Swap the elements of lower and upper triangular matrix

The problem to be addressed involves swapping the elements of the lower and upper triangular portions of a given matrix. A matrix is a two-dimensional array with rows and columns, and the goal is to interchange the elements below the main diagonal with those above the main diagonal.

Problem Statement

Given a square matrix of size ROW x COL (where ROW = COL), the objective is to swap the elements below the main diagonal with the elements above the main diagonal and display the modified matrix.

Example

Consider the following matrix:

6  1  5  3
0  3  2  6
4  0  4  7
1  2  9  1

After swapping the elements of the lower and upper triangular portions, the modified matrix becomes:

6  0  4  1
1  3  0  2
5  2  4  9
3  6  7  1

Idea to Solve

To solve this problem, iterate through the matrix and swap each element below the main diagonal with the corresponding element above the main diagonal. As the matrix is square (ROW = COL), swapping elements with their corresponding elements will ensure that the lower and upper triangular portions are interchanged.

Pseudocode

Here's the pseudocode for the algorithm:

function swapElement(matrix):
    if ROW != COL:
        return // Not a square matrix
    for i from 0 to ROW-1:
        for j from i+1 to COL-1:
            swap(matrix[i][j], matrix[j][i])

Algorithm Explanation

1. Define a function swapElement that takes a 2D matrix matrix as its input.
2. Check if the matrix is square by comparing ROW and COL. If they are not equal, return from the function as the swapping is not possible.
3. Iterate through the matrix using two nested loops. The outer loop iterates through the rows, and the inner loop starts from i+1 to iterate through the columns, effectively focusing on elements above the main diagonal.
4. Within the nested loops, swap the element at matrix[i][j] with the element at matrix[j][i]. This step swaps the lower triangular element with the corresponding upper triangular element.
5. After the loops complete, the matrix will have its lower and upper triangular portions swapped.

Code Solution

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Time Complexity

The time complexity of this algorithm is O(ROW * COL), where ROW and COL are the number of rows and columns in the matrix, respectively. The algorithm iterates through each element of the matrix once to perform the swapping.

In conclusion, the provided C code snippet effectively solves the problem of swapping the elements of the lower and upper triangular portions of a square matrix. The pseudocode and algorithm provide a clear step-by-step approach, and the time complexity analysis elucidates the efficiency of the solution.