Snake in Matrix - Video Solutions

Problem Overview: You start with a snake at the top-left corner of an n x n matrix (cell index 0). A list of movement commands such as UP, DOWN, LEFT, and RIGHT is given. After applying each move, return the final cell number assuming the matrix is indexed in row-major order.

Approach 1: Coordinate Mapping Approach (O(k) time, O(1) space)

Track the snake’s position using two integers: row and col. Initialize both to 0. Iterate through the command list and update coordinates based on the direction: decrement row for UP, increment row for DOWN, decrement col for LEFT, and increment col for RIGHT. After processing all moves, convert the 2D position into the matrix’s linear index using row * n + col. The key insight is that the matrix numbering follows row-major order, so a simple arithmetic mapping gives the final answer without storing the grid.

This method is a straightforward simulation. Each command results in a constant-time coordinate update. No extra data structures are required, making the space complexity O(1). This approach is easy to implement and works efficiently even for large command lists.

Approach 2: Direction Vector Approach (O(k) time, O(1) space)

Instead of multiple condition checks, store movement offsets in a direction map. For example, map each command to a vector: UP (-1,0), DOWN (1,0), LEFT (0,-1), and RIGHT (0,1). Iterate through the commands and update the current position using these vectors. This reduces branching logic and keeps the movement rules centralized.

The vector-based solution is common in grid traversal problems involving arrays and directional movement. Each iteration performs a constant-time vector addition to update the coordinates, keeping time complexity at O(k) where k is the number of commands. Space remains O(1) since only a few variables and a small direction map are used.

Recommended for interviews: The Coordinate Mapping approach is usually what interviewers expect first. It shows you understand how row-major indexing works and can simulate movement in a grid efficiently. The Direction Vector approach is slightly cleaner and scales better when more directions or movement rules are added. Demonstrating both shows strong understanding of string-driven simulations and grid traversal patterns.