1. Boundary Traversal of Matrix

The problem of boundary traversal of a matrix can be found at the following link: Question Link

Approach

To perform the boundary traversal of a matrix, I followed these steps:

• Initialize an empty vector out to store the boundary elements.

• Initialize variables i and j to track the current position in the matrix, both starting at 0.

• Traverse the top row from left to right, incrementing j while adding elements to out.

• Increment i and decrement j to position at the last column if there is more than one row.

• If there are more than one rows and more than one columns, traverse the rightmost column from top to bottom while decrementing i and adding elements to out.

• If there are more than one rows, return to the first column by incrementing j and traverse the bottom row from bottom to top while decrementing i and adding elements to out.

• Return the out vector as the result.

Time and Auxiliary Space Complexity

• Time Complexity: The time complexity of this solution is O(N + M), where N is the number of rows in the matrix and M is the number of columns in the matrix. We visit each element of the matrix once.

• Auxiliary Space Complexity: The auxiliary space complexity is O(N+M) because we only use a single vector to store the result.

Code (C++)

class Solution {
public:
    vector<int> boundaryTraversal(vector<vector<int>>& matrix, int n, int m) {
        vector<int> out;
        int i = 0, j = 0;
        for(; j < m; ++j) out.push_back(matrix[i][j]);
        ++i; --j;
		
        if(n > 1) {
            for(; i < n; ++i) out.push_back(matrix[i][j]);
            --i; --j;
			
            if(m > 1) {
                for(; j >= 0; --j) out.push_back(matrix[i][j]);
                --i; ++j;
				
                for(; i > 0; --i) out.push_back(matrix[i][j]);
            }
        }
        return out;
    }
};

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