Alphabet Board Path

Alphabet Board Path

What is this problem about?

The "Alphabet Board Path interview question" involves navigating a 2D grid that represents a keyboard. The board is a $5 imes 5$ grid containing 'a' through 'z' in order, with 'z' being alone on the last row. Given a target string, you need to find a sequence of moves ('U', 'D', 'L', 'R') and an '!' (to select a character) that spells out the string starting from 'a'.

Why is this asked in interviews?

Google uses the "Alphabet Board Path coding problem" to test a candidate's ability to map 1D data (the alphabet) to 2D coordinates and handle specific edge cases in a simulation. It evaluates coordinate geometry skills and the ability to think through ordering—specifically why moving to the letter 'z' requires a different sequence of moves than moving away from it.

Algorithmic pattern used

This problem follows the Coordinate Geometry and Simulation pattern.

1. Mapping: Convert each character to a coordinate $(row, col)$. For example, 'a' is $(0, 0)$, 'b' is $(0, 1)$, and 'z' is $(5, 0)$. The formula is row = charCode / 5 and col = charCode % 5.
2. Pathfinding: Calculate the difference between your current $(r1, c1)$ and target $(r2, c2)$.
3. Edge Case Management (The 'z' rule): Because 'z' is at $(5, 0)$ and there are no characters at $(5, 1)$ through $(5, 4)$, you must be careful:
   • When moving to 'z', move Left first, then Down.
   • When moving away from 'z', move Up first, then Right. This prevents the path from stepping into the "empty" space on the last row.

Example explanation

Target: "bz"

1. Start at 'a' $(0, 0)$. Target 'b' $(0, 1)$.
   • Move: Right ('R'), then '!'. Current: 'b'.
2. Target 'z' $(5, 0)$.
   • Row diff: +5 (Down), Col diff: -1 (Left).
   • Order: Move Left ('L'), then Down ('DDDDD'), then '!'. Total Path: R!LDDDDD!

Common mistakes candidates make

• Incorrect 'z' handling: Crashing the simulation by moving "Down" into the empty space next to 'z' before moving "Left."
• Coordinate calculation: Using 1-based indexing instead of 0-based, which complicates the modulo math.
• Inefficient pathing: Trying to use BFS for the path when simple coordinate differences ($dx, dy$) are much faster and sufficient.

Interview preparation tip

When dealing with grids, always check for "irregular" shapes. The Alphabet Board is almost a rectangle but has a single character in the last row. This is a huge hint that the order of 'U/D' and 'L/R' moves will matter.