Find the element at specified index in a Spiral Matrix in Java

A spiral matrix is like a grid with numbers arranged in a twisting pattern, usually starting from the top-left corner and moving around in a circle towards the middle. To find a specific number in this grid, you have to follow the twisty path until you get to the right spot. It's like going on a treasure hunt in a maze! You figure out where you are by keeping track of your position and moving in the right direction. This way, you can quickly find any number you're looking for in the spiral matrix.

The journey starts from the top-left corner of the matrix and proceeds towards the center. It involves moving right, down, left, and up while collecting elements in this sequential order. This approach is commonly used to address the challenge of pinpointing elements within a spiral matrix in various programming scenarios.

Find the element at specified index in a Spiral Matrix in Java

Examples 1

Input: i = 1, j = 1

Output: 1

Explanation: When i = 1 and j = 1, the element at grid[1][1] is 1.

Example 2

Input: i = 2, j = 3

Output: 7

Explanation: For i = 2 and j = 3, the element at grid[2][3] is 7.

Example 3

Input: i = 4, j = 2

Output: 18

Explanation: When i = 4 and j = 2, the element at grid[4][2] is 18.

Approach: Spiral Grid Element Calculation

Spiral Grid Element Calculation is a concise approach for efficiently determining the value of an element at the given row and column indices within a spiral grid, taking into account grid patterns and index parity.

Algorithm:

Step 1: Create a Java class named SpiralMatrixElementFinder.

Step 2: Add a static method named findElement inside the class to find the element at the specified (row, col) index.

Step 3: Implement the logic in the findElement method as follows:

Step 4: To find the element if the row is equal to col, calculate the element on the diagonal using (row * row - (row - 1)).

Step 5: When the row is greater than col, determine whether the row is even or odd. Depending on this:

For even rows, calculate the element using row * row - (col - 1).
For odd rows, calculate the element using (row - 1) * (row - 1) + 1 + (col - 1) to adjust for the column.

Step 6: Whent the col is greater than row, determine whether col is even or odd. Depending on this:

For even columns, calculate the element using (col - 1) * (col - 1) + 1 + (row - 1) to adjust for the row.
For odd columns, calculate the element using col * col - (row - 1).

Step 7: In the main method, call the findElement method with the desired (row, col) values and print the result.

Step 8: The complete code will include the class, the findElement method, and the main method as described in the steps. You can adjust the row and col values in the main method to find elements at different indices in the spiral grid.

Implementation:

Filename: SpiralMatrixElementFinder.java

public class SpiralMatrixElementFinder {
    // Method to find the element at (row, col) index in a spiral grid
    static int findElement(int row, int col) {
        if (row == col) {
            // When the row and column indices are the same, the element is on the diagonal.
            // The formula to find the element on the diagonal of a matrix is (row * row - (row - 1)).
            return (row * row - (row - 1));
        } else if (row > col) {
            // When the row index is greater than the column index, we are in the upper half of the matrix.
            // Whether the row is even or odd, we calculate the element accordingly.
            if (row % 2 == 0) {
                // Even row, calculate element using row number.
                return row * row - (col - 1);
            } else {
                // Odd row, calculate the element using (row - 1) and adjust for the column.
                return (row - 1) * (row - 1) + 1 + (col - 1);
            }
        } else {
            // If the column index is greater than the row index, we are in the lower half of the matrix.
            // Depending on whether col is even or odd, we calculate the element accordingly.
            if (col % 2 == 0) {
                // Even col, calculate the element using (col - 1) and adjust for the row.
                return (col - 1) * (col - 1) + 1 + (row - 1);
            } else {
                // Odd col, calculate element using col number.
                return col * col - (row - 1);
            }
        }
    }

    public static void main(String[] args) {
        int row = 3, col = 4;

        // Method Call
        int result = findElement(row, col);
        System.out.println("Element at (" + row + ", " + col + "): " + result);
    }
}

Output:

Element at (3, 4): 12

Time Complexity: The time complexity of this algorithm is O(1) because the calculations to find the element at a given (row, col) index in the spiral matrix are based on simple mathematical formulas.

Space Complexity: The space complexity is also O(1) because the algorithm only uses a constant amount of memory to store the input parameters row and col, as well as the intermediate variables used in the calculations.

Next TopicFind The Index of An Array Element in Java

← prev next →