Snake in Matrix

Snake in Matrix

What is this problem about?

"Snake in Matrix" is a simulation-based problem that is frequently categorized as an "Easy" difficulty question, making it a common warm-up in interviews at companies like Google. The problem typically involves a grid (matrix) of size $N \times N$, where each cell is numbered from $0$ to $(N^2 - 1)$ in a row-major order. A "snake" starts at the top-left cell (index 0) and follows a series of commands: "UP", "DOWN", "LEFT", and "RIGHT".

Your goal is to track the snake's position as it moves through the grid and return the final cell index after all commands have been executed. It’s a test of your ability to map 2D coordinates (row, column) to a 1D index and vice versa, which is a fundamental skill in grid-based programming.

Why is this asked in interviews?

Even though it is simple, this coding problem is asked because it tests basic implementation skills, attention to detail, and familiarity with coordinate systems. Interviewers look for how cleanly you handle the boundary conditions (though in some versions of this problem, the snake is guaranteed to stay within the grid) and how efficiently you convert between the cell's index and its row/column position. It also serves as a baseline for more complex "Snake" game problems that might involve body segments and growth.

Algorithmic pattern used

The algorithmic pattern used is Simulation. You maintain the current state (the snake's row and column) and update that state based on each instruction in the input list. The mathematical relationship between a 1D index and 2D coordinates is: index = row * N + col. Conversely, row = index // N and col = index % N. By following the directions and updating these values, you can determine the final position.

Example explanation

Suppose we have a $3 \times 3$ matrix and the commands are ["RIGHT", "DOWN"].

• The matrix cells are: 0 1 2 3 4 5 6 7 8
• Start at (0, 0), which is index 0.
• "RIGHT" moves the snake to (0, 1).
• "DOWN" moves the snake to (1, 1).
• The final index is 1 * 3 + 1 = 4. The output for this snake in matrix interview question would be 4.

Common mistakes candidates make

One mistake is incorrectly applying the row/column updates—for example, thinking "UP" increases the row index when it actually decreases it in a standard 0-indexed grid. Another error is neglecting to use the grid size $N$ correctly when calculating the final 1D index. Some candidates also overcomplicate the problem by creating the actual 2D matrix in memory, which is unnecessary and consumes extra space when simple coordinate tracking is sufficient.

Interview preparation tip

When preparing for a "Snake in Matrix coding problem," focus on grid navigation. Practice converting indices between 1D and 2D formats fluently. Also, always check if you need to handle out-of-bounds cases. Even if the problem statement says the snake won't leave the grid, mentioning that you're aware of the boundary check shows the interviewer that you're thinking about robust code.