major diagonal for (int i = 0; i < M; i++) { int sm = a[i, i]; int pos = i; // Loop to find the minimum // element from the unsorted matrix for (int j = i + 1; j < N; j++) { if (sm > a[j, j]) { sm = a[j, j]; pos = j; } } // Swap to put the minimum // element at the beginning of // the major diagonal of matrix swap(a, i, i, pos, pos); } // Loop to print the matrix for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) Console.Write(a[i, j]+ " "); Console.WriteLine(); } } static void swap(int[,] a, int i, int i2, int pos, int pos2) { int temp = a[i, i2]; a[i, i2] = a[pos, pos2]; a[pos, pos2] = temp; } // Driven Code public static void Main(String[] args) { int[,]a = { { 4, 2 }, { 3, 1 } }; // Sort the major Diagonal sortDiagonal(a, 2, 2); } } // This code is contributed by 29AjayKumar |
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Output:
1 2 3 4
Performance Analysis:
- Time Complexity: O(min(M, N)2)
- Auxiliary Space: O(1)
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