LeetCode, 𝐃𝐚𝐲-6/365-DSA-Coding 𝐉𝐨𝐮𝐫𝐧𝐞𝐲…Google.

Solving the “1138. Alphabet Board Path” Problem: A Step-by-Step Guide

Today, I tackled an intriguing problem called “Alphabet Board Path.” It involves navigating a 5x6 alphabet board to spell a target word. The challenge is to calculate the sequence of moves required to spell the word, using only ‘U’, ‘D’, ‘L’, ‘R’, and ‘!’ to navigate and select letters.

Problem Description

The board looks like this:

Given a target string (e.g., “leet”), you must find a sequence of moves to spell it out starting from the top-left corner ('a'). You can move up (U), down (D), left (L), or right (R) to navigate, and '!' is used to select the current letter.

My Solution

To solve this problem, I mapped each character to its (row, column) position on the board using a dictionary. Starting from 'a', I calculated the difference between the current position and the target character's position. Depending on the direction, I added the necessary moves to the result list.

Here’s the Python code:

class Solution:
    def alphabetBoardPath(self, target: str) -> str:
        position_map = {char: (i // 5, i % 5) for i, char in enumerate("abcdefghijklmnopqrstuvwxyz")}
        x0, y0 = 0, 0
        result = []
        for char in target:
            x, y = position_map[char]
            if y < y0:
                result.append('L' * (y0 - y))
            if x < x0:
                result.append('U' * (x0 - x))
            if x > x0:
                result.append('D' * (x - x0))
            if y > y0:
                result.append('R' * (y - y0))
            result.append('!')
            x0, y0 = x, y
        return "".join(result)

LeetCode-1138.

Logic Overview:

1. Mapping the Board: Precompute the positions of each character.
2. Navigate to Target Letter: Adjust rows (x) and columns (y) based on the difference between the current and target positions.
3. Special Case for ‘z’: Ensure vertical moves are made before horizontal moves to avoid invalid positions when navigating near 'z'.

Other Possible Solutions

1. Breadth-First Search (BFS):
   Use BFS to calculate the shortest path from one character to another. Though accurate, this approach can be computationally expensive due to repeated pathfinding.
2. Recursive Backtracking:
   A recursive solution could explore all paths to spell the target, but it may be inefficient compared to direct calculation.
3. Dynamic Programming:
   Precompute paths between all pairs of characters to make navigation faster, trading space for time efficiency.

Real-World Applications

This problem has practical applications in:

• Pathfinding Algorithms: Used in robotics or game development for movement across grids.
• Keyboard Typing Optimization: Helps in optimizing text entry on custom keyboard layouts.
• Route Planning: Similar logic can be applied to GPS systems for navigating grids.

Learnings

1. Efficient Mapping: Precomputing character positions reduces the complexity of lookups.
2. Edge Cases: Always account for unique scenarios like the single row of 'z'.
3. Path Optimization: Minimize redundant calculations by directly computing the necessary moves.

Thanks for Reading!

I hope you found this walkthrough insightful. If you have alternative solutions, ideas, or suggestions, feel free to share! Let’s discuss and learn together.