Spiral Order Traversal

vector<int> spiralOrder(vector<vector<int> >& matrix) {
    vector<int> ans; // This will store the spiral order of elements
    int row = matrix.size();  // Number of rows in the matrix
    int col = matrix[0].size(); // Number of columns in the matrix

    int count = 0;  // Keeps track of the number of elements added to the result
    int total = row * col; // Total number of elements in the matrix

    // Index initialization to keep track of boundaries of the spiral
    int startingRow = 0;
    int startingCol = 0;
    int endingRow = row - 1;
    int endingCol = col - 1;

    // The loop continues until all elements are processed
    while(count < total) {

        // Traverse the starting row from left to right
        for(int index = startingCol; count < total && index <= endingCol; index++) {
            ans.push_back(matrix[startingRow][index]);
            count++;
        }
        startingRow++;  // Move the starting row downwards (since it's already processed)

        // Traverse the ending column from top to bottom
        for(int index = startingRow; count < total && index <= endingRow; index++) {
            ans.push_back(matrix[index][endingCol]);
            count++;
        }
        endingCol--;  // Move the ending column leftwards

        // Traverse the ending row from right to left (if elements remain)
        for(int index = endingCol; count < total && index >= startingCol; index--) {
            ans.push_back(matrix[endingRow][index]);
            count++;
        }
        endingRow--;  // Move the ending row upwards

        // Traverse the starting column from bottom to top (if elements remain)
        for(int index = endingRow; count < total && index >= startingRow; index--) {
            ans.push_back(matrix[index][startingCol]);
            count++;
        }
        startingCol++;  // Move the starting column rightwards
    }

    return ans;  // Return the result containing spiral order
}

Example:

vector<vector<int>> matrix = {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
};

vector<int> result = spiralOrder(matrix);

Step-by-Step Example:

Given the matrix:

1  2  3
4  5  6
7  8  9

1. First layer:
   • Traverse top row (1, 2, 3).
   • Traverse right column (6, 9).
   • Traverse bottom row (8, 7).
   • Traverse left column (4).
   • After the first layer: ans = {1, 2, 3, 6, 9, 8, 7, 4}.
2. Second layer:
   • Traverse the remaining single element in the center (5).
   • After the second layer: ans = {1, 2, 3, 6, 9, 8, 7, 4, 5}. Final spiral order traversal is: [1, 2, 3, 6, 9, 8, 7, 4, 5].